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Role of transition metal impurities on the functional properties of dilute magnetic nitride semiconductors and high-performance microwave oxide dielectrics

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ROLE OF TRANSITION METAL IMPURITIES ON THE FUNCTIONAL
PROPERTIES OF DILUTE MAGNETIC NITRIDE SEMICONDUCTORS AND
HIGH-PERFORMANCE MICROWAVE OXIDE DIELECTRICS
by
Hongxue Liu
A Dissertation Presented in Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
ARIZONA STATE UNIVERSITY
May 2007
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UMI Number: 3243892
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ROLE OF TRANSITION METAL IMPURITIES ON THE FUNCTIONAL
PROPERTIES OF DILUTE MAGNETIC NITRIDE SEMICONDUCTORS AND
HIGH-PERFORMANCE MICROWAVE OXIDE DIELECTRICS
by
Hongxue Liu
has been approved
December 2006
APPROVED:
. Chair
Supervisory Committee
ACCEPTED:
Director of the Program
Dean, Division of Graduate Studies
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ABSTRACT
The thesis investigates transition metal doping in two types of materials: wide
bandgap semiconductors for spintronic applications and oxide dielectrics for mi­
crowave applications.
MBE grown Cr-doped GaN has been found to exhibit ferromagnetism at over
900 K. The measured magnetic moment per Cr atom in Cr-doped GaN varied signifi­
cantly as a function of Cr concentration, with a maximum magnetic moment occurring
at 3% Cr. Transport measurements of Cr-doped GaN revealed properties characteris­
tic of hopping conduction. These measurements also inferred th at the carrier concen­
tration is similar in magnitude to the measured concentration of magnetically active
Cr. This fits well into the scenario th at electrons at the partially filled Cr £2 level
contribute to the hopping conduction. These results, along with extensive structural
characterization, suggest that ferromagnetism in Cr-doped GaN best fits the double
exchange like mechanism as a result of hopping between near-midgap substitutional
Cr impurity band.
Exchange biasing effects were observed in sample structures of Cr-doped GaN
thin films with an antiferromagnetic MnO overlayer. The center of the magnetic hys­
teresis loop shifts to negative magnetic field by ~ 70 Oe when measured after field
cooling. Enhancement of the coercive field of the Cr-doped GaN film is also found.
The mechanism responsible for the exchange bias is attributed to the exchange cou­
pling at the ferromagnetic Cr-doped GaN/antiferromagnetic MnO interface. The
observed exchange biasing indicates that Cr-doped GaN has properties of a conven­
tional ferromagnet and has potential use in practical magnetoelectronic devices.
iii
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The effect of Ni-doping on the structural, dielectric and optical properties of
Ba(Cd 1/ 3Ta 2/ 3)03 (BCT) dielectrics has been explored.
Rietveld analysis of the
X-ray diffraction (XRD) data indicates th at the BCT structure is similar to other
Ba(B/1^3B,2^ 3)0 3 perovskites, although the Ta-O-Cd is distorted to an angle of ~ 173°;
very close to the earlier theoretical prediction of 172°. The XRD analysis also in­
dicates th at Ni doping significantly enhances the extent of Cd-Ta ordering in BCT.
The tem perature coefficient of resonant frequency decreases with Ni concentration
up to 2 wt%. While the loss tangent of BCT is reduced at small levels of Ni doping
(up to 0.5 wt%), it increases abruptly at higher concentrations. A correlation exists
between the loss tangent of Ni-doped BCT samples and the intensity of a continuous
absorption background in the optical spectra. This optical activity results from the
presence of optically active point defects and is suggestive th at these defects play an
important role in the microwave loss in BCT dielectrics.
iv
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ACKNOWLEDGMENTS
First and foremost, my greatest gratitude goes to my advisor, Professor Nathan
Newman, who provided me with expert guidance, generous support and continuous
encouragements, and who shared the excitement of scientific discovery through the
course of my Ph.D. study.
I would like to thank the other members of my committee, Prof. Subhash Mahajan, Professor M ark van Schilfgaarde, Professor Ralph Chamberlin, and Professor
George Wolf. I am especially grateful to Professor Mark van Schilfgaarde, Professor
Ralph Chamberlin, and Professor George Wolf for their generous help th at they gave
during my thesis research.
My research has been performed in several projects, where I have enjoyed the
opportunities of collaborating with colleagues in Newman research group and other
groups at ASU. My appreciation extends to the following collaborators: Dr. Stephen
Wu, Dr. Shaojun Liu, Dr. Rakesh Singh, Mr. Victor Zenou, Dr. Lin Gu, Professor
David Smith, and Professor Mark van Schilfgaarde. Dr. Stephen Wu and Dr. Shaojun
Liu have kindly made samples for me to measure, which made this thesis possible,
as well as explained the growth process. Dr. Rakesh Singh has been a long time
mentor of the group and kindly shared some data and his knowledge on RBS. Mr.
Victor Zenou has helped perform X-ray diffraction measurements as well as Rietveld
analysis, for which I am especially grateful. Dr. Lin Gu and Professor David Smith
have shared their knowledge on TEM characterization.
Thanks also go to all other colleagues in Newman research group for sharing
knowledge and academic discussions. They are Dr. Lei Yu, Dr. Jihoon Kim, Mr.
v
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Mark Espinasse, Mr. Raghu Gandikota, Mr. B rett Strawbridge, Mr. Raghu Nandivada, Mr. Subhasish Bandyopadhyay, Mr. Yafei Chen, Mr. Zhizhong Tang, and Mr.
Prabhu Bharathan. I am also grateful for the countless technical help provided by
Mr. Jack Guerrier.
I acknowledge DARPA and ARO for funding the research in this thesis.
Last but not least, I would like to thank my family for their continuous support
during my studies. I am indebted to my wonderful wife, Yan Li, who is my champion
and who made my life at ASU enjoyable and memorable.
vi
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TABLE OF CONTENTS
Page
LIST OF T A B L E S ........................................................................................................
x
LIST OF F I G U R E S ....................................................................................................
xi
CHAPTER 1 MOTIVATION AND IN T R O D U C T IO N ....................................
1
1.1. In tro d u c tio n ....................................................................................................
1
1.2. Dilute Magnetic Sem iconductors.................................................................
3
1.2.1. In tro d u ctio n .........................................................................................
3
...........................
7
1.2.3. Theory of Dilute Magnetic Sem iconductors..................................
16
1.3. Microwave D ielectrics....................................................................................
20
1.3.1. In tro d u c tio n .........................................................................................
20
..................................................................
20
Thesis O rganization......................................................................................
27
1.2.2. Advances in Dilute Magnetic Semiconductors
1.3.2. Materials Requirements
1.4.
CHAPTER 2
PROPERTIES OF Cr-DOPED GaN DILUTE MAGNETIC
SEM IC O N D U C TO R .................................................................................................
29
2.1. In tro d u c tio n ....................................................................................................
29
2.2. E x p e rim e n ta l.................................................................................................
32
2.3. Results and D iscu ssion.................................................................................
33
2.3.1. Magnetic Properties
.........................................................................
33
2.3.2. Structural P ro p e rtie s .........................................................................
38
vii
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Page
2.3.3. Role of Cr Substitution on Ferromagnetic P r o p e r t i e s .............
41
2.3.4. Transport P r o p e rtie s .......................................................................
43
2.3.5. Origin of Ferromagnetism in Cr-doped G a N .............................
47
2.4. Summary
CHAPTER 3
.......................................................................................................
49
EXCHANGE BIASING OF FERROMAGNETIC Cr-DOPED
GaN USING A MnO OYERLAYER
.................................................................
50
3.1. In tro d u ctio n ....................................................................................................
50
3.2. E x p e rim e n ta l.................................................................................................
52
3.3. Results and D iscu ssio n .................................................................................
54
.......................................................................................................
58
3.4. Summary
CHAPTER 4
EFFEC T OF Ni DOPING ON THE STRUCTURAL, DIELEC­
TRIC, AND OPTICAL PROPERTIES OF BARIUM CADMIUM TANTAL A T E ........................................................................................................................
59
4.1.
In tro d u c tio n ...................................................................................................
59
4.2.
E x p e rim e n ta l................................................................................................
61
4.3.
Results and D iscu ssio n ...............................................................................
63
4.3.1. Structural P ro p e rtie s .......................................................................
63
4.3.2. Dielectric P r o p e r tie s .......................................................................
67
4.3.3. Optical Properties
..........................................................................
70
......................................................................................................
74
4.4.
Summary
viii
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Page
CHAPTER 5
CONCLUSIONS AND O U T L O O K .............................................
76
5.1. C o n c lu sio n s....................................................................................................
76
5.2. Outlook for Future W o rk ..............................................................................
78
R E F E R E N C E S ..............................................................................................................
81
APPENDIX A LIST OF PUBLICATIONS DURING THE PHD STUDY . .
94
ix
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LIST OF TABLES
Table
Page
1.1. List of reported magnetic properties of various DMS. The TM content
listed corresponds to the magnetic properties in the “Note” and “Tc ”
columns..............................................................................................................
8
4.1. The lattice parameters of Ni-doped Ba(Cd 1(/3Ta 2/ 3) 0 3 samples for the
cubic and hexagonal structures inferred from the Rietveld analysis.
The standard deviation is not given for the undoped sample since the
decomposition products were determined using the profile matching
with constant factorwithout atomic positions (Ref. [119]).....................
65
4.2. Atomic Wyckoff positions of B a(C di/ 3Ta 2/ 3) 0 3 in space group P3ml
inferred from Rietveld analysis (Ref. [119])...............................................
x
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66
LIST OF FIGURES
Figure
1.1.
Page
Schematic of a spin field-effect transistor with a ferromagnetic source
and a drain, separated by a narrow semiconducting channel (Ref. [10,
12])......................................................................................................................
1.2.
4
Three types of semiconductors: (a) a magnetic semiconductor, in which
a periodic array of magnetic elements is present, (b) a diluted magnetic
semiconductor, and (c) a non-ferromagnetic semiconductor, which con­
tains no magnetic ions (Ref. [3])..................................................................
1.3.
7
Schematic diagram of properties of (Ga,Mn)As films in relation to the
growth parameters of substrate tem perature Tg and Mn concentration.
Lines are provided to act as a rough guide (Ref. [3, 45])........................
1.4.
10
Concentration of transition metal dopants Cr and Mn incorporated
into AIN as a function of substrate tem perature (Ref. [63])..................
15
1.5. Optical absorption of GaN:Mn, GaN:Mn:Si, and AlN:Mn with Mn con­
centration of ~ 1020 cm-3. Transition A with the onset around 1.8 eV
in GaN is assigned to the direct emission of holes from Mn3+ acceptors
to the valence band, and transition B around 1.5 eV to the internal
spin-allowed 5E —>■5T transition of the deep neutral Mn3+ state, as
shown in the inset with the spin-polarized one-electron densities of
states DT(E) and D j(E ) (Ref. [69]).............................................................
xi
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19
Figure
Page
1.6. Fields in a microwave resonance dielectric in the simplest standing wave
mode: (a) magnetic field; (b) electric field; (c) variation in Ev and Ez
with r a t z = 0, with reference to cylindrical coordinates. The z axis
is perpendicular to the plane of the disc and the origin is at the disc
center (Ref. [ 7 4 ] ) .....................................................................................
22
1.7. Schematic representation of a Q measurement in transmission. The Q
is defined as the peak frequency divided by the width of the peak at
half its maximum amplitude A/ .............................................................
23
2.1. Field dependence of magnetization curve at 10 K of a 2% Cr-doped
GaN sample grown on 6 H-SiC substrate by M BE..............................
34
2.2. Temperature dependence of magnetization curve from 10 K to 300 K
of a 2% Cr-doped GaN sample grown on 6 H-SiC substrate byMBE. .
35
2.3. Temperature dependence of zero field cooled (bootm curve) and field
cooled (top curve) magnetization for a 2% Cr-doped GaN sample.
. .
36
2.4. Field dependence of magnetization curve at 325 K and 800 K of a 2%
Cr-doped GaN sample...............................................................................
37
2.5. Temperature dependence of magnetization curve from 10 K to 900 K of
a 2% Cr-doped GaN sample showing ferromagnetism persisting above
900 K ............................................................................................................
38
2.6. Ion channeling angular scans in the (0001) axial direction for a 3%
Cr-doped GaN film grown at 775 °C (Ref. [46])..................................
xii
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39
Figure
Page
2.7. XRD spectra for a 2% Cr-doped GaN grown at 825 °C on a SiC sub­
strate by MBE (Ref. [34])..............................................................................
2.8.
40
Change in substitutional Cr (top) and magnetization (bottom) after
annealing at 825 °C for 3% Cr-doped GaN samples grown at tempera­
tures from 700 to 825 °C (Ref. [4 6 ]) ..........................................................
2.9.
42
Temperature dependence of resistance of a 4% Cr-doped GaN gown
on sapphire. The insert shows the exponential law relationship, R =
R qexp[(T0/ T ) 1/4], which is characteristic of variable range hopping. .
44
2.10. Magnetoresistance A R /R , the relative change of sheet resistance in a
magnetic field, of a 4% Cr-doped GaN grown on sapphire substrate
(Ref. [25])..........................................................................................................
46
2.11. Fitting of the magnetoresistance data to the transport model proposed
for magnetic semiconductor by Yu (Ref. [100]).........................................
47
3.1. Schematic of a GMR read sensor in spin valve structure. The magnetic
layer in blue is exchange-biased by an antiferromagnetic layer so its
magnetic property is hard to switch, called pinned layer........................
51
3.2. Schematic illustration of exchange bias mechanism.................................
52
3.3. RBS spectra indicating th at a 130 nm thick GaN is doped with 4% Cr
and has a 20 nm thick MnO overlayer (Ref. [110])..................................
53
3.4. Magnetic hysteresis loops of a 4% Cr-doped Cr-doped GaN with MnO
overlayer after zero-field cooling and 5 kOe field cooling (Ref. [110]). .
xiii
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54
Figure
3.5.
Page
Magnetic hysteresis loops of a 4% Cr-doped Cr-doped GaN with MnO
overlayer after zero-held cooling and -5 kOe held cooling (Ref. [110]).
3.6.
55
Magnetic hysteresis loop of a 3% Cr-doped GaN single layer after 5
kOe held cooling measured at 10 K (Ref. [110]).......................................
56
3.7. Temperature dependence of coercivity and exchange held of a 4% Crdoped GaN with MnO overlayer (Ref. [110])..............................................
57
4.1. Two crystal structures for B a ^ ^ B ^ ^ O s complex perovskites, where
B ' = Mg, Zn, Ni, or Cd, and B" = Ta or Nb. (a) disordered (cubic),
(b) ordered (hexagonal)...................................................................................
60
4.2. Rietveld analysis of X-ray diffraction spectra of 0.1 wt% Ni-doped
B a(Cdi/ 3Ta 2/ 3)03 samples. The calculated Bragg peak positions and
intensities of ordered (hexagonal, “I”) and disordered (cubic, “II”)
structures are derived using Rietveld analysis and appear as lines. The
difference between the measured data (dots) and calculated (lines) is
shown below. The crystallographic planes of hexagonal structure are
given (Ref. [119]).............................................................................................
63
4.3. Lattice parameters of Ni-doped Ba(Cdi/ 3Ta 2/ 3)03 as a function of Ni
concentration. For lattice constant at 100 % we used a — 5.758
c = 7.052
A
A
and
for Ba(Ni1/ 3Ta 2/ 3) 0 3 (ICDD card # 00-018-0181). The
results clearly ht, Vegards law.......................................................................
xiv
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66
Figure
Page
4.4. Ball
and
stick
model
of
(a)
Ba(Zn 1/ 3Ta 2/ 3)03
and
(b)
Ba(Cd 1/ 3Ta 2/ 3) 0 3 (Ref. [117])......................................................................
67
4.5. Dependence of Q x / on Ni doping concentrations in Ba(C di/ 3Ta 2/ 3) 0 3
samples (Ref. [119])........................................................................................
68
4.6. The variation in the tem perature coefficient of resonant frequency as
a function of Ni doping concentrations (Ref.[119])....................................
69
4.7. Visible absorption spectra of B a(C di/ 3Ta2/ 3) 0 3 samples doped with
varying concentrations of Ni (Ref. [119])....................................................
70
4.8. Schematic demonstration of Ni ions surrounding by oxygen near neigh­
bors in an octahedral geometry when Ni is incorporated on Cd sites in
BCT lattice.......................................................................................................
71
4.9. Results of crystal field analysis of the electronic energy of the Ni2+
orbitals as a function of the strength of the ligand field, denoted 10Dq.
Transition energies and 10Dq values for aqueous solutions of nickelous
salts are included as black dots. 10 Dq values for solids are also shown
(Ref. [86 ])..........................................................................................................
73
4.10. Near infrared absorption spectra of Ba(C di/ 3Ta 2/ 3) 0 3 samples doped
with varying concentrations of Ni (Ref. [119])..........................................
xv
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74
CHAPTER 1
M O TIV A T IO N A N D IN T R O D U C T IO N
1.1. Introduction
The transition metals (TM) are elements found in groups 3-12 of the periodic
table1. These elements make the transition between the representative metals in
groups 1 and 2 and the metalloids, metals, and nonmetals in groups 13-18. Because
it is in this block of elements in the periodic table that the d-orbitals are being filled
with electrons, they are also called d-block elements.
In transition metals, the d-orbitals are partly filled with valence electrons. These
five d-orbitals are degenerate, th at is, they have the same energy, in free space. How­
ever, in a solid the d-electrons are surrounded by neighboring atoms which are com­
monly referred to as ligand atoms. The electrons from the ligand will be closer to
some of the transition m etal’s d-orbitals and farther away from others. The electrons
in the d-orbitals and the electrons in the ligand repel each other and so d-electrons
closer to the ligands will have a higher energy than ones further away because they
feel more repulsion. Thus, the d-orbitals will split in energy. The orientation of the
xMore strictly, a transition m etal is defined as an element whose atom has an incomplete d
sub-shell, or which can give rise to cations with an incomplete d sub-shell [1].
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2
ligands with respect to the metal d orbitals determines the sign and magnitude of the
splitting [2 ].
It is the rj-orbital feature th at plays an im portant role in determining the many
interesting physical properties of transition metal ions. For example, if there is ex­
change interaction between the neighboring transition ions, the electrons may couple
antiferromagnetically, or ferromagnetically. Transition metal ions often have spectac­
ular colors which arise from the absorption of light from internal transitions within
the transition m etal’s d orbitals.
In recent years, there have been a surge of interest in transition metal doping in
conventional semiconductors to make dilute magnetic semiconductors (DMS). This
effort is aimed at taking advantage of both the charge and spin of electrons to create
new device configurations and explore new functionalities [3, 4]. The development
of DMS forms the basis for this emerging research field known as semiconductor
spin dependent electronics, normally abbreviated as spintronics. In another material
system, microwave oxide dielectrics, transition metal dopants have been introduced
to optimize the microwave properties. For example, Ni has been added to tune the
temperature coefficient of resonant frequency (7f) of Ba(Zni/ 3Ta 2/ 3)03 (BZT) to near
zero [5]. In another example, small amounts of Zr doping can decrease annealing
times required to attain low microwave loss and thus achieve a high quality factor
(Q) [6 ].
The goal of this thesis research is to investigate the role of transition metal
impurities on the functional properties of both dilute magnetic nitride semiconduc­
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3
tors and high-performance microwave oxide dielectrics. As the introduction of this
thesis, the basics of DMS and microwave dielectrics, and their recent developments
are reviewed. At the end of this chapter, the outline of this thesis is presented.
1.2. D ilu te M agnetic Sem iconductors
1.2.1. Introduction
The utilization of the charge and spin of electrons has laid down the foundation
of modern information technology. Integrated circuits (ICs) based microelectronics
use the control of charged carriers through semiconductor devices to enable amplifi­
cation and digital information processing. In contrast, the spin of carriers is the key
component in the hard drive and other components of magnetic data storage. The
fast development of all-metal giant magnetoresistance (GMR) and metal/oxide tun­
neling magnetoresistive random access memories (MRAMs) has shown th at the use of
advanced magnetoelectronic devices holds a huge potential for industrial applications
[7, 8], Both these effects are based on the transport of spin-polarized carriers and it
is obvious th at realizing similar effects in semiconductors might enhance the perfor­
mance and create new functionalities in semiconductor devices. This emerging held of
semiconductor spintronics, seeks to utilize simultaneously the charge and spin of car­
riers through the production, injection, manipulation and detection of spin-polarized
carriers in semiconductors [9, 10, 11].
While it is not completely envisaged what kind of devices the semiconductor
spintronics will apply to, several prototypes of device structures has been proposed
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4
to exploit the spin functionalities in semiconductors. One good example is the spinpolarized field-effect transistor (Spin FET) proposed by D atta and Das in 1990, as
shown in Fig. 1.1 [12]. In a conventional FET, a narrow semiconductor channel runs
between two electrodes named the source and the drain.
W hen a specific polarity of
F errom agn etic
G ate (no v o lta g e ap p lied )
F errom agn etic
so u rc e
Spin-poiarized
current flow
V oltage app lied
Figure 1.1. Schematic of a spin field-effect transistor with a ferromagnetic source and
a drain, separated by a narrow semiconducting channel (Ref. [10, 12]).
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5
voltage is applied to the gate electrode above the channel, the resulting electric field
drives carriers out of the channel, for instance, turning the channel into an insulator.
The Datta-Das spin FET has a ferromagnetic source so th at the current flowing
into the channel is spin-polarized. When a voltage is applied to the gate, the spin
orientation of its two-dimensional electron gas (2DEG) can be adjusted via the electric
field produced by the gate voltage due to the Rashba effect [13]. The spin orientation
of the electrons with respect to the relative magnetization direction of the source and
drain determines whether the spin transistor shows a high or low resistance. A spin
FET would have several advantages over a conventional FET. Flipping an electron’s
spin takes much less energy and can be done much faster than pushing an electron
out of the channel. One can also imagine changing the magnetic orientation of the
source or drain with a magnetic field, introducing an additional type of control that
is not possible with a conventional FET: logic gates whose functions can be changed
on the fly.
For the realization of this kind of novel spin devices, one of the key steps is
the controlled injection of spin-polarized carriers in semiconductors.
For decades
spin-polarized carriers have been created in semiconductors simply by illuminating
the material with circularly polarized light [14]. It has also been demonstrated that
spin information can be probed with such a scenario using optical pump-probe tech­
niques [15, 16]. However, practical electrical spintronic devices should not have to
rely on optics. A purely electrical method for injecting spin-polarized carriers into
semiconductors is needed to guarantee the success of spintronics. To achieve that, a
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6
magnetic m aterial must be brought in close contact with the semiconductor. A com­
mon way to combine these materials is to epitaxially grow the magnetic materials
on the semiconductor substrates [17]. The first obvious choice of magnetic material
is conventional ferromagnetic metals such as Fe because they commonly have high
Curie temperatures (Tc), are economically available, and enjoy a high level of mate­
rials development. But efficient spin injection in the diffusive transport regime is not
possible as a result of the mismactch in carrier density at the metal/semiconductor
interface [18, 19]. Although it has been a topic of growing importance during the
past years, only recently has significant levels of electrical spin injection from ferro­
magnetic metals been demonstrated through an introduction of tunnel barriers with
tunneling resistance comparable to or larger than the resistance of semiconductors
[2 0 ,
21 ].
Theoretically, the problems associated with the metal/semiconductor interface
can be circumvented if ferromagnetism and semiconducting properties coexist in semi­
conductors. Europium chalcogenides (EU2O 3, EuS, EuSe) are an example of magnetic
semiconductors th a t have a periodic array of magnetic elements. Unfortunately, these
materials have Tq much less than 100 K and are extremely hard to synthesize [22, 23].
An approach to overcome this limitation is to make conventional nonmagnetic semi­
conductors magnetic through doping with magnetic elements.
The DMS are this kind of materials based on non-magnetic semiconductors,
and are formed by introducing a sizable amount (a few percents or more) of magnetic
ions, such as Mn, to substitute constituent atoms in nonmagnetic semiconductors
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7
A
B
1
t
t
© a
©
?
'■
:
;
;
;
®:w: ;©
;
;
©" s ' " ©
Figure 1 .2 . Three types of semiconductors: (a) a magnetic semiconductor, in which a
periodic array of magnetic elements is present, (b) a diluted magnetic semiconductor,
and (c) a non-ferromagnetic semiconductor, which contains no magnetic ions (Ref.
[3])(Fig. 1.2b). One of the most important advantages of DMS is th at they are highly
compatible with current semiconductor technology, thus offering a unique opportu­
nity to integrate conventional semiconductors and ferromagnetic technologies. Such
an all-semiconductor design enjoys the opportunity to use established principles of
bandgap engineering to optimize spin injection across the heterointerface and create
new functionalities. It also makes possible to realize all the capabilities of current
magnetic, electronic and photonic devices in a single integrated chip.
1.2.2. A dvances in D ilu te M agnetic Sem iconductors
The field of DMS is not new. From the early work on Mn-doped CdSe by Kasuya
et al. [22], to the recent report of high tem perature ferromagnetism in transition
metal doped wide bandgap nitride and oxide semiconductors [24, 25, 26, 27, 28], a
large number of theoretical and experimental studies have been performed. There is
an intense interest in discovering new DMS which exhibit ferromagnetism above room
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Compound
(Cd,Mn)Te
TM content (%)
4
(Ga,Mn)As
(Ga,Mn)N
60
40
5.3
1- 2
(Ga,Cr)N
3
3
(Zn,Mn)Te
T c(K )
2.5
Notes
antiferromagnetic
antiferromagnetic
110
228 - 370
940
280
(Al,Cr)N
(Zn,Mn)0
(Zn,Co)0
(Zn,Ni)0
> 900
> 900
2
> 420
> 300
1.5
1 - 2.5
[30]
[47]
[24]
[31]
[32]
> 400
3
0.7
Reference
[29]
[30]
[33]
[25, 34]
[25, 34]
[27]
[35]
super paramagnetic
> 350
(Ti,Co)0
5 - 15
2- 7
> 300
[36]
[37]
[28]
(Ti,C r)0
2 - 15
> 300
[38]
(Zn,V)0
Table 1.1. List of reported magnetic properties of various DMS. The TM content
listed corresponds to the magnetic properties in the “Note” and “7 c” columns.
temperature for practical applications. Table 1.1 lists some DMS and their reported
magnetic properties.
Most of the earlier work on DMS had been centered on II-VI semiconductors
such as (Cd,Mn)Te. In these materials, the valence of group II cations is identical
to th at of most magnetic transition metals, which made them relatively easy to grow
and achieve high doping concentration [39, 40]. There also has been great success in
understanding the basic physics and materials science of II-VI DMS. However, the
magnetic properties of II-VI DMS are dominated by the antiferromagnetic superexhange interactions among the localized spins, which result in paramagnetic, spin-
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9
glass or antiferromagnetic behaviors depending on doping concentrations and growth
conditions. Besides that, difficulties in doping these materials to either n-type or ptype and in preparing heterostuctures made them less attractive for applications. The
following sections center on the recent advances in III-V DMS which has attracted a
lot of attention in the DMS and semiconductor spintronics community.
1 .2.2. 1 . C hallenges w ith G row th o f I I I - V D M S . For practical device
applications, a homogeneously doped DMS material system which contain spin po­
larized carrier is needed. Unlike II-VI DMS, the synthesis of III-V dilute magnetic
semiconductors is challenging as a result of the extreme low solubility of the most
commonly used magnetic elements in III-V semiconductors as well as the high volatil­
ity of the dopants. If the growth occurs near equilibrium and the doping concentration
of transition metal elements is above the solubility limit, segregation and secondary
phase formation will occur during the growth. For example, secondary phases or
clustering form when over 0.1% Mn is incorporated into III-V compounds under ther­
modynamic equilibrium growth conditions [41]. To overcome this difficulty, molecular
beam epitaxy (MBE), a non-equilibrium growth technique for thin film deposition,
can be used. The strategy is to keep the growth at suitable low temperatures, which
will still provide efficient energy to facilitate epitaxial growth but not enough energy
for rapid surface diffusion that leads to segregation and secondary phase formation
[42].
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10
f
^
300
^
Growth inhibited,
formation of MnAs
^
\
s
\
\
s x
\
O
o
Metallic (Ga,Mn)As
/v ^ %
N
/
N
200
/
x
/Insulating(Ga,Mn)As
Roughening
Polycrystal
100
0.00
«
................................................... —
0.02
*
..........................................
0.04
0.06
0.08
Mn composition x in G a 1_xM nA s
Figure 1.3. Schematic diagram of properties of (Ga,Mn)As films in relation to the
growth parameters of substrate tem perature Ts and Mn concentration. Lines are
provided to act as a rough guide (Ref. [3, 45]).
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11
1 . 2 . 2 . 2 . I I I - A s D M S . The first successful growth of homogeneous III-V
based DMSs was performed by Munekata et al. [42], T hat work reported the MBE
synthesis of high quality (In,Mn)As films on GaAs. This was followed by the real­
ization of ferromagnetic (Ga,Mn)As by Ohno et al. in 1996 [43]. These studies used
unconventionally low growth temperatures of 200 °C and 250 °C. (Ga,Mn)As with
a wide range of Mn concentrations can be successfully grown on GaAs with a sub­
strate tem perature from 200 to 300 °C [44, 45], as shown in Fig. 1.3. At suitably low
temperatures (300 - 350 °C lower than the standard GaAs growth temperatures by
MBE), Mn-doped GaAs can be formed without the formation of secondary phases.
However, if the tem perature is too low, a large concentration of Asca defects (As
occupying Ga site, also called As antisites) form. This results in the formation of
insulating (Ga,Mn)As. If the Mn flux or substrate tem perature is too high, the for­
mation of MnAs secondary phase occurs. The similar behaviors were also found in
Cr-doped GaN. Cubic CrN phase formed when the growth tem perature was above
800 °C although CrN is antiferromagnetic [46].
In (Ga,Mn)As grown under optimal temperatures, a square hysteresis loop was
observed at low temperatures, confirming the ferromagnetism in the samples. The
Tq of as-grown (Ga,Mn)As increases with increasing Mn concentration up to ~ 5%
with a highest Tq of 110 K. This originates from the free holes created by the Mn
in (Ga,Mn)As [47, 48], indicating a direct correlation between hole concentration
and magnetization.
Extended X-ray absorption fine structure (EXAFS) and ion-
Channeling Rutherford Backscattering Spectrometry (RBS) measurements revealed
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12
that Mn are incorporated substitutionally in the Ga sites, resulting in p-type doping
in (Ga,Mn)As [49, 50]. However, the Tq of (Ga,Mn)As decreases with increasing
Mn concentration above 5% [51, 52]. By contrast, the saturation magnetic moment
per Mn ion decreases monotonically with Mn concentration over the entire doping
range. These observation indicates th at a large fraction of Mn does not participate
in ferromagnetic ordering [52].
Besides the known double donor Asoa defects th at are produced during low tem­
perature growth [53], the Mn interstitials, Mn/, has been found to form in (Ga,Mn)As
[50]. The presence of both of these defects result in heavy compensation in (Ga,Mn)As
due to their donor nature. The consequence is a reduced hole density and less than
optimal magnetization in (Ga,Mn)As [52]. Further experimental work shows that
the Tc of (Ga,Mn)As can be significantly improved by low tem perature annealing.
For examples, Ku et al. report Tq up to 150 K in (Ga,Mn)As annealed for 90 min
at 250 °C in a nitrogen atmosphere [54]. A larger concentration of free holes exist
in annealed samples and this quantity can be directly correlated with the
Tq-
This
annealing behavior has been attributed to the decrease in hole compensation as Mn
interstitials diffuse out of the bulk sample [55].
1.2.2.3.
I I I - N D M S . Despite the well established understanding of many
properties of (Ga,Mn)As and the realization of Ga,Mn)As based magnetic tunnel
junctions (MTJ) [56], the below room tem perature Tc of this material is a major
obstacle to its use in practical applications. The continuous search for DMS with
ferromagnetism above room tem perature has aroused a surge of interest. This has
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13
been largely inspired by Dietal et al.'s theoretical calculations in 2000 [4]. This work
was based on the Zener mean-held model. It predicted th at 5% Mn-doped p-GaN
and p-ZnO with hole concentrations of 3.5xlO 20 cm -3 should have a Tq above room
temperature.
The very hrst attem pt to synthesize of (Ga,Mn)N involved bulk microcrystallites
produced by ammonothermal method [57]. However, a small percentage (< 5%) of
Mn3N2 phase formed during growth and magnetic measurements revealed that the
samples exhibited paramagnetic property. In another study [24], room temperature
ferromagnetism has been found in epitaxial GaN layers grown on sapphire substrates
by metalorganic chemical vapor deposition (MOCVD) and then subsequently doped
with Mn using solid state diffusion. By varying the growth and annealing conditions
of Mn-doped GaN, the Tc was reported to be in the range of 228 - 370 K.
Further studies of Mn-doped GaN mostly centered on MBE grown films syn­
thesized at relatively low temperatures. Since high concentrations of magnetic ions
are essential to achieve ferromagnetism, the non-equilibrium MBE process is typically
chosen over any other growth technique. Single phase MBE grown(Ga,Mn)N layers
containing 3-9% Mn have been reported to show room tem perature magnetization
hysteresis loops [58, 59]. No second phases were observed in either high resolution
transmission electron microscopy (TEM) or selected area diffraction (SAD) patterns.
Of those samples, the material with 3% Mn composition showed the highest degree
of magnetic ordering per Mn atom. However, a Mn concentration higher than 9%
was found to enhance the antiferromagnetic coupling, resulting in a reduced magnetic
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14
moment per Mn.
The structural properties of (Ga,Mn)N have been found to play an important
role in the magnetic properties. Thaler et al. studied (Ga,Mn)N with a 3% Mn
concentration th a t was produced on bare and GaN buffered sapphire substrates [60].
XRD on all samples revealed that no secondary phases were present. The very simi­
larity of the experimental data with simulated curves of EXAFS measurements for all
the samples indicated th at Mn was indeed located on Ga substitutional sites. How­
ever, the magnetic moment of these materials was found to strongly depend on the
thickness of the GaN buffer layer. Films grown without any buffer layer, along with
those grown on a 20 nm thick buffer layer, were weakly ferromagnetic at room tem­
perature. In contrast, the films grown on a 2000 nm thick GaN buffer layer showed
around a thirty fold increase increase of magnetic moment. This result suggests that
a reduction in defect density may be responsible for the enhanced magnetization.
While Mn has been the most common dopant in III-V DMS, Cr is another at­
tractive magnetic dopant. Actually Cr-doped GaN was found to have the most stable
ferromagnetic state in TM-doped GaN according to the first principles calculation by
Sato et al [61] and Das et al [62], Wu et al. reported th a t Cr can be incorporated
at a much higher concentration than Mn, presumably because of its lower vapor pres­
sure [63]. Figure 1.4 shows the concentration of transition metal dopants Cr and Mn
incorporated into AIN as a function of substrate temperature.
Experimentally, Cr-doped GaN single crystals with a Tc of 280 K have been
grown by the addition of Cr into GaN single crystals using a sodium flux growth
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15
8
6
Mn
4
2
a
o
400
500
600
700
800
900
1000
1100
Substrate Temperature (°C)
Figure 1.4. Concentration of transition metal dopants Cr and Mn incorporated into
AIN as a function of substrate tem perature (Ref. [63]).
method [32], The coercive field at 250 K is 54 Oe. The Tc was verified by the tem­
perature dependence of both magnetization and electrical resistance measurements.
In another study of (Ga,Cr)N thin films grown by MBE, non-zero magnetization per­
sisted up to 400 K [33]. A specific Tq was not determined as a result of the limitation
of the author’s measurement system limitation. Later experimental work indicated
that optimized materials can have a Tq above 900 K in MBE grown Cr-doped GaN
and Cr-doped AIN [25], and sputtered Cr-doped AIN [64]. Ion-Channeling RBS ex­
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16
periments indicate th a t high quality epitaxial Cr-doped GaN can be grown by MBE
under well-controlled conditions [46]. It should be pointed out th at there is disagree­
ment on the properties from different reports, such as the observed saturation mo­
ments and dependence of saturation moment on Cr concentration, which presumably
reveals th at the magnetic properties depend sensitively on the growth conditions.
It is worth noting th at room temperature ferromagnetic (Ga,Mn)N samples
have been reported to be either n-type or highly resistive [24, 59]. Ferromagnetic
Cr-doped AIN is highly resistive [25, 46] whereas ferromagnetic Cr-doped GaN is
partially conductive [25, 65]. There is no evidence for p-type conductivity to date.
These are far away from the condition of hole concentrations of 3.5 xlO 20 cm -3 needed
for the carrier-mediated ferromagnetism and thus make the capability of this theory
applied to (Ga,Mn)N questionable.
1.2.3. T heory o f D ilu te M agnetic Sem iconductors
Along with an extensive increase in the number of experimental efforts in spintronics, a lot of theoretical work has been initiated recently. The early attem pt to
explain ferromagnetism in (Ga,Mn)As by hole mediated Ruderman-Kittel-KasuyaYosida (RKKY) interaction predicted the Tc close to th at observed experimentally
[47]. In the case of semiconductors where the mean distance between carriers is much
greater than th at between spins, the quantum (Friedel) oscillations of the electron
spin polarization averages to zero. This forms the basis for the seminar theoretical
work based on the Zener mean-field model of ferromagnetism by Dietl et al. [4, 66 ].
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17
In this model, the dominating exchange interaction between localized Mn spin
(d orbital) and free carriers (holes with p character), the so-called p —d exchange, is
considered. The Ginzburg-Landau free-energy of the system is thus composed of two
parts, the free energy of the localized Mn spins and the free energy of the carriers. The
magnetization of the localized spins results in a spin splitting of the bands and hence
decreases the carrier energy. However, the same magnetization increases the energy
in the localized Mn spin system. At the Curie tem perature, the two energies balance.
A further reduction of tem perature leads to the spontaneous spin splitting and spinpolarization, resulting in ferromagnetism. Equating these energies at a mean-held
level leads to the following expression for
Tq,
Tc = xN0S ( S + l)A FPs(EF)p2/12kh - TAF
(1.1)
where xN0 is the effective spin concentration, S the localized spin state, @ the p-d
exchange integral, AF the Fermi-liquid parameter, ps the spin density of states at the
Fermi energy, and TAF the contribution of the antiferromagnetic interactions.
The Zener mean-held model has been quite successful in explaining ferro­
magnetism in (Ga,Mn)As and (Zn,Mn)Te, including the observed
Tq
and magnetic
anifit,ropy. Based on this model, Dietl et al. predicted th at 5% TM-doped p-type GaN
and ZnO with hole concentrations of 3.5xlO 20 cm -3 are ferromagnetic at tempera­
tures greater than room temperature, which stimulated the research efforts to achieve
high tem perature ferromagnetism by using GaN and ZnO based DMS. However, this
model is not appropriate given that transition metal dopants, such as Mn and Cr, are
found to form midgap levels. This does not facilitate mediation from the free carriers
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18
characteristic of Zener model. This consistent with the fact th at there have not been
any reports of Mn-doped and Cr-doped III-nitride semiconductors which have found
p-type conductivity to date.
In contrast to (Ga,Mn)As where Mn is a relatively shallow acceptor providing
high concentration of holes, the Mn level in (Ga,Mn)N is believed to be near the
middle of the bandgap [67, 68 , 69, 70]. Graf et al. have demonstrated th at the
majority of Mn was present in the neutral Mn3+ state in (Ga,Mn)N with 0.2-0.6 %
Mn grown by MBE [69, 70]. In samples co-doped with Si, electrons are transferred
to the Mn acceptors as shown in Fig. 1.5. The transition associated with Mn3+ and
Mn2+ levels, also referred to as Mn3+/2+ acceptor level is located at 1.8T0.2 eV above
the valence band. Thus the deep level nature of Mn states would be expected to
pin the Fermi level midgap and thus hinder the formation of free electrons or holes
in (Ga,Mn)N. Similar to Mn in GaN, Cr in GaN is predicated theoretically [68 ] and
known experimentally [71], to form a deep level at 2.0 eV above the valence band.
Recent theoretical calculations reveal th at the Cr d level in GaN and AIN is split into
a threefold degenerate t 2 and a doubly degenerate e level [68 ]. The majority t 2 would
be expected to be 1/3 filled for Cr. The partial filling of the majority t 2 level suggests
a ferromagnetic ground state associated with the double exchange mechanism might
be possible.
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19
GaN
GaN:Mn
pure (Mn )
.3
10'
Si*codoped
AIN:Mn
[Mn]>10
cm
9-104
[Mn]<10
cm
.2
10‘
1.0
2.0
3.0
4.0
5.0
6.0
Photon Energy (eV)
Figure 1.5. Optical absorption of GaN:Mn, GaN:Mn:Si, and AlN:Mn with Mn con­
centration of ~ 1020 cm-3. Transition A with the onset around 1.8 eV in GaN is
assigned to the direct emission of holes from Mn3+ acceptors to the valence band,
and transition B around 1.5 eV to the internal spin-allowed 5E —►5T transition of the
deep neutral Mn3+ state, as shown in the inset with the spin-polarized one-electron
densities of states D |(E ) and D j(E) (Ref. [69]).
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20
1.3. M icrowave D ielectrics
1.3.1. Introduction
Microwaves usually refer to electromagnetic waves with frequencies between
300 MHz and 300 GHz, with a corresponding wavelength between 1 m and 1 mm,
respectively. The m ajority of microwave applications are related to radar and com­
munication systems [72], among which the satellite and mobile radio communication
is one of the fastest growing industries in recent years. The microwave ceramic com­
ponents made from dielectric materials are the key to these wireless communication
systems, such as cellular networks and global positioning systems (GPS). W ith con­
tinuing advances in microwave devices, more systems are being developed for the
millmeter portion of the microwave band [73].
The expanding microwave communication market and the progress in the semi­
conductor technology have placed increasing demands to develop minimized, narrow
band and frequency-stable microwave circuits concentrating on monolithic integrated
microwave components, which requires the continuous development of high perfor­
mance microwave dielectric materials.
1.3.2. M aterials R equirem ents
In microwave communications, dielectric resonator filters are used to discrimi­
nate between wanted and unwanted signal frequencies in the transm itted and received
signal. When the wanted frequency is extracted and detected it is necessary to main­
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21
tain a strong signal. For clarity it is also critical th at the wanted signal frequencies
are not affected by tem perature changes. The rapid advancement and miniaturization
of satellite and cellular communication systems require continuous miniaturization of
active microwave components. For these purposes, the dielectric materials have to ful­
fill the requirements of high dielectric constant, high quality factor (i.e., low dielectric
loss) and near zero tem perature coefficient of resonant frequency.
1.3.2.1.
D ie le c tr ic C o n sta n t. A high dielectric constant, sT, is desirable for
circuit miniaturization, because the size the size of a resonant microwave component is
inversely proportional to the square root of its dielectric constant. In its simplest form,
a dielectric resonator is a cylinder of ceramic with sufficient high er for a standing wave
to be sustained with its volume because of reflection at the dielectric-air interface.
The electric and magnetic field components of the fundamental mode of a standing
electromagnetic field are illustrated in Fig. 1.6. When microwaves enter a dielectric
material they are slowed down by a factor equal to the square root of the dielectric
constant, which implies th at the wavelength decreases by the same amount with the
frequency unaffected. Mathematically, this law takes the following form [75],
where Aci is the wavelength in the dielectric and A0 the wavelength in air. The width
of a cylindrical resonator must be an integral multiple of a wavelength to resonate.
If th at wavelength is reduced, then the physical dimensions of the resonator must be
reduced as well. Thus, a high er is required for the minimization of modern device
design.
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22
©
m
Figure 1.6. Fields in a microwave resonance dielectric in the simplest standing wave
mode: (a) magnetic field; (b) electric field; (c) variation in Ev and Ez with r at z =
0, with reference to cylindrical coordinates. The z axis is perpendicular to the plane
of the disc and the origin is at the disc center (Ref. [74])
1.3.2.2.
Q u a lity Factor. The quality factor, or Q, is a figure-of-merit to
measure the power-loss of a dielectric resonator. A high Q means very fine tuning (a
fine resonant peak). It is determined experimentally from the shape of the resonance
peak, as shown in Fig. 1.7. A peak occurs in the transm itted signal amplitude at the
resonant frequency, and the peak has some finite breadth, which is the width of the
peak at half its maximum amplitude. Q is thus defined as the peak frequency divided
by the band width A /.
The unloaded Q-factor describes the energy loss attributed to the measurement
fixture has been removed, leaving losses defined as [76]
1 -
1
1
1
Q ~ Qd + Q~c + Or
{ ' ]
where, Qd, Qc, Qc are quality factors of the dielectrics, conductor, and radiation, re­
spectively. If both conductance and radiative losses are negligible, then Q = 1/ tan S,
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23
CD
max
p
i—
a>
?
3dB
a
■g
^
Pmax
E
to
c
ca
CD
>
J3
CD
a;
fr
Frequency
Figure 1.7. Schematic representation of a Q measurement in transmission. The Q is
defined as the peak frequency divided by the width of the peak at half its maximum
amplitude A/ (Ref. [74]).
where tan (5 is the dielectric loss of the dielectric. Dielectric losses normally increase
with increasing frequency. Therefore, Q also depends on frequency. So its results are
often quoted in terms of Q x f [74],
A low dielectric loss, or high Q, is essential for high-performance microwave de­
vices to achieve low noise characteristics. Experimentally the dielectric loss has been
found to be very sensitive to material preparation and processing conditions. While
there has been dramatic progress in material development of microwave dielectrics,
the mechanism for dielectric loss in the microwave frequencies is still far from un­
derstood. Wersing et al. has indicated that the losses are currently believed to be
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24
dominantly by the following mechanisms [75]:
1. In perfect crystals, the anharmonic lattice forces mediate the interaction be­
tween the phonons. This leads to damping of the optical phonons. These losses
are the lower limit of dielectric loss.
2. Losses in homogeneous crystals or crystallites can arise from scattering of
phonons by periodicity or point defects such as dopant atoms, vacancies or
defect pairs.
3. Losses in inhomogeneous ceramics are caused by extended dislocations, grain
boundaries, inclusions and second phases.
Intrinsic Loss: Intrinsic loss refers to the lower limit of dielectric loss in a perfect
crystal. This loss is related to phonon damping and dominated by the energy transfer
from the exciting microwave with the frequency ui -C ujtOj (he. u> ~ 0 ) and the wave
vector k = 0 to transverse optical (TO) phonons [75]. The optical phonons can then
generate acoustical (thermal) phonons through interaction with other phonons, which
leads to microwave loss. The dielectric loss at microwave frequencies can be calculated
in the framework of classical dispersion theory as
(1.4)
A linear increase in the intrinsic losses with frequency is characteristic of these phonon
effects. In addition to the frequency dependence, the dielectric loss also feature a
tem perature dependence. Gervais et al found th at the lifetime of TO phonons in
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25
rutile (Ti 0 2 ) crystal is basically limited by the anharmonic three phonon coupling.
This dominating process is the decay of one TO phonon into two acoustical phonons.
The damping constant of the TO modes increases linearly with temperature, which
leads to the linear increase in the dielectric loss [77].
Extrinsic Loss: It is generally agreed th at dielectric loss in most classes of
materials can be attributed to defect-mediated mechanisms [78, 79, 80, 81, 82], This
comes primarily from the observation that the loss tangent is sample dependent and
is large in structurally defective and chemically impure material [83]. One of the most
appreciated defect-mediated models is th at from Debye in which the energy loss is
associated with atomic motion over an energy barrier [78]. The model is found to fit
the experimental dependence of the loss tangent on tem perature and frequency for a
number of materials. Proof of the microscopic basis for this model is however lacking.
The dielectric loss has been studied as a function of various types of defects
such as porosity, im purity level, and paramagnetic defects. For example, a reduction
of dielectric losses in (Ba,Sr)(Zr,Ti)C >3 compounds to less than 6 x ICC4 at 4 GHz
was reported with increased sintered density by the addition of 1 mol% of Ta [84].
Sintering Ba(Mn!/ 3Ta 2/ 3)0 3 in nitrogen gas was also found to increase Q from 1,550
to 10,400 with reduced porosity [85]. Braginsky et al. has shown good agreement
between the observed loss tangent [81] and the loss th at would be expected from the
measured paramagnetic defect concentration (5 x 1017 cm3, Cr). Based on this result,
they suggested th at paramagnetic resonant absorption by defects with a non-zero
net angular momentum within the solid dominates the microwave loss for many the
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26
ultra-high- Q dielectrics. Another study reported th at the dependence of composition
of an alloy system (Zri-^Sn^TiC^) correlates with the density of extended defects
associated with cation ordering [80]. Although a detailed microscopic mechanism was
not proposed, the authors hypothesized th at the segregation of Sn at these boundaries
might be responsible for the changes in microwave loss. Rong et al. has found a direct
correlation between the concentration of optically active point defects and the loss
tangent in temperature-compensated commercial Ba(ZnTa)03 ceramics [86 ].
1.3.2.3. T em p era tu re C oefficient o f R e s o n a n t Frequency. The temper­
ature coefficient of resonant frequency, Tf or TCF, defines the thermal stability of the
resonator, th at is, how much the resonant frequency drifts when temperature changes.
Thus, the microwave resonators should have r f near zero for practical applications.
Tf is related to the expansion coefficient, a, which affects the resonator’s dimensions,
and the tem perature dependence of the dielectric constant. This relationship can be
derived from Eq. 1.2 and f \ = c [74], As the wavelength of the standing wave ap­
proximates to the width (D ) of the resonator (Ad ~ D) in the simplest fundamental
mode, the frequency of the standing wave is,
c
c
c
(1.5)
If the tem perature changes, the relative change of f 0 can be w ritten as,
l<9/o
ldD
yo~ d T ~ ~ D ~ d T
llder
2 ev d T
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( 1.6 )
27
where -7-- 77^ is Tf,
is a , and —
is the tem perature coefficient of sT, rs .
jo oT
D oT
er oT
Thus the relationship can be expressed more compactly as,
ri = - ( a + fT )
(1.7)
It is imperative th at a microwave dielectric material has a Tf close to 0 and
preferably tunable with composition and processing so th at changes in the surround­
ing circuit can be balanced.
1.4. T hesis O rganization
This chapter has given an introduction to and some motivation for the re­
search in this thesis, transition metal doping in two types of materials: wide bandgap
semiconductors for spin dependent electronics applications and oxide dielectrics for
microwave applications.
Chapter 2 focuses on the properties of Cr-doped GaN grown with MBE. We
highlight several im portant advances, namely the observation of high temperature
ferromagnetism with
T q,
over 900 K and hopping transport characteristics in Cr-
doped GaN. Based on these results and extensive structural characterization, the
origin of ferromagnetism in Cr-doped GaN is discussed.
As an effective method to manipulate the magnetic properties of ferromagnetic
materials, the exchange biasing of Cr-doped GaN using a MnO overlayer is described
in Chapter 3. Two most obvious phenomena characteristic of exchange bias, namely a
shift of magnetic hysteresis loop along the field axis and an increase in the loop width,
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28
are observed. Then we discussed the the mechanism responsible for the observed
exchange bias.
Chapter 4 discusses the effect of Ni-doping on the structural, dielectric and opti­
cal properties of B a(C di/ 3Ta 2/ 3) 0 3 (BCT) dielectrics. We highlight several important
findings in this chapter. Ni doping significantly improves the sintering density, stabi­
lizes the structural quality, and enhances the extent of Cd-Ta ordering in BCT. Then
we bring our attention to the microwave and optical properties. Finally we elucidate
the correlation between the loss tangent of Ni-doped BCT samples and the intensity
of a continuous optical absorption background caused from the presence of optically
active point defects in Ni-doped BCT dielectrics.
We give conclusions in Chapter 5. Also, included in this chapter is the proposed
future work.
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CHAPTER 2
PR O P E R T IE S OF C r-D O PE D G aN D IL U T E M A G N E TIC
S E M IC O N D U C T O R
2.1. Introduction
Dilute magnetic semiconductors (DMSs) are attractive materials for use in spintronic applications [3,11]. In these structures, the electron charge and spin are utilized
simultaneously to create new functionalities. Such devices offer a unique opportunity
to integrate conventional semiconductor and ferromagnetic technologies. The original
report of ferromagnetism in Mn-doped GaAs above 100 K aroused intense interest
in theoretical and experimental studies of related III-V compound semiconductors
doped with magnetic impurities [43].
For useful practical applications, ferromagnetism must be achieved above room
temperature. Ferromagnetic behavior has been recently reported over room temper­
atures in a number of semiconductor systems including Co-doped TiC>2 [28], V-doped
TiC>2 [87], Mn-doped ZnCb [88 ], Co-doped Sn 0 2 [89], Cr-doped AIN [26, 63, 25], Crdoped GaN [25, 34], and Mn-doped GaN [33]. (Ga,Mn)N films grown by molecular
beam epitaxy were reported to be ferromagnetic above room temperature, with a
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30
Curie temperature, Tc, of 940 K [31]. Another study of the same system synthesized
using solid-state diffusion reported a Tq in the range of 220-370 K [24], while bulk
Cr-doped GaN fabricated using the sodium flux method was reported to have a Tq
of 280 K [32]. Compared to other material systems, GaN as a host of DMS has the
following advantages [90]:
1. Ferromagnetism achieved in nitride semiconductors could complement the
widely explored excellent optical and electrical functionalities of this wide-gap
material system.
2. Bandgap engineering can be easily applied to the fully epitaxial system to op­
timize the spin injection and create new functionalities.
3. The short bondlength and small spin-orbit coupling lead to large exchange cou­
pling in transition-metal-doped Ill-nitride semiconductors, which is related to
predicted ferromagnetism over 300 K [63].
4. The spin-orbit coupling due to the light nitrogen is small in this system. Thus
Ill-nitide semiconductors expect to be an excellent choice of a host material for
the transport of spin-polarized electrons over significant times and distances. It
has been predicted th at electron spin lifetime in pure GaN is about three orders
of magnitude longer than in GaAs at all temperatures [91].
5. The enhanced growth temperatures of III-nitrides makes it possible to perform
high quality epitaxial transition metal-doped growth with small levels of donor
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31
compensation, especially when compared to the Asca and M n/ populations that
readily form in low tem perature grown Mn-doped GaAs [50, 53, 68 ].
The search for the physical mechanism responsible for the observed ferromag­
netic properties and the question of the applicability of the classical magnetic models
have become topics of intense interest. For example, it is critical to answer whether
these TM-doped semiconductor material systems are true DMS or just semiconductors
showing ferromagnetic hysteresis because any trace undetected amount of a ferromag­
netic secondary phase could induce the ferromagnetism. We chose to study Cr-doped
GaN because the secondary phases that may be expected to form, including Cr metal,
CrN, Cr 2N, and Cr^Ga, are not ferromagnetic [92], thus excluding the problem of pos­
sible contribution of ferromagnetic secondary phases. Besides that, we chose to study
Cr-doped GaN for the following reasons. Cr has a lower vapor pressure than Mn, so
it would be expected to have a larger sticking coefficient at elevated growth tempera­
tures. The limited growth tem perature used during deposition of other ferromagnetic
Mn-doped III-V semiconductors to overcome the high volatility of Mn is presumably
responsible for the observed poor crystalline quality and high levels of compensation
in these materials [68 ]. Since the C raa G defect level would be expected to be 1/3
filled, the partial compensation from the commonly observed background donors that
make GaN naturally n-type would be expected to drive the system towards optimal
doping. Thus, this partial compensation will increase the filling in the Cr defect
band from 1/3 towards the optimal 1/2 filling for the double exchange mechanism of
ferromagnetism [68 ].
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32
In this chapter we report the observation of ferromagnetism in Cr-doped GaN
above 900 K, and describes the structural, electrical, and magnetic properties of the
materials. Our results indicate th at Cr-doped GaN materials are true dilute magnetic
semiconductors as we have found high quality epitaxial Cr-doped GaN without any
detectable secondary phases exhibits ferromagnetism and we have shown th at Cr
substitutional defects are strongly involved in the observed ferromagnetism [25, 34,
46, 93].
2.2. E xperim ental
The Cr-doped GaN films were grown on 6 H-SiC (0001) and sapphire (0001)
substrates in a custom-built UHV reactive MBE system with a base pressure better
than 5xlO -10 Torr. The films were grown on substrates over a range of temperatures.
To ignite the plasma, ulta-high purity (UHP) N2 gas and Ar gas was flowed during
growth. Typical pressures used during film growth ranged from ICC5 - 10-4 Torr. The
Ga and Cr diffusion cells were set at appropriate fluxes using tem perature controllers.
The film growth was initiated by igniting the nitrogen plasma and then opening
the shutters to the Knudsen effusion cells and nitrogen source sequentially. In-situ
thickness monitoring was carried out using a water-cooled 5 MHz quartz crystal rate
monitor (Maxtek TM-400). Samples were typically grown for 3 hours.
Structural properties were characterized using XRD (Rigaku D/MAX-IIB),
high-resolution XRD (Bede D1 system with dual channel single crystal Si monochro­
mator), and TEM (JEOL 4000EX). The thickness and depth profile of chemical com­
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33
position were characterized by Rutherford backscattering spectroscopy (RBS), with
a 2.0 MeV He++ beam used to obtain channeling yields of Ga and Cr, and a 3.73
MeV He++ used to obtain the channeling yiedls of N by NRA. Nuclear resonant
elastic scattering, 14N (a, a) 14N was used for N detection. The magnetic properties
were characterized from 10 K to 350 K with a SQUID (superconducting quantum
interference device) magnetometer (SHE VTS900) and from 300 K to 950 K with a
Quantum Design vibrating sample magnetometer (VSM) equipped with the recently
developed oven option for the Physical Property Measurement System (PPMS). Mag­
netic fields were applied parallel to the film plane during susceptibility measurements
and perpendicular to the film during magnetoresistance (MR) measurements. The
diamagnetic background contributions originating from the substrate and the sample
holder were subtracted from the measured magnetic moment to infer the magnetic
properties of the deposited thin films. For zero-field-cooled (ZFC) and field-cooled
(FC) measurements, the sample was cooled down to 10 K in zero magnetic field at
first, and then a magnetic field was applied to the sample to execute the zero-fieldcooled (ZFC) d ata taking until T = 370 K. After that, the tem perature was decreased
to 10 K with the same magnetic field to take the field-cooled (FC) measurement.
2.3. R esu lts and D iscussion
2.3.1. M agnetic P roperties
Both the magnetic field dependence on magnetization, M, and the temperature
dependence on magnetization were measured with the external magnetic field parallel
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34
4.0
§
0.0
N
-
2.0
T = 10 K
-4.0
1
0
1
2
Magnetic Field (kOe)
Figure 2.1. Field dependence of magnetization curve at 10 K of a 2% Cr-doped GaN
sample grown on 6H-SiC substrate by MBE.
to the film plane. Figure 2.1 shows the magnetization as a function of applied external
magnetic field at 10 K. The magnetization saturates at around 2000 Oe. The welldefined soft hysteresis loops confirm that the film is ferromagnetic. We have observed
spontaneous magnetization values, Ms, of 3.12 em u/cm 3 at 10 K for 2% Cr-doped
GaN. This Ms values indicates th at the effective magnetic moment in Cr-doped GaN
is 0.42
hb/G v
atom at 10 K. The expected magnetic moment of a C rca defect is 3
Hb / C t atom and thus our result indicates that 14% of the Cr is magnetically active.
The coercivity, H q , is ~ 200 Oe at 10 K.
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35
Figure 2.2 shows the tem perature dependence on magnetization from 10 K to
300 K. Magnetization was kept nearly constant at 0.1 T and no sudden drop in
magnetization was observed as the tem perature was increased up to 350 K, indicating
a Curie tem perature greater than 350 K. In order to further confirm the temperature
dependent result, we performed ZFC and FC measurements, as shown in Fig. 2.3.
The clear separation between ZFC and FC curves indicated th at ferromagnetism
persists above 350 K.
3.0
2.5
2.0
<u
w
&
.2
«
N
’-3
s
W
D
«
£
1.0
0.0
0
50
100
150
200
250
300
Temperature (K)
Figure 2.2. Temperature dependence of magnetization curve from 10 K to 300 K of
a 2% Cr-doped GaN sample grown on 6H-SiC substrate by MBE.
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36
4.0
2.0
—
0
1—
1—
1—
1—
1—
100
1—
1—
1—
1—
1—
1—
1—
1—
200
1—
1—
1—
1—
300
1—
1—
400
Temperature (K)
Figure 2.3. Temperature dependence of zero field cooled (bootm curve) and field
cooled (top curve) magnetization for a 2% Cr-doped GaN sample.
The measured magnetic moments per impurity dopant in Cr-doped GaN vary
significantly with Cr concentration range with a maximum magnetic moment occur­
ring at 3% Cr. The similar trend has been reported in the studies of Cr-doped AIN
[25] and Mn-doped GaN [60] grown by MBE. But more variation exists in the case
of Cr-doped GaN. The film with 3% Cr grown at 775 °C has the highest saturation
magnetic moment of 0.5 /jb /C i', which indicates that ~ 17% of the Cr is magnetically
active.
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37
2% Cr-doped GaN
4
u
"s
S
Oi
325 K
3
2
800 K
1
q
iff
3■V
sa
•opn 0
«S
.H -1
'S
c -2
6JD
-3
-4
________ 1________ 1________
-3000
-2000
-1000
0
1
1
1000
2000
(a)
3000
Magnetic Field (Oe)
Figure 2.4. Field dependence of magnetization curve at 325 K and 800 K of a 2%
Cr-doped GaN sample.
Figure 2.4 shows the magnetic held dependence curve at 325 K and 800 K.
Hysteresis loops are observed at both temperatures, indicating th at the him is ferro­
magnetic. The coercive held is ~ 100 Oe at 325K and decreases to ~ 60 Oe at 800
K. The tem perature dependent magnetization curve shows th at the ferromagnetism
persists to tem perature above 900 K, as showed in Fig. 2.5.
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38
3
♦♦
♦♦
2
♦♦♦♦
♦♦
1
0
0
200
600
400
Tem perature (K)
800
1000
Figure 2.5. Temperature dependence of magnetization curve from 10 K to 900 K of
a 2% Cr-doped GaN sample showing ferromagnetism persisting above 900 K.
2.3.2. Structural P roperties
In order to exclude the contribution of any secondary phase to the observed
ferromagnetism, extensive structural and compositional characterizations have been
performed. The lattice constants of Cr-doped GaN inferred from XRD results de­
crease with increasing Cr concentration. The variation in the c-axis lattice parameter
follows a nearly linear variation from the undoped value of 5.18053 A to 5.17198 A
for 7.4% Cr doping. This variation of lattice constant with doping concentration is
characteristic of the introduction of impurity point defects, rather than secondary
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
phases. A similar trend is found in Mn-doped GaN th at has been attributed to the
incorporation of substitutional impurities on the group-III site [60].
1.0
Cr Ga =90%
Cr a
0.8
>
13
•P4 0.6
7?
o
\ •* \ .
\
\
Cjf /
/
*
\
\
\
®\
©
/
\
\ \
0.2
/ •>
/
o
\
\
0.4
su
£
/ /
\
'O
4>
.3
7/
Ga \ °\
o
*
* % '■Xmi„ = 12%
: 775°C
\
Growth Temp. *
< ' "Ga Xmin = 2-5%
0.0
-
1.0
-0.5
0.0
0.5
1.0
T ilt A ngle (cleg)
Figure 2.6. Ion channeling angular scans in the (0001) axial direction for a 3% Crdoped GaN film grown at 775 °C (Ref. [46]).
TEM observations reveal that the Cr-doped GaN films grown at substrate tem­
perature < 775 are high quality epitaxial and single phase. This is also confirmed by
the ion channeling RBS result as shown in Fig. 2.6. The low ion channeling minimum
yield (xmin) of Ga and Cr indicate th at high quality epitaxial growth and 90% of Cr
sits on the substitutional sites. Further XRD as well as electron-energy-loss spec-
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40
troscopy (EELS) do not detect any possible secondary phases. For Cr-doped GaN
grown at tem peratures above 800 K, both XRD and TEM studies indicated that the
films contained very small amounts (0.2% by volume) of the CrN phase. No evidence
for the formation of Cr2N was found. Figure 2.7 shows the XRD spectra for a 2%
Cr-doped GaN grown at 825 °C on a SiC substrate by MBE.
(002)
GaN
100000
(006)
SiC
(0012)
SiC
s
V)
fi
a>
e
(004)
GaN
10000
an)
CrN
SiC
1000
SiC
(222)
CrN
100
10
20
30
40
50
60
70
80
90
2 0 (°)
Figure 2.7. XRD spectra for a 2% Cr-doped GaN grown at 825 °C on a SiC substrate
by MBE (Ref. [34]).
To address the influence of these compounds on our results, we grew Cr-N films
using growth conditions identical to those used for Cr-doped III-N films but without
the group-III flux. Characterization of the Cr-N films indicated that the dominant
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41
Cr 2N phase comprised ~ 99.8% of the material, while only ~ 0.2% was the minority
CrN phase. The volume fraction of the CrN phase is fortuitously similar to that
in the Cr-doped GaN films. Magnetization measurements of the Cr-N film did not
show hysteresis over the tem perature range from 10K to 900K and the signals were
2 orders lower than those of Cr-doped GaN. Careful comparisons with measurement
background signals suggest that neither C ^N nor CrN is ferromagnetic. These find­
ings, combined with the varied magnetic and structural properties of Cr-doped GaN,
allow us to rule out the role of any known secondary phases in contributing to the
magnetic properties.
2.3.3. R ole o f Cr S u b stitu tion on Ferrom agnetic P roperties
As mentioned earlier, Cr-doped GaN films grown under optimized conditions
show very small ion channeling minimum yield (Xmin)- Using the measured XGa and
Xcr and the expression CrQa = (1 - Xcr)/(1 - XGa), we can calculate fraction of Cr
in substitutional site (Crca) of the Cr-doped GaN films. The results indicate that
78%, 87% and 90% of Cr occupies substitutional sites for Cr-doped GaN films grown
at substrate temperatures of 700 °C, 740 °C and 775 °C, respectively. Only a small
fraction of Cr (< 20%) is located in substitutional sites for film grown at 825 °C [46].
Subsequent magnetic measurements show that the Cr-doped GaN film grown at
775 °C has the highest saturation magnetic moment (Ms) of 0.35 jx-^jCr, indicating
th at ~ 12% of Cr is magnetically active. For the films grown at 825 °C, with low
faction of substitutional Cr content (< 20%), the saturation magnetic moment, and
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42
the fraction of magnetically active Cr in the film, drop to 0.13 /ir and 4%, respectively.
These results present clear evidence th at substitutional Cr is strongly related to the
observed ferromagnetism of these films.
u 80
o
<S 60
As grown
o
Post annealed
(0
■Q
3
w
L_
12
o
“co0.3
wSL
10 O
<D
8 £
As grown
o
■2 0.2
<
>.
4 75
o
6
n
N
s
C 0.1
U)
2 o
Post annealed
ns
S
0
700
720
740
760
780
800
820
840
(B
5
Growth Temperature (°C)
Figure 2.8. Change in substitutional Cr (top) and magnetization (bottom) after
annealing at 825 °C for 3% Cr-doped GaN samples grown at temperatures from 700
to 825 °C (Ref. [46])
Another interesting observation is that the magnetic moment of Cr-doped GaN
shows a consistent drop after high temperature magnetic measurements up to 825 °C
which is similar to an annealing process. In order to find the reason for this magne­
tization drop, we performed ion channeling RBS measurements on the samples again
after annealing. The results is summarized in Fig. 2.8. All the samples show a sys­
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43
tematic drop in both the fraction of substitutional Cr and the magnetic moment after
annealing at 825 °C. This provides another importance evidence th at Cr substitutional
defects is responsible for the ferromagnetic properties of Cr-doped GaN. However, it
should also be pointed out th at the magnitude of the reduction of magnetization is
greater than th a t of the substitutional Cr fraction. This indicates that in addition to
the decreased fraction of Cr on the substitutional site, there are other factors leading
to the magnetization drop. A recent theoretical study by Cui et al. shows th at CrQa
has a strong tendency to form embedded clusters [94]. Antiferromagnetic states are
energetically favored for C rca clusters larger than 2 atoms. They subsequently pro­
posed th at the annealing can cause redistribution of the Cr ions which thus enhances
the formation of clusters and causes magnetization reduction. Another possible fac­
tor is the change in compensation of the Cr t% band as a result of transfer of charge
to or from other defects after annealing. As mentioned before, in the framework of
double exchange mechanism, this change of compensation will result in a change in
the magnetization.
2.3.4. Transport P roperties
To perform electrical measurements, Cr-doped GaN thin films were grown on
insulating sapphire substrates. The Cr-doped GaN samples are quite conductive. Fig­
ure 2.9 shows the tem perature dependent of resistance of a 4% Cr-doped GaN th at ex­
hibits ferromagnetic properties, with 3% Cr magnetically active at room temperature.
The thermally activated process follows the exponential law, R = R0 exp[(T0/T ,)1,/4],
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44
which is characteristic of variable range hopping between localized states with a
Coulomb gap [26] We attribute the conduction in the GaN films to variable range
hopping in the Cr impurity bands. Cr is known experimentally [71], and predicted
theoretically [68], to form a deep level in the bandgap of GaN at an energy of ~ 2.0
eV from the valence band. A more detailed study by Wu et al. linked this transport
behavior with uniform Cr distribution in Cr-doped GaN without formation secondary
phases [95].
45.0
10.70
10.30
S 35.0
JS
O
2
x
9.90
25.0
9.50
0.90
0.70
m m<i /k 1m)
15.0
5.0
0
50
100
150
200
250
300
Temperature (K)
Figure 2.9. Temperature dependence of resistance of a 4% Cr-doped GaN gown on
sapphire. The insert shows the exponential law relationship, R = R0 exp[(To/T)1,/4],
which is characteristic of variable range hopping.
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45
The electron carrier density and Hall mobility at 300 K were measured to be
1.4 x 1020 cm-3 and 0.06 cm2/V.s, respectively, for magnetic fields up to 5 T. The ex­
tremely low mobility is related to the observed hopping conductivity. This low value
also prevented us from having sufficient measurement accuracy at small magnetic
fields to investigate the anomalous Hall effect. Note th at the carrier concentration
is similar in magnitude to the measured concentration of magnetically-active Cr,
4.9 x 1019 cm-3 . Since the majority e level of Cr substitutional defect is completely
filled with two electrons [68], the remaining electrons th at partially fill the t2 level
contribute to conduction. Compensating defects in the III-N compounds could in­
crease or decrease the amount of filling of this level. The reason for the quantitative
difference is unclear although it may primarily result from an uncertainty in the Hall
measurement as a result of localized trapping and magnetic-field-dependent scattering
influencing the transport.
Figure 2.10 shows the temperature dependence of the magnetotransport prop­
erties of Cr-doped GaN with a magnetic field up to 7 T applied perpendicular to
the sample plane. The sheet resistance showed a strong negative magnetoresistance
(MR) from 2K to 300K. The relative change of resistance in magnetic field (AR/R)
is -3% at 10K, gradually decreasing in magnitude with increasing temperature. The
deviation from the parabolic behaviour at high fields and low temperatures is presum­
ably attributed to the conventional path-length-related positive MR, characteristic of
traditional semiconductor transport. Negative MR has been observed in other di­
lute magnetic semiconductors [96]. We attribute the negative MR observed in our
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46
300
-0.5
-1.5
<
-2.5
■7
■5
■3
1
1
3
5
7
Magnetic Field (T)
Figure 2.10. Magnetoresistance A R /R , the relative change of sheet resistance in a
magnetic field, of a 4% Cr-doped GaN grown on sapphire substrate (Ref. [25]).
films to a mechanism originally proposed by Sivan, Entin-Wohlman, and Imry for non­
magnetic semiconductors th at takes into account the influence of the magnetic field on
the quantum interference between the many paths linking two hopping sites [97, 98].
In the variable range hopping regime and at small magnetic fields, the MR obeys the
expression A R / R = T~S/2B 2, which is expected in the presence of a Coulomb gap in
the density of states [99], and is consistent with the result of tem perature dependent
resistance. Recently, another transport model has been developed for the case of
magnetic semiconductors [100]. This model considers the fluctuations caused by the
local exchange interaction between the carrier and magnetization, which introduce
additional energy disorder between different carrier hopping sites. The predictions of
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47
0 .0
-0.5
c -2.0
CD
-2.5
-
3 .0
F ield (T)
Figure 2.11. Fitting of the magnetoresistance data to the transport model proposed
for magnetic semiconductor by Yu (Ref. [100]).
this model also are found to fit, our data, as shown in Fig. 2.11.
2.3.5. Origin o f Ferrom agnetism in C r-doped G aN
As pointed out earlier, the Cr-doped GaN materials are ideal for the explo­
ration of the ferromagnetic properties of DMS since essentially all of the potentially
secondary phases, including Cr metal, CrN, and CrxGa alloys, are not ferromagnetic.
Only Cr2N has been reported to be ferromagnetic [101], although there is very little
data on this material and even its Curie temperature has not been reported. Exten­
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48
sive characterization by TEM, XRD, and electron energy loss spectroscopy (EELS)
revealed th at the Cr-doped GaN films under optimized conditions were epitaxial and
single phase. Only for Cr-doped GaN grown at tem peratures higher than 800 K, both
XRD and TEM studies indicated th at the films contained very trace amounts of the
non-ferromagnetic CrN phase.
It is also worthy noting th at other Cr - Group V compounds such as zincblende
CrAs and CrSb [102] and hexagonal MnAs [103], have been reported to have Curie
temperatures above room temperature. Nanocrystalline CrxN phases have also been
theoretically predicted to have a Curie tem perature above room tem perature [104].
It is difficult to conclusively rule out the presence of a minute amount of extraneous
secondary phases using techniques such as XRD and TEM alone. Our use of RBS
channelling does, however, prove th at the majority of Cr is on substitutional lattice
sites and give indisputable evidence that substitutional C rca defects are involved in
the magnetic behavior [46].
Currently, there is no consensus on the nature of ferromagnetism in DMS ma­
terials. Several theoretical models have been proposed to understand this magnetic
ordering. A free-carrier-mediated model has been proposed to explain the magnetic
properties of Mn-doped III-V semiconductors [4]. The presence of free holes due to
the shallow acceptor nature of Mn2+ + h+ in GaAs might be a reasonable approx­
imation, but it most certainly does not apply to the ferromagnetism in Cr-doped
GaN since these defects form near midgap deep levels [71, 68]. The Cr d level in
GaN is split by exchange and the crystal field into a threefold degenerate t2 and a
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49
doubly degenerate e level [68]. The majority
for Cr. The partial filling of the majority
would be expected to be 1/3 filled
level suggests a ferromagnetic ground
state associated with the double exchange mechanism. In such cases, the Fermi level
is pinned within the defect bands. The observed hopping transport characteristics, in
conjunction with the similarity between the concentration of transport electrons and
the density of magnetically active Cr atoms, support this theory.
2.4. Sum m ary
High-quality Cr-doped GaN thin films grown by MBE have been demonstrated
to exhibit ferromagnetism with a Curie tem perature above 900 K. The magnetic
properties are found to strongly vary as a function of magnetic impurity concentration
with the best characteristics resulting at 3% Cr in GaN. The ion channeling RBS
results establish th at the location of Cr sites in the Cr-doped GaN lattice plays a
crucial role in determining its magnetic properties. Extensive structural, magnetic,
and electrical characterization suggesta that ferromagnetism in Cr-dope GaN best
fits the double exchange mechanism as a result of hopping between near-midgap
substitutional Cr impurity bands.
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CHAPTER 3
E X C H A N G E B IA S IN G OF F E R R O M A G N E T IC C r-D O P E D G aN
U S IN G A M nO O V ER LA Y E R
3.1. Introduction
In Chapter 2, we have showed th at MBE epitaxially grown Cr-doped GaN thin
films exhibit ferromagnetism over 900 K. This indicate th at they are attractive for
spintronic applications. To develop practical applications, and in particular magne­
toresistive random access memory (MRAM) type devices, it is im portant to develop
methods to manipulate the magnetic properties of Cr-doped GaN. Exchange bias, a
proximity effect th at is found at the interface between ferromagnetic (FM) and anti­
ferromagnetic (AFM) materials, has been used to bias the bottom electrode of spin
valves for magnetic sensor and magnetic storage device applications [105]. Figure 3.1
shows a schematic demonstration of a giant magnetoresistance (GMR) sensor widely
used in modern current drives.
This exchange bias effect occurs when a FM /AFM system (with a Tq larger than
the Neel temperature, TN) is cooled through TN of the AFM [107], as shown in Fig.
3.2. Several phenomena are normally observed, with the most obvious being a shift
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51
pinned
□
spacer
□
t r e e !o
□
'
■
Figure 3.1. Schematic of a GMR read sensor in spin valve structure. The magnetic
layer in blue is exchange-biased by an antiferromagnetic layer so its magnetic property
is hard to switch, called pinned layer (Ref. [106]).
of magnetic hysteresis loop along the held axis, referred to as the exchange bias ( He ) ,
and an increase in the loop width, referred to as the coercivity ( H e ) enhancement [105]
Specifically, the exchange bias has also been successfully demonstrated to overcome
the superparamagnetic limit, which occurs in ultra small devices when a reduction
in the anisotropy energy per magnetic particle results in superparamagnetism [108].
There have been also reports on the manipulation of (Ga,Mn)As magnetic properties
by the proximity effect using MnTe, ZnMnTe and MnO layers [109, 110].
In this chapter we demonstrate the exchange biasing of a layer structure of FM
Cr-doped GaN with an epitaxially grown AFM MnO overlayer.
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52
#>■
Field cool
T «Tn
Figure 3.2. Schematic illustration of exchange bias mechanism (Ref. [107]).
3.2. E xperim ental
The samples were grown on 6H-S\C (0001) substrates in a custom-built reac­
tive MBE system with a base pressure of ~ 5 x 10“ 10 Torr. After the growth of
Cr-doped GaN under an optimized condition at 775 °C [46], the Ga and Cr effusion
cells were shut down and the sample was cooled. The Mn overlayer was then grown
at room temperature. The sample was subsequently annealed at 200 °C for 15 min
in an oxygen atmosphere. The thickness and depth profile of the chemical composi­
tion were characterized by Rutherford backscattering spectroscopy (RBS) with a 3.05
MeV He++ beam at an incident angle of 8°. Structural properties were character­
ized using X-ray diffraction (XRD) [Rigaku D/MAX-IIB], The magnetic properties
were measured with a Quantum Design vibrating sample magnetometer (VSM) in
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53
2500
Ga
2000
2
j3 1500
T3
o
S
a
Mn
io o o
E
•-
j®
500
Cr
100
150
200
250
300
350
400
450
Channel
Figure 3.3. RBS spectra indicating that a 130 nm thick GaN is doped with 4% Cr
and has a 20 nm thick MnO overlayer (Ref. [111]).
the Physical Property Measurement System (PPMS). The diamagnetic background
contributions originating from the substrate and the sample holder were subtracted
from the measured magnetic moment to infer the magnetic properties of the deposited
thin films.
After being removed from the MBE chamber, the Mn overlayer was oxidized by
the exposure to air. The Mn to oxygen ratio was 1.00:0.40±0.02 according to RBS
measurement. The samples were subsequently cut in pieces for magnetic measure­
ments. After being annealed in oxygen, the Mn overlayer was completely oxidized to
a stoichiometric ratio of M n:0 of 1.00:1.00±0.02. Figure 3.3 shows the RBS spectra of
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54
a sample after annealing. Analysis of the data indicates th a t the epitaxial Cr-doped
GaN film is 130 nm thick and has a Cr concentration of 4 at.%. The thickness of
the top Mn layer was 16 nm after growth and increased to 20 nm after the oxygen
annealing. There was no detectable evidence th at oxygen diffused into the Cr-doped
GaN layer in these samples.
3.3. R esu lts and D iscussion
Zero field cooled (ZFC) and field cooled (FC) hysteresis loops for the 4% Crdoped GaN sample with a MnO overlayer were measured at temperatures ranging
from 10 K to 300 K. In the FC experiment, the sample was cooled down from 300 K
8
4
Field cooled
H = 5 kOe "
2
0
Zero field cooled
•2
a
wo
4
4
6
8
-4000
-2000
0
2000
4000
Magnetic Field (Oe)
Figure 3.4. Magnetic hysteresis loops of a 4% Cr-doped Cr-doped GaN with MnO
overlayer after zero-field cooling and 5 kOe field cooling (Ref. [111]).
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55
8
4
Field cooled
H = -5 kOe
2
0
Zero field cooled
■2
6
8
-4000
-2000
0
2000
4000
Magnetic Field (Oe)
Figure 3.5. Magnetic hysteresis loops of a 4% Cr-doped Cr-doped GaN with MnO
overlayer after zero-held cooling and -5 kOe held cooling (Ref. [111]).
under a magnetic held of 5 kOe or -5 kOe applied parallel to the him plane. Figure
3.4 and 3.5 show the magnetic ZFC and FC hysteresis loops measured at 10 K after
5 kOe and -5 kOe held cooling, respectively. The magnetization saturates at around
3 kOe, similar to those observed in Cr-doped GaN single layers. The 5 kOe FC
loop shows a clear shift to the negative held while the -5 kOe FC loop shifts to the
positive held, when compared with the ZFC loop. This is a clear signature of exchange
coupling in the bilayer structure.The exchange held is calculated to be 70 Oe using
the equation: HE =
+ Hright)/2\, where Hieft and Hright are the points where
the loop intersects the held axis [112],
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56
3
Field cooled
H = 5 kOe
2
fj
'a
£0)
1
S
O
«8
0
V0>
1
w
/
$
X
&
ex
C! - Z<■>
‘eH
______________ J
P ^ ,fl
-4000
1
-2000
0
2000
4000
Magnetic Field (Oe)
Figure 3.6. Magnetic hysteresis loop of a 3% Cr-doped GaN single layer after 5 kOe
field cooling measured at 10 K (Ref. [111]).
For comparison, the FC hysteresis loop of a single Cr-doped GaN layer grown
under the same substrate tem perature and with similar Cr concentration is depicted
in Fig. 3.6. The loop is quite symmetric around zero magnetic field with a He of 200
Oe. For the Cr-doped GaN with the MnO overlayer, there is a noticeable increase
of He to 275 Oe, characteristic of exchange biasing, which is another important
indication of exchange biasing effect.
Figure 3.7 shows the tem perature dependence of H q and H e of the same sample.
Both He and H e decrease with the increasing temperature. While Hq persists to 300
K, suggesting ferromagnetism occurs at over room tem perature, He only appears
below ~ 105 K, indicating a blocking temperature, TB, of 105 K. This is below the
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57
90
300
75
250
60
200
ow
45
“w
150 O
30
n 100
St!
0
0
50
100
150
200
250
300
Temperature (K)
Figure 3.7. Temperature dependence of coercivity and exchange field of a 4% Crdoped GaN with MnO overlayer (Ref. [111]).
reported Tn of H 8 K of MnO [110], but above 95 K, the TN of pure Mn [105],
indicating MnO acts as a AFM layer in the system.
R. K. Zheng reported that
the exchange interaction between FM (Zn,Mn)Mn20 4 and AFM phase exists in Mn
doped ZnO [88]. However, this scenario obviously does not apply to Cr-doped GaN
since no exchange biasing is observed in single Cr-doped GaN layers. Previous studies
indicated th at there is no evidence for the presence of a secondary phase in Cr-doped
GaN synthesized under optimized conditions [46], which suggests the exchange bias
comes from the coupling between the ferromagnetic Cr-doped GaN and AFM MnO
layers.
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58
To quantify the magnitude of the exchange bias, the exchange coupling energy
is calculated to be 6.4 x 10-3 erg/cm 2 at 10 K. This value is quite small compared
to those of conventional exchange bias systems, as a result of the low saturation
magnetization of the Cr-doped GaN layer (< 8 em u/cm 3) which is 1-2 orders of
magnitude smaller than those of conventional ferromagnets. We do not believe that
these results imply unconventional magnetic properties of the Cr-doped GaN or an
anomalous coupling mechanism at the interface. The role of surface roughness and
the presence of interfacial contamination or phases in determining the exchange field
is unclear and under further investigation.
3.4. Sum m ary
Exchange biasing of a Cr-doped GaN layer by an MnO overlayer has been
demonstrated. The magnetic measurements show th at the sample has a larger co­
ercive field (275 Oe), than is typically observed in single layer Cr-doped GaN (200
Oe). The hysteresis loop shows a clear shift to negative magnetic field when measured
after field cooling. The same effect is not present in single Cr-doped GaN films. The
observed exchange bias is attributed to exchange coupling at the interface between
the ferromagnetic Cr-GaN and the antiferromagnetic MnO.
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CHAPTER 4
E FFE C T OF N i D O P IN G O N TH E S T R U C T U R A L , D IELE C TR IC ,
A N D O PT IC A L PR O P E R T IE S OF B A R IU M C A D M IU M
TA N TA LA TE
4.1. Introduction
Microwave dielectric ceramics are widely used in modern telecommunication
systems in such devices as resonators and filters typically operating at frequencies of
400 MHz to 13 GHz [113]. For the future development of compact high performance
devices, ceramic resonators with high e (dielectric constants), high quality factors (Q)
(i.e. low dielectric loss), and near zero tem perature coefficient of resonant frequency
(rf) are required [114]. B a ^ ^ B ^ ^ O s with a complex perovskite structure (Fig.
4.1), where B' can be Zn or Mg and B” can be Ta or Nb, have attractive microwave
properties for these applications [115, 116].
Typically, high-e oxides contain ionic bonds between large atomic number and
thus polarizable metallic cations and oxygen, resulting in relatively large lattice con­
stants, non-directional ionic bonding, soft phonons and enhanced microwave loss.
Recent theoretical calculations indicate that the covalent nature of the directional d-
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60
(a)
V
b
So
(b)
Figure 4.1. Two crystal structures for B a ^ ^ B ^ ^ O r-s complex perovskites, where
B ' = Mg, Zn, Ni, or Cd, and B” = Ta or Nb. (a) disordered (cubic), (b) ordered
(hexagonal).
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61
electron bonding in the B a ^ ^ g B ^ j O s oxides plays an im portant role in producing
a more rigid lattice [117]. The authors of reference 5 suggest th at this is an essential
factor in achieving the inherently low intrinsic microwave loss of Ba(Zn1/3Ta2/3) 0 3
(BZT) and B a(C di/ 3Ta 2/3)0 3 (BCT) crystals th at also have a high e. In BCT, the
contribution of d-electron bonding is even stronger than in BZT. Liu et al. reported
single-phase BCT sintered at 1550 °C with ZnO as a sintering aid exhibited a dielectric
constant of 33 and loss tangent of smaller than 5 x l0 ~ 5 at 2 GHz [118].
Undoped BCT has a large positive Xf. One common approach to reduce the Xf
is to mixing a positive Xf dielectric material with a negative xf material. For example,
Ni doping into BZT is used in commercial BZT products to tune the tem perature
coefficient of resonant frequency to near zero [5] because Ba(N ii/3Ta2/3) 0 3 (BNT) has
a negative Xf. In this chapter we describe the effect of Ni doping on the structural,
optical and microwave dielectric properties of BCT ceramics.
4.2. E xperim ental
Undoped and Ni-doped (0.1, 0.5, 1, and 2 wt% Ni) BCT samples were synthe­
sized by conventional solid-state reaction. Reagent-grade oxide powders of B aC 03,
CdO, Ta 20 5 , and NiO were blended by using Z r0 2 ball milling media and distilled
water for 16 hours to deagglomerate the powder and provide a homogeneous mixture.
The powders were subsequently calcined at 1350 °C for 6 hours in air and then milled
again in an aqueous slurry with polyethylene glycol to reduce the particle size to
that which will facilitate densification during sintering. The resulting slurry was then
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62
dried and pressed to 60% of theoretical density and sintered at 1520 °C for 48 hours
in air.
The crystallographic structure of the samples was studied using X-ray diffrac­
tion (XRD) using a Rigaku D/MAX-IIB diffractometer operated at 50 kV and 30
mA with 1° divergence and scattering slits. 9 — 29 XRD scans were collected over
10 to 120° using a step size of 0.02°. Each step was measured for 5 seconds in or­
der to achieve adequate statistics. The XRD data was subsequently analyzed by the
Rietveld method (FullProf 2000, Version 3.20), in which the entire diffraction profile
is calculated for a given model and compared with the observed profile [119]. Cor­
rections to the model are made iteratively and subsequently compared using a least
squares fitting algorithm to the experimental results. The microwave quality factor
and tem perature coefficient of resonant frequency were measured using a TEm$ mode
of the dielectric resonator enclosed in an Au-coated cylindrical cavity. Absorption
measurements were performed at room tem perature with an Ocean Optics DS200
spectrometer in the visible spectra region. Absorption infrared spectra were collected
on a Bruker IFS 6 6 /VS Fourier transform spectrometer in the near-infrared range
(4000 - 14000 cm-1) utilizing a liquid nitrogen cooled MCT detector. The sample
was first cut with a diamond saw then subsequently polished to a thickness of 0.1 0.3 mm for absorption measurements.
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63
4.3. R esu lts and D iscussion
4.3.1. Structural P roperties
In undoped samples, evidence of small amounts of the BCT decomposition prod­
ucts, Ba 5Ta 40 i 5 and Ba 4Ta 20g, were observed in the XRD spectra. The absence of
these compounds in all Ni-doped BCT indicates th at Ni might stabilize the formation
of BCT in the conditions used for sintering.
o
o
o
xt
O*
m
S
■a
rg
O
:o
-o
— ^
10
24
38
52
20 (deg)
—
66
80
Figure 4.2. Rietveld analysis of X-ray diffraction spectra of 0.1 wt% Ni-doped
Ba(Cd 1/'3Ta 2/a)O 3 samples. The calculated Bragg peak positions and intensities of
ordered (hexagonal, “I”) and disordered (cubic, “II”) structures are derived using
Rietveld analysis and appear as lines. The difference between the measured data
(dots) and calculated (lines) is shown below. The crystallographic planes of hexago­
nal structure are given (Ref. [120]).
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64
In the XRD patterns, multiple peaks were found at the high angle diffraction
angles. It is well known th at B-site ordering occurs in B a ^ ^ E ^ ^ C h perovskites,
particularly in samples th a t have been annealed for a long time. Ordering in the
B' - B” lattice produces a distortion from the cubic lattice primarily along the (111)
direction which results in the formation of a hexagonal crystal structure [6]. Fitting of
the XRD data using Rietveld analysis method indicates th a t the sample is composed
of a mixture of ordered (hexagonal) and disordered (cubic) structures. As an example,
Figure 4.2 shows the measured (dots) and calculated (line) XRD patterns for the BCT
sample doped with 0.1 wt% Ni.
The calculated lattice parameters and percentages of hexagonal and cubic struc­
tures are summarized in Table 4.1. R q and G in the table, i?wp, and Rexp are the
Bragg R factor, Goodness of fitting, weighted pattern R factor, and expected weighted
pattern R factor, respectively, in Rietveld analysis as defined below.
R b = 100
£
l^obs
where 2/obs and yca\c are the observed and calculated intensities, /obs and Ica\c the
observed and calculated integrated intensities, A the number of statistically indepen­
dent observations, P the number of parameters refined and w the weights associated
with yobs. The standard deviation is not given for the undoped sample since the
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65
Cubic
Ni
a (A)
i?B
wt%
a (A)
-
5.87112(37) 7.24160(61) 15.7 70
3.60
5.86214(9) 7.23296(14) 2.5 93.91(55) 1.58
5.85769(12) 7.22498(18) 3.4 94.69(71) 1.54
(%)
0
0.1
-
-
Hexagonal
c (A)
R b wt%
(%)
6.09(18)
0.5
4.17492(16) 4.9
4.17099(22) 8.4
1.0
4.16969(57) 6.9
2.0
4.16739(107) 10.7 1.43(5)
5.31(23)
4.81(44)
5.84512(18) 7.20308(33) 4.7
5.84110(22) 7.19860(34) 7.3
95.19(74)
G
1.58
98.57(271) 0.66
Table 4.1. The lattice parameters of Ni-doped B a(C di/ 3Ta 2/ 3)03 samples for the
cubic and hexagonal structures inferred from the Rietveld analysis. The standard
deviation is not given for the undoped sample since the decomposition products were
determined using the profile matching with constant factor without atomic positions
(Ref. [120]).
decomposition products were determined using the profile matching with constant
factor without atomic positions. Table 4.1 shows th at the Ni-doped BCT samples
exhibit a small increase in the extent of ordering with increasing Ni concentration.
The i?B shows the quality of the agreement between observed and calculated profiles.
The larger RB and larger relative deviations of the wt% in minority cubic phase com­
pared to the majority hexagonal phase presumably reflect the larger uncertainty of
fitting the less intense peaks from the cubic phase. The general trend th at the lattice
parameters decreases with increasing Ni concentrations is expected and fits Vigard’s
law as shown in Fig. 4.3 since the ionic radius of Ni2+ is smaller th at that of Cd2+.
Recent ab initio calculations within the local density approximation (LDA) of
BCT and BZT predicted the space group of BCT is P321 [117], a little different from
the P 3m l space group of BZT [121, 122]. The main difference between these two
space groups in BCT is the distortion of the oxygen atoms th at lie between the Ta
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66
8
7
6 iT ▲
▼
w
<
u
N
•P<
ft
"3
U
A
▼
A
▼
5
4
♦ c
■a
— Linear (a)
— Linear (c)
3
2
1
0
0
l
1
0.5
1
1.5
Ni concentration (wt%)
Figure 4.3. Lattice parameters of Ni-doped Ba(Cdi/ 3Ta 2/ 3)03 as a function of Ni
concentration. For lattice constant at 100% we used a — 5.758 A and c — 7.052 A for
Ba(Ni1/3Ta2/ 3) 0 3 (ICDD card # 00-018-0181). The results clearly fit Vegards law.
Atom
B al
Ba2
x
1/3
0
y
2/3
0
z
0.6627(5)
0
Ta
Wyckoff
2d
la
2d
1/3
2/3
0.1707 (4)
Cd
la
3e
0
0
1/2
01
02
0
1/2
6i
0.1711(11)
0.8289(11)
0
0.3103(16)
Table 4.2. Atomic Wyckoff positions of Ba(C di/3Ta2/3) 0 3 in space group P3ml in­
ferred from Rietveld analysis (Ref. [120]).
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67
I 80deg
(a)
(b)
Figure 4.4. Ball and stick model of (a) B a(Zni/ 3Ta 2/ 3)03 and (b) Ba(Cdi/3Ta2/3) 0 3
(Ref. [118]).
and Cd found, resulting in the theoretically predicted Ta - O - Cd bond angle of 172°,
as shown in Fig. 4.4. From the analysis of the measured XRD data, it is not possible
to unambiguously determine which space group occurs, although the best fit is to the
P 3rnl space group. The atomic positions from fitting the XRD data as summarized
in Table 4.2 indicate th at the Ta - O - Cd bond angle is 173.1±0.3°, very close to the
previously reported prediction of 172° [117].
4.3.2. D ielectric P roperties
Figure 4.5 illustrates the BCT Q x f (quality factor times frequency) product as
a function of Ni doping concentration. The Q of undoped BCT is low. The structural
quality of the undoped BCT is not very high. In fact, the undoped sample has a
relative density of 78% indicating th at there is a great amount of open interconnected
porosity in the samples. In contrast, the Ni-doped samples all have similar relative
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68
35000
30000
3
0\mS
25000
x
O)
20000
15000
0
0.5
1
1.5
2
Ni concentration (wt% )
Figure 4.5. Dependence of Q x / on Ni doping concentrations in Ba(C di/ 3Ta 2/ 3)03
samples (Ref. [120]).
density of ~ 95% and structural quality. A theoretical density of 7.94 g/cm3 is used
in these determinations. The increase of density could be due to the enhanced atomic
diffusion in the Ni-doped BCT samples during sintering process. It is well appreciated
that porosity in ceramics often leads to a degradation of microwave properties [123,
124], The degradation is considered to be related to the appearance of a free surface
such as pore observed here th at leads to a relaxation of the crystal lattice [124]. This
might explain the low Q value of the undoped BCT. The Q value of Ni-doped BCT
increases with Ni doping up to 0.5 wt% but decreased abruptly when the Ni doping
concentration exceeds 1 wt%. Since the samples with higher Ni doping concentration
show even higher magnitude of B-site ordering, the change of Q in this case cannot
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69
85
75
e
45
0
0.5
1
1.5
2
Ni concentration (w t% )
Figure 4.6. The variation in the tem perature coefficient of resonant frequency as a
function of Ni doping concentrations (Ref. [120]).
be correlated with the extent of ordering. It should be pointed out th at the best
Q values of the BCT samples in this study are approximately one half of that for
commercially available BZT. We believe th at the low Q values may occur because
the synthesis process is not fully optimized. A maximum Q value has been found in
BCT samples sintered at a higher sintering tem perature [117]. We found some Cd
deficient regions in these samples using electron microprobe analysis, especially near
the external surface of the specimen. Thus, it appears th at there may be a chance
that the stoichiometry and the microwave properties might be significantly improved
through process optimization.
Figure 4.6 shows the T{ decreases constantly with Ni concentration up to 2 wt%.
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70
Since BNT has a negative Tf [5], the doping of Ni in BCT can compensate the large
positive value of Tf of BCT and thus reduce the Tf. Note th at the values are in the
range of 50 - 70 ppm/°C. Unfortunately, Ni-doping cannot be used to tune the Tf of
BCT to near zero, as can be done for BZT. Even if the quality factor of BCT could
be improved through process refinement, the large value of
Tf
will most likely make
this material of limited utility for commercial applications.
4.3.3. O ptical P roperties
As shown in Fig. 4.7, the absorption spectra of Ni doped BCT feature both
discrete peaks and varying levels of a continuous absorption background. Note th at
240
220
200
2%
o
V
o
U
s
•2
180
1
140
<
1%
160
0.1%
0.5%
120
1.3
1.8
2,3
2.8
3.3
Energy (eV)
Figure 4.7. Visible absorption spectra of Ba(Cd1y3Ta2/ 3)03 samples doped with vary­
ing concentrations of Ni (Ref. [120]).
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71
the discrete absorption peaks are absent in undoped BCT samples, clearly indicating
th at they are Ni related.
The discrete peaks in the spectra are similar to those
found in Ni-doped BCT, as well as other Ni-containing oxides and are associated
with forbidden internal transitions between the Ni d-states.
o
Ni (Cd, Ta)
Ba
Figure 4.8. Schematic demonstration of Ni ions surrounding by oxygen near neighbors
in an octahedral geometry when Ni is incorporated on Cd sites in BCT lattice.
Further evidence th a t the Ni is incorporated on the Cd sites comes from the
detailed ligand field analysis.
When Ni is incorporated on Cd sites in the BCT
lattice, it will be surrounded by oxygen nearest neighbors in an octahedral geometry,
as shown in Fig. 4.8. According to crystal field theory, the Ni d-orbitals are spitted
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72
by interaction with oxygen ligand ions located in an octahedral configuration. The
strength of this interaction, denoted by 10Dq, can be inferred from the absorption
spectra in the near infrared region [125]. This theory can be used to assign the
different absorption peaks in Fig. 4(a) to transitions from the 3T2 (F) Ni2+ ground
state to the 3r 4 (F ), 1T3(F), 1r 5(F), and 3r 4(P) excited states. As shown in Fig.
4.10, the measured 10Dq is 6990 cm-1 for 0.1 wt% Ni-doped BCT and 7400 cm-1 for
2 wt% Ni-doped BCT. The spectra features in Fig. 4.7 are similar to those observed
in Ni doped BZT [86], with the internal forbidden transition peaks between Ni2+ d
orbitals shifting to relatively higher energies due to a larger ligand field energy in
Ni-doped BZT, as shown in Fig. 4.9. This is consistent with expectation given that
the BCT lattice is larger than the BZT lattice.
A variation in appearance is found between the samples with the more heav­
ily doped samples being darker in color. Absorption spectra were studied to better
quantify this observation. The small amount of absorption from 1.9 eV to 2.3 eV
compared to other parts of the visible spectra results in the observed yellow color
for the Ni-doped BCT samples. The range in the shades of yellow exhibited by the
different samples is attributed to the varying levels of the continuous absorption back­
ground. This observed absorption background is similar to th at previously reported
in defective single crystal NiO and attributed to non-stoichiometry related point de­
fects in th at case [125]. We found a correlation existed between the increasing level of
absorption background and the decrease in the quality factor in Ni-doped BCT sam­
ples. This suggests th at the concentration of point defects can be directly correlated
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73
0
10 D q (Ligand Field Energy, eV)
0.25 0.50 0.75 1.00
1.25 1.50
1.75
2.0
S 1.5x10
2
'53
is
2
%
ts(d )
Ni2+in NiO
4
10
w
Ni2+in MgO
3
1.0
■
7Zfr;
• | 5x10
s
ta
A
e
1.5
■0.5
h0
0
-0.5
3
r3(D)
® -5x10
to
Ni in lightly-doped
Ba(ZnTa)03
Ni2+ (0.1-2%) in
Ba(CdTa)03
24.
'«
<U
S
Vi
h.
ta
w
2
3
u
CS
'W )
s-
ta
IS
2
Ni in heavily-doped
Ba(ZnTa)03
W
-
tg
Vi
2
.-w
M
U
o
■o
to
1.0
o
-1 .5
Ml
S.
<U
3
fed
5x10
10
10 D q (Ligand Field Energy, cm"l)
Figure 4.9. Results of crystal field analysis of the electronic energy of the Ni2+ orbitals
as a function of the strength of the ligand field, denoted lODg. Transition energies
and lODg values for aqueous solutions of nickelous salts are included as black dots.
lODg values for solids are also shown (Ref. [86]).
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74
i
*
7220 c m 1, 0.5% Ni
7400 c m 1, 2% Ni
220
£w
-M
c
<u
S 180
fa
<U
o
U
&
©
140
7290 cm , 1% Ni
6900 cm , 0.1% Ni
100
0.5
0.7
0.9
1.1
1.3
1.5
1.7
Energy (eV)
Figure 4.10. Near infrared absorption spectra of B a(C di/ 3Ta 2/ 3)03 samples doped
with varying concentrations of Ni (Ref. [120]).
with increased microwave loss.
4.4. Sum m ary
In summary, the structural, dielectric and optical properties of Ni-doped BCT
ceramics have been investigated. Rietveld analysis of the XRD data indicates that
the BCT structure is similar to other B a ^ ^ B ^ ^ O s perovskites, although the Ta 0 - Cd is distorted to an angle of ~ 173°; confirming our earlier theoretical prediction.
A small amount of Ni doping (above 0.1 wt%) is found to significantly enhance the
extent of Cd - Ta ordering in BCT. The XRD analysis also indicates th at Ni doping at
a concentration above 0.1 wt% is found to significantly enhance the extent of Cd - Ta
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75
ordering in BCT with ~ 95% of the sample being in the ordered hexagonal structure
and 5% in the cubic structure. The tem perature coefficient of resonant frequency is
found to decrease with Ni concentration up to 2 wt%. While the Q value of BCT
increases with a small Ni doping (up to 0.5 wt%), it decreases abruptly with further
Ni doping. The optical characterization indicates th a t the Q value change can be
directly correlated to the concentration of optically active point defects in BCT.
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CHAPTER 5
C O N C L U SIO N S A N D O UTLO O K
5.1. C onclusions
In this thesis, the effects of transition metal doping on two types of materials,
wide bandgap semiconductors for spin dependent electronics applications and oxide
dielectrics for microwave applications, have been investigated.
We have found th at MBE grown Cr-doped GaN exhibits ferromagnetism at over
900 K. The magnetic properties of Cr-doped GaN varied significantly as a function of
Cr concentration, with a maximum magnetic moment occurring at 3% Cr. Electrical
transport measurements of Cr-doped GaN revealed the conduction features the ther­
mally activated process following the exponential law, R = R0 exp[(7o/T)1//4], which
is characteristic of variable range hopping between localized states with a Coulomb
gap. We attribute the conduction in Cr-doped GaN to variable range hopping in
the Cr impurity bands. The transport measurements also inferred th at the carrier
concentration is similar in magnitude to the measured concentration of magnetically
active Cr. This fits well into the scenario that electrons at the partially filled Cr 12
level contribute to the hopping conduction. A large negative magnetoresistance was
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77
observed th at is attributable to the influence of the magnetic field on the quantum
interference between the paths linking two hopping sites. These results, along with
other extensive structural characterization, suggest th a t ferromagnetism in Cr-doped
GaN best fits the double exchange like mechanism as a result of hopping between
near-midgap substitutional Cr impurity band, and th a t Cr-doped GaN is appealing
for spintronic applications.
We have demonstrated th at the magnetic properties of Cr-doped GaN could be
manipulated through exchange bias. Exchange biasing effects were observed in sam­
ple structures of Cr-doped GaN thin films with an antiferromagnetic MnO overlayer,
which formed after an annealing process. The center of the magnetic hysteresis loop
shifts to negative magnetic field by ~ 70 Oe when measured after field cooling. En­
hancement of the coercive field of the Cr-doped GaN film is also found when compared
to single layer samples without MnO overlayer. The mechanism responsible for the
exchange bias is attributed to the exchange coupling at the ferromagnetic Cr-doped
GaN/ antiferromagnetic MnO interface. The observed exchange biasing indicates that
Cr-doped GaN has properties of a conventional ferromagnet and has potential use in
practical magnetoelectronic devices.
We have studied the effect of Ni-doping on the structural, dielectric and op­
tical properties of Ba(Cd 1/ 3Ta 2/ 3)03 (BCT) dielectrics.
Rietveld analysis of the
X-ray diffraction (XRD) d ata indicates th at the BCT structure is similar to other
Ba(B,1^3B2^3)0 3 perovskites, although the Ta-O-Cd is distorted to an angle of ~ 173°;
very close to the earlier theoretical prediction of 172°. The XRD analysis also in­
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78
dicates th at Ni doping significantly enhances the extent of Cd-Ta ordering in BCT,
from 70% for undoped BCT to over 90% for Ni-doped BCT. The undoped sample has
a relative density of 78% indicating th at there is a great amount of open intercon­
nected porosity in the samples. In contrast, all AT-doped samples all similar relative
density of ~ 95%.The tem perature coefficient of resonant frequency decreases with
Ni concentration up to 2 wt%. However, the value of
tj
is still too large, which most
likely make this material of limited utility for commercial applications. While the loss
tangent of BCT is reduced at small levels of Ni doping (up to 0.5 wt%), it increases
abruptly at higher concentrations. We found a correlation between the loss tangent
of Ni-doped BCT samples and the intensity of a continuous absorption background in
the optical spectra. This optical activity is similar to th a t found in defective NiO and
Ni-doped BZT, and can be attribute to the presence of optically active point defects.
This result suggests th at point defects play an im portant role in the microwave loss
in BCT dielectrics.
5.2. O utlook for Future W ork
While it has been presented in this thesis th at the ferromagnetism in Cr-doped
GaN best fits the double exchange mechanism, the experimentally observed Tq is
much higher than theoretical predictions. This means th at there is still much careful
experimental and theoretical work to be done to clarify the discrepancy. The major
point in the theory is th at the ferromagnetism should be tunable by means of Fermi
level engineering [68], for example, through secondary doping, which has not been
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79
explored in this thesis. Future work can focus on the co-doping of Si, a shallow donor,
or Mg, a shallow acceptor, in Cr-doped GaN to tune the Fermi level and see how
they are related to the ferromagnetism. Careful electrical transport characterization
should also be considered to see how the co-doping affects the dominant transport
mechanism.
Spin polarization in ferromagnetic materials is im portant for performance of
spintronic devices, thus it is im portant to investigate the spin dependent density of
states in Cr-doped GaN. While magnetic tunnel junctions (MTJ) is one possible way
and also im portant in device fulfillment perspective, the magnetoresistance of tunnel
junctions depends criticallly on the electronic states at the interface and the choice of
barrier layers, which makes the measured spin polarization is not exactly an intrinsic
property of the ferromagnetic material [126]. Instead, we can use superconducting
tunnel junctions, also called Tedrow-Meservey Method [127], incorporating a super­
conducting electrode and a Cr-doped GaN electrode to probe the spin polarization of
Cr-doped GaN.
The study of Ni-doped BCT presented in this thesis shows th at point defects
play an im portant role in microwave loss. However, the defect chemistry in BCT type
dielectrics in complex perovskite structure is largely unknown. Thus it is important to
propose a study to understand the defect chemistry in undoped samples. The densely
packed structure suggests th at there is a high probability of presence of Schottky type
point defects, which may be paramagnetic active due to unpaired electron spin, in
these materials [128]. Hence, we can use spin sensitive techniques, such as EPR and
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80
magnetic susceptibility to characterize these defects. This, along with optical and
microwave measurements, will facilitate the identification of the nature of various
point defects and understanding of their effects on the microwave properties.
It
is also possible to compare the measured magnetic susceptibility with theoretical
calculations, for example, in the case of covalent or ionic bonding, which can thus
experimentally verify if the B -0 bonds in B a ^ ^ B ^ ^ O a has a covalent nature as
predicted theoretically [117].
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APPENDIX A
LIST OF PUBLICATIONS DURING THE PHD STUDY
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95
Listed in the following are the publications reporting my research study towards
PhD degree. This thesis is based on part of them, which are referred to where is
applicable in the text.
REFERRED JOURNALS
1. H. X. Liu, S. J. Liu, V. Zenou, C. Beach, N. Newman, “Dielectric, structural
and optical properties of Ni-doped barium cadmium tantalate”, Jpn. J. Appl.
Phys. 45, 9140 (2006).
2. N. Newman, S. Y. Wu, H. X. Liu, J. Medvedeva, L. Gu, R. K. Singh, Z. G.
Yu, I. L. Krainsky, S. Krishnamurthy, D. J. Smith, A. J. Freeman, and M.
van Schilfgaarde, “Recent progress towards the development of ferromagnetic
nitride semiconductors for spintronic applications” , Phys. Stat. Sol. (a) 203,
2729 (2006).
3. H. X. Liu, S. Y. Wu, R. Singh, and N. Newman, “Exchange biasing of (Ga,Cr)N
thin films using a MnO overlayer”, J. Appl. Phys. 98, 046106 (2005).
4. R. Singh, S. Y. Wu, H. X. Liu, L. Gu, D. J. Smith, and N. Newman, “The Role
of Cr Substitution on the Ferromagnetic Properties of Cr-GaN” , Appl. Phys.
Lett. 86, 012504 (2005).
5. L. Gu, S. Y. Wu, H. X. Liu, R. Singh, N. Newman, and D. J. Smith, “Chemical
and Structural Characterizations of Cr-doped GaN” , J. Magn. Magn. Mater.
290-291, 1395 (2005).
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6. L. Yu, R. Singh, H. X. Liu, S. Y. Wu, J. M. Rowell, N. Newman, R. Hu, D.
Durand, and J. Bulman, “Fabrication of Niobium Titanium Nitride Thin Films
with High Superconducting Transition Temperatures and Short Penetration
Lengths” , IEEE Trans. Appl. Supercond. 15, 44 (2005).
7. H. X. Liu, S. Y. Wu, R. Singh, L. Gu, D. J. Smith, N. R. Dilley, L. Montes, M.
B. Simmonds, and N. Newman, “Observation of ferromagnetism above 900 K
in Cr-GaN and Cr-AIN” , Appl. Phys. Lett. 86, 4076 (2004).
8. S. Y. Wu, H. X. Liu, L. Gu, R. Singh, L. Budd, M. van Schilfgaarde, M. R.
McCartney, D. J. Smith, and N. Newman, “Synthesis, characterization, and
modeling of high quality ferromagnetic Cr-doped AIN thin films” , Appl. Phys.
Lett. 82, 3047 (2003).
CONFERENCE PROCEEDINGS
1. S. Y. Wu, H. X. Liu, L. Gu, R. Singh, M. van Schilfgaarde, D. J. Smith, N. R.
Dilley, L. Montes, M. B. Simmonds, and N. Newman, “Synthesis and charac­
terization of high quality ferromagnetic Cr-doped GaN and AIN thin films with
Curie tem peratures above 900 K” , in GaN and Related Materials, 2003, eds.
H.M. Ng, et al. V.798, Y10.57.
2. H. X. Liu, G. N. Ali, K. C. Palle, M. K. Mikhov, B. J. Skromme, Z. J. Reitmeyer, and R. F. Davis, “Evolution of subgrain boundaries in heteroepitaxial
GaN/AlN/6H-SiC grwon by MOCVD” , in GaN and Related Materials, 2002,
eds. E.T. Yu, et al. V.743, L6.3.
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97
3. K. C. Palle, L. Chen, H. X. Liu, B. J. Skromme, H. Yamane, M. Aoki, C. B.
Hoffman, and F. F. Disalvo, “Optical Characterization of Bulk GaN Grown
from a N a/G a Flux” , in GaN and Related Materials, 2002, eds. E.T. Yu, et al.
Vol. 743, L3.36.
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