Magnetotransport in cleaved-edge-overgrown Fe/GaAs

Magnetotransport in
Cleaved-Edge-Overgrown Fe/GaAs-based
and
Rare-Earth-Doped GaN-based
Heterostructures
Dissertation
zur Erlangung des Grades eines
Doktors der Naturwissenschaften
in der Fakultät für Physik und Astronomie
der Ruhr-Universität Bochum
vorgelegt von
Fang-Yuh Lo
geboren in Taipei, Taiwan
Lehrstuhl für Angewandte Festkörperphysik
2007
Der erste Gutachter: Prof. Dr. Andreas D. Wieck
Der zweite Gutachter: Prof. Dr. Daniel Hägele
Date of Disputation: 05.07.2007
1
Table of contents
Table of contents
1
List of abbreviations
3
List of symbols
5
1
Introduction
7
2
Theoretical background
11
2.1
Introduction to GaAs- and GaN-based heterostructures
11
2.2
Magnetism
14
2.2.1
Isolated atoms
14
2.2.2
Magnetism in materials
15
2.2.2.1
Exchange interactions
15
2.2.2.2
Molecular field theory and ab-initio calculations
16
2.2.2.3
Magnetic materials
18
2.3
Magnetotransport and electrical spin injection
20
2.3.1
Magnetoresistance in nonmagnetic materials
20
2.3.2
Magnetoresistance in ferromagnetic materials
22
2.3.3
Electrical spin injection
24
2.4
GaN-based diluted magnetic semiconductors
29
2.5
Focused ion beam
32
2.5.1
Focused ion beam system
33
2.5.1.1
Liquid metal ion source
33
2.5.1.2
Focused ion beam column
34
2.5.2
Focused ion beam milling
36
2.5.2.1
sputtering
36
2.5.2.2
Redeposition
37
2.5.2.3
Implantation and amorphization
38
2
3
4
Magnetotransport in cleaved-edge-overgrown Fe/GaAs-based heterostructures
39
3.1
Cleaved-edge overgrowth
39
3.1.1
Properties of the interface and the metal thin films
41
3.1.2
Properties of the metal-semiconductor contacts
42
3.2
Focused ion beam milling
44
3.3
Electrical properties and magnetoresistances of the spin valves
48
3.3.1
Electrical properties of the spin valves
48
3.3.2
Magnetoresistances of the spin valves
49
3.4
Longitudinal magnetoresistances of the electrodes
52
3.5
Summary and Discussion
54
Magnetic properties in rare-earth elements doped GaN and its heterostructures
56
4.1
Gd-doped zinc-blende GaN with focused ion beam
57
4.2
Eu-doped wurtzite GaN with focused ion beam
62
4.3
Magnetotransport in Gd-implanted GaN-based heterostructures
64
4.3.1
I-V characteristics after Gd implantation
65
4.3.2
Magnetotransport in Gd-implanted GaN-based HEMT structures
66
4.3.2.1
Hall effect
67
4.3.2.2
Magnetoresistances of van der Pauw structures
69
4.3.2.3
Magnetoresistances of transmission line structures
70
4.4
5
Summary
Summary and outlook
5.1
5.2
72
73
Magnetotransport in cleaved-edge-overgrown Fe/GaAs-based
heterostructures
73
Magnetotransport in rare-earth-doped GaN-based heterostructures
74
References
77
Acknowledgement
84
Curriculum Vitae
86
List of publications
87
3
List of abbreviations
2DEG
two-dimensional electron gas
3DEG
three-dimensional electron gas
AFM
atomic force microscope
AlGaAs
AlxGa1-xAs
AlGaN
AlxGa1-xN
AMR
anisotropic magnetoresistance
CBM
conduction band minimum
CEO
cleaved-edge overgrowth
CPP-GMR
the current perpendicular to the plane giant magnetoresistance
DOS
density of states
DMS
diluted magnetic semiconductor
F
ferromagnet/ferromagnetic region
FC
field cooled
FET
field-effect transistor
FIB
focused ion beam
GMR
giant magnetoresistance
HB
Hall-bar
HCl
salt acid
HEMT
high electron mobility transistor
InGaAs
InxGa1-xAs
hh
heavy hole
LEED
low-energy electron diffraction
lh
light hole
LMIS
liquid metal ion source
LDA
local density approximation
LSDA
local spin density approximation
MOCVD
metal-organic chemical vapor deposition
MOKE
magneto-optical Kerr effect
4
MBE
molecular beam epitaxy
MR
magnetoresistance
MRAM
magnetoresistive random access memory
MTJ
magnetic tunnel junction
N
nonmagnet/nonmagnetic region
PL
photoluminescence
RE
rare-earth (elements)
RKKY interaction
Ruderman-Kittel-Kasuya-Yoshida interaction
RT
room temperature
SEM
scanning electron microscope (microscopy)
SFET
spin-FET, spin field-effect transistor
SIC-LSDA
self-interaction corrected local spin density approximation
so
split-off hole
SRIM
stopping and range of ions in matter
SQUID
superconducting quantum interference device
TE
total energy
TM
transition metal
TML
transmission line
TMR
tunneling magnetoresistance
TR
temperature-dependent remanent
UHV
ultra-high vacuum
VBM
valence band maximum
vdP
van der Pauw (geometry or structure)
WZ
wurtzite
XRD
X-ray diffraction
ZB
zinc-blende
ZFC
zero-field cooled
5
List of symbols
In this work, the symbols for vectors are written in bold face.
a
area
B
magnetic field, magnetic induction
D
diffusion constant
D(E)
density of states
d
thickness
E
Energy
e
electron charge
F, F
force
g
g-factor
H
magnetic field
Ĥ
Hamiltonian
h
Planck constant
ħ
reduced Planck constant
I, I
electric current
I±
light intensity for left (+) and right (–) circularly polarized light, respectively
J, J
total angular momentum
j
current density
kB
Boltzmann constant
L, L
total orbital angular momentum
M, M
magnetization
m
magnetic moment
m
mass
N
number of charge carriers
n
density
nxD, nxD
x-dimensional carrier density
P
spin polarization
p
momentum
6
q
charge
R
resistance
r
position
r
resistance
S, S
total spin angular momentum
T
temperature
V
voltage
v, v
velocity
w
width
X
a certain physical quantity
Y
sputtering yield
Z
atomic number
γ
gyromagnetic ratio

electric field

permitivity (dielectric constant)
μ0
permeability in vacuum
μB
Bohr magneton
μ
electro-chemical potential
ρ
resistivity
σ
conductivity
σ±
left (+) and right (–) circularly polarized light, respectively
τ
relaxation time

electrical potential
χ
susceptibility
ω
(angular) frequency
7
1 Introduction
Spintronics is an exciting and up and coming field in both scientific researches and the applications and aims ambitiously at combining the spin and the charge characteristics of a charge carrier to
create novel devices or to provide the existing devices new functionalities. An operating spintronic
device requires efficient injection of nonequilibrium spins into a device and manipulation of the injected spin polarization at given locations.
Electrical spin injection from ferromagnetic metals into paramagnetic metals was first observed
by M. Johnson and R. H. Silsbee [1]. Such spin injection was proved to be efficient, and it led to the
discovery of famous effects, such as giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR). Spintronics exploiting GMR and/or TMR can be called metal-based spintronics or
magnetoelectronics [2, 3]. Unfortunately, spin injection from ferromagnetic metals into semiconductors are not as highly efficient as from ferromagnetic metals into paramagnetic metals, and the
modern trends in semiconductor spintronics are based on employing spin-orbit coupling to achieve
efficient spin injection and the manipulation of injected spins [4]. Generally, spintronics is interdisciplinary and integrates spins (magnetizations) with modern micro-, nano-, and opto-electronics,
and people working on it may meet some of the following fields of physics: magnetism, semiconductor physics, mesoscopic physics, optics, and superconductivity.
Historically, the observations of the magnetoresistances (MRs) date back to the 19th century.
Lord Kelvin, then William Thomson, was the first to measure the anisotropic magnetoresistance
(AMR) in 1856 [5], and the Hall effect was discovered by E. C. Hall in 1879. The magnetic tunnel
junction (MTJ), or TMR, was discovered by M. Jullieré in 1975 [6], and GMR was observed independently by two different groups in 1988 [7, 8]. Dieny et al. fabricated a spin-valve structure based
on GMR effect [9], and this was later applied in the industry to make magnetoresistive read/write
heads and the new type of nonvolatile memory, the magnetoresistive randon access memory
(MRAM). The read/write heads and the MRAMs are, to the author's knowledge, the only commercially available spintronic devices.
8
Semiconductor spintronics attracted great interest since S. Datta and B. Das proposed the prototype of a spin field-effect transistor (Spin-FET or SFET) by using Fe for the source and drain contacts
on an InAs-based field-effect transistor (FET) in 1990 [10]. In this Spin-FET the spins of the electrons flowing from source to drain can be controlled by the gate voltage. The first GaAs-based diluted magnetic semiconductor (DMS) was fabricated by Ohno et al. in 1996 by introducing Mn into
GaAs [11], and this achievement opened up new possibilities to study spin-related properties and
phenomena in semiconductors and to create new spintronic devices.
The theory of electrical spin injection was first developed by A. G. Aronov and G. E. Pikus in
1976 [12]. Later on, it was expanded separately by, just to name a few, E. I. Rashba, A. Fert and
H. Jaffrès, and others. Due to the conductivity mismatch [13] and spin-related properties of the metal-semiconductor contact and the spin relaxation in semiconductors, the electrical spin injection
from ferromagnetic metals into semiconductors has until now only successfully observed via optical
methods [14 – 17].
Table 1.1 Historical events of spin electronics
Year
1856
Event
First observation of the anisotropic magnetoresistance, AMR
Contributor
Lord Kelvin
1879
Discovery of the Hall effect
E. C. Hall
1921
Discovery of (atomic) spins
O. Stern and W. Gerlach
1975
1976
First observation of the tunneling magnetoresistance, TMR
First theoretical work on electrical spin injection
1985
First observation of electrical spin injection
1988
Discovery of the giant magnetoresistance, GMR
1990
M. Jullieré
Source
[5]
[6]
A. G. Aronov and G. E. Pikus [12]
M. Johnson and R. H. Silsbee [1]
M. N. Baibich et al.
[7]
G. Binasch et al.
[8]
Proposal of the spin field-effect transistor
S. Datta and B. Das
[10]
1995
First hot-electron spin transistor
D. J. Monsma et al.
[18]
1996
First appearance of the name, spintronics
S. A. Wolf
[3]1
Freescale Semiconductor
[19]
End of
1990s
2005
Commercial magnetoresistive read/write head
First commercial magnetoresistive random access memory, MRAM
1 Cited from footnote Nr.2 on page 324.
9
In order to manipulate the spin in a given material, the knowledge of the spin-polarized transport
and the spin relaxation in materials is required. The two-resistor model suggested by N. F. Mott in
1963 provided us a basis to understand the spin-polarized transport [20]. The theoretical [21 – 27]
and the experimental [28 – 31] studies of spin relaxation and spin decoherence help us to not only
understand the mechanisms of spin relaxation and decoherence in materials but also design the possible devices in spintronics. Most recently, spin noise spectroscopy was applied to study spin dynamics without disturbing the spins in the material [32]. Some important historical events are listed in
Table 1.1.
The first part of this work focuses on the electrical observation of spin injection from iron (Fe)
thin films into GaAs-based heterostructures. The study was carried out in a cleaved-edge-overgrowth (CEO) geometry. Because of the shape anisotropy of Fe, the CEO geometry has the advantage in
that the magnetic easy axis of Fe thin films lays along the growth direction of the heterostuctures,
where the electrons have clear spin splitting. The other advantage of this geometry is the uncontaminated interface between iron and the heterostructures, which avoids the undesired scattering from
impurities. Spin valve structures were fabricated with focused ion beam (FIB) on the cleaved-edgeovergrown Fe thin films, and the magnetoresistances (MRs) of the spin valves were investigated.
The second part of this work covers the studies on GaN-based DMS. GaN doped with Mn was
theoretically predicted [33, 34] and experimentally observed [35 – 37] to be ferromagnetic above
room temperature (RT). Incorporation of rare-earth (RE) elements could possibly make GaN ferromagnetic due to the strong atomic magnetic moment of the RE elements. In this work, GaN thin
films were implanted with rare-earth (RE) elements in order to fabricate GaN-based DMS, and their
magnetic properties were studied. Since Gd-implanted wurtzite (WZ) GaN is known to be ferromagnetic above 300 K [38, 39], Gd was implanted into WZ GaN-based heterostructures for the study
on the magnetotransport.
In this thesis, Chapter 2 provides brief reviews of the necessary background knowledge on GaAsand GaN-based heterostructures, magnetism, magnetoresistances in material, electrical spin injection, GaN-based DMS, and the focused ion beam. In Chapter 3, the properties of the Fe thin films
overgrown on the cleaved edge of GaAs-based heterostructures are investigated. The MRs across
the spin valves, of the Fe contact, and due to the external field are measured, respectively, and discussed. The magnetic properties of RE-FIB-implanted GaN thin films are investigated in Chapter 4,
and some discussion about the possible mechanism in yielding the RT ferromagnetism in highly
10
resistive WZ GaN. WZ GaN-based heterostructures were FIB-implanted with Gd, and the transport
properties in magnetic field are examined. At the end, Chapter 5 offers the summary and the outlook of the works in this thesis.
11
2 Theoretical Background
In this chapter, the underlying background knowledge to this work will be discussed. The discussion begins with a brief description of the GaAs- and GaN-based heterostructures, which is followed by the discussions of magnetism, the magnetotransport and the theory of spin injection, the diluted magnetic semiconductors, and finally, the focused ion beam.
2.1 Introduction to GaAs- and GaN-based heterostructures
Semiconductor heterostructures are semiconductors composed of different materials, e.g., AlAs,
GaAs, InAs, or their alloys [40]. Because the components of the heterostructures have different
band gaps, the band profile of a heterostructure looks totally different from each component. This
offers the opportunity to manipulate the behavior of electrons and holes through band engineering.
Therefore, it is possible to tune the device properties for specific applications. The best heterostructures are the layer structures fabricated by molecular beam epitaxy (MBE) or by metal-organic chemical vapor deposition (MOCVD). These structures are epitaxial and have highly abrupt interface
between any two adjacent layers.
The conduction electrons or holes in semiconductor devices are introduced by doping. Usually,
the dopant atoms are incorporated into the regions, where the electrical current is directed to flow
across the device. After the charge carriers are released from the the dopants, what remains is the
ionized dopant atoms. This in turn induces the scattering between the carrier and the ionized impurities, and thus, reduces both the carrier mobility and the device performance. The other method is
modulation doping, where the dopants are introduced in one region but the carrier subsequently migrate to another. For example, an n-type Si-doped Al0.35Ga0.65As is grown on a undoped GaAs
layers, and since the GaAs has the lower conduction band edge, the charge carrier will travel into
GaAs. There, the carriers lose energy, becomes trapped, and form a two-dimensional electron gas
12
(2DEG) at the AlGaAs-GaAs interface. Fig. 2.1 shows the idea of modulation doping schematically.
(a)
(b)
Fig. 2.1 Schematic depiction of the conduction band around a heterojunction between n-AlGaAs and undoped GaAs,
noted as i-GaAs, (a) before and (b) after the charge migration.
An alternative doping technique is called δ-doping, where a large amount of the dopant atoms
(but still small enough not to form a monolayer) are deposited on the semiconductor layer during a
very short growth interruption period instead of the entire growth period. In this case, the dopant
atoms are distributed in one or two semiconductor monolayers, resulting in a very high doping concentration.
Among the semiconductor heterostructures, the AlAs/GaAs-system is lattice-matched. Such a
system has the following advantages: (i) Due to no change in the lattice constant when a layer is
grown on to another, there is no change in the physical properties of each component in a heterostructure. The physical properties of the heterostructure can be directly derived from each component. (ii) There are fewer technical challenges for the fabrication. As mentioned above, the latticematched semiconductor heterostructures have generated great interest in physics and applications.
However for certain applications, for example the InxGa1-xAs (InGaAs) in fiber optics communications and GaN for the blue laser diode [41], the lattice-mismatched materials are needed. The latticemismatched systems such as InAs/GaAs-, Si/Ge-, and AlN/GaN-heterostructures, are of great importance as well. The lattice mismatch will introduce strain into the heterostructures, and therefore,
it induces changes in further the band offset and the effective masses in these structures. This in turn
broadens the available materials for our desired electronic and optoelectronic applications. The
epitaxial strained heterostructures are also called pseudomorphic heterostructures.
For a high electron mobility transistor (HEMT) structure consisting of GaN, AlN, and their al-
13
loys, the 2DEG is formed at the interface between AlxGa1-xN (AlGaN) and GaN even without doping. This is because of the autodoping effect: the nitrogen vacancies are usually formed during the
GaN film growth, and the nitrogen vacancies are calculated [42, 43] and found [44] to be shallow
donor. Additional contribution to the carrier density of the 2DEG is the piezoelectric effect and the
spontaneous electric polarization in those materials [45]. The spontaneous electric polarization arises from the strong electron affinity of the N atom and the local tetrahedral arrangement of the Ga
(or Al) and N atoms. However the autodoping has two big disadvantages: (i) It makes the p-type
doping in GaN films difficult, and (ii) there is a bulk conducting channel parallel to the 2DEG in the
GaN-based HEMT structures. The properties of 2DEG dominate only at low temperatures where
the carriers in the bulk channel are frozen out [45].
(a)
(c)
(d)
(b)
Fig. 2.2 Room temperature conduction (red) and valence (blue) band edge profiles of (a) a δ-doped HEMT structure
and (b) a bulk n-GaAs. (c) and (d) are the conduction band edges from (a) and (b), respectively. The zero
energy represents the Fermi level. The intrinsic GaAs layers are in green; the intrinsic AlAs layers are in yellow; the intrinsic Al0.35Ga0.65As are in dark purple; the light blue lines represents the Si δ-doping, and the nGaAs are in bright purple.
14
The conduction and valence band edge profiles of a heterostructure can be calculated by solving
the Poisson equation. Fig. 2.2 shows the profiles of the band edge profiles from two of the heterostructures applied in this work: a δ-doped HEMT and an n-GaAs (n3D = 1 × 1017 cm-3). The calculations were carried out with a 1DPoisson program written by Prof. Gregory Snider at the University of Notre Dame, USA [46].
2.2 Magnetism
The effect of magnets have been known to human beings for several thousand years, but its microscopic origin was not understood until the observation of current-induced magnetic field by
H. C. Øersted in 1821 and the discovery of the atomic spin by O. Stern and W. Gerlach a century later. An electrical current, or a moving charged particle, behaves like a magnetic dipole and induces
a magnetic field perpendicular to the current or the motion. This magnetic field (or magnetic induction), B, is described by the Biot-Savart law,
B=
0 d I ×r
0 ∫ dq v×r 
,
=
∫
3
3
4
4
r
r
(2.1)
where μ0 is the permeability in vacuum, I is the current, r is the position, and v is the velocity of the
charged particle. Note that the induced magnetic filed is related to the angular momentum of the
charged particle with the (v × r)-term. The magnetic (dipole) moment, m, is then written as,
m = I∫ d a ,
(2.2)
where a is the vector area of the current.
2.2.1 Isolated atoms
On the atomic scale, the magnetic moment of an atom is related to the total angular momentum,
J, of the atom, mainly of the electrons, and written as
m =  J =  L  S ,
(2.3)
where γ is the gyromagnetic ratio of the atom, L and S are the total orbital and spin angular momenta of the electrons, respectively. Based on minimizing the energy, the magnetic moment of an atom
can be estimated by the Hund's rule:
15
1) To arrange the wavefunctions to maximize the total spin, S,
2) then, to maximize to total angular momentum, L, for the wave functions given by 1),
3) finally, the total angular momentum, J, is found to be |L-S| if the shell is less than half-filled,
and |L+S| if the shell is more than half-filled, respectively.
The energy of an atom with the atomic number, Z, in a magnetic field can be calculated from the
Hamiltonian, Ĥ,
2
e
 B×r i 2 ,
H = H 0   B  L g S⋅B 
∑
8me i
(2.4)
2
Z
eℏ
pi

 V i  is the original Hamiltonian,  B =
where H 0 = ∑ 
is the Bohr magneton, V is
2m
e
i = 1 2me
the electrical potential, and g is the g-factor, which is 2 for free electron. The second term is called
the paramagnetic term and the third is the diamagnetic term. The paramagnetic elements, like Mg,
Al, V, Cr, etc., have the dominating second term while the diamagnetic elements, like Cu, Zn, Si,
Ge, etc., have the dominating third term.
2.2.2 Magnetism in materials
2.2.2.1 Exchange interactions
Most materials do not exist in atomic form, but in molecules or in „crystal“, and the electrons of a
single atom interact with those of the neighboring atoms. There are the magnetic dipole interaction
and exchange interactions, and the latter is nothing more than the electrostatic interaction, arising
because charges of the same sign cost energy when they are close together and save energy when
they are apart. The frequently mentioned exchange interactions are (direct) exchange, double exchange, superexchange, and the RKKY interaction (named after the first letter of the surname of its
discoverer: Ruderman, Kittel, Kasuya, and Yosida; also called itinerant exchange). The latter three
are all indirect and „long-range“ exchange interactions.
The (direct) exchange is the mechanism that the electrons of the neighboring atoms interact with
each other through the overlap of their orbitals, which has a very weak effect. If the magnetic ions
in the crystal have two different charged states, or valencies, the coupling between these two states
16
by virtually hoping of the „extra“ electron through valence p-orbitals is called the double exchange.
The superexchange correlates the magnetic ions due to the exchange interaction between each of the
two ions and the valence p-orbitals. The RKKY interaction is the exchange interaction between the
magnetic ions through free charge carriers, which extends to a rather long range.
2.2.2.2 Molecular field theory and ab-initio calculations
Since exchange interaction is electrostatic interaction, it is possible to understand the magnetism
in crystals by introducing an effective magnetic field into the electronic band structure and separating the response of spin-up and spin-down electrons. This is the molecular field theory, which assumes that all spins are subjected to an identical average exchange field, λM, produced by all their
neighbors, where M is the magnetization defined as the magnetic moment per unit volume of an
material. The resulting magnetization of this molecular field will in turn be responsible for the molecular field. Such a positive feedback can, under the Stoner criterion, lead to spontaneous ferromagnetism.
Suppose in the absence of an external magnetic field, some spin-down electrons are changed into
spin-up (shown in Fig. 2.3), and the electrons have ±δE from the Fermi energy, EF. Then the numbers of the spin-up (spin-down) electrons and the total energy difference, ΔEDOS, are therefore
N =
1
N  D E F  E ,
2
(2.5)
N =
1
N − D E F  E ,
2
(2.6)
and
 E DOS = 2 D E F   E2 ,
(2.7)
where N is the total number of the electrons, and D(EF) is the density of states (DOS) at Fermi level.
The magnetization due to the unequal numbers of both spins is then
M =  B  N  − N   = 2  B D  E F  E
(2.8)
by assuming an electron has the magnetic moment 1 μB, and the energy reduction, ΔEMB, from the
molecular field is
M
1
 E MB = − ∫  0  M '  dM ' = − 0  M 2 = −20 2B  D E F  E 2 .
2
0
2
Writing U = 0  B  , the total energy, ΔE, is
(2.9)
17
2
 E =  E DOS   E MB = 2 D E F   E  1 − U D  E F  .
(2.10)
When ΔE < 0, i.e., U D(EF) ≥ 1, spontaneous ferromagnetism is possible, and this is the aforementioned Stoner criterion.
Fig. 2.3 Spin-resolved density of states for a ferromagnet. If
some spin-down electrons are changed into spin-up,
the spin-up electrons have higher energy than the
Fermi energy and the spin-down electrons have
lower energy. The energy difference from the Fermi
level is ±δE.
It is also possible to study the magnetism by first-principle ab-initio electronic band structure calculations. Different from the discussion of the molecular field theory, where only the free electron
model was considered, the real system for such calculation is more complicated. In a crystal, the interactions between electrons and the effect of exchange interactions on the motion of the electrons
correlate all particles and can not be neglected. This leads to difficulty, and a useful and successful
approach to do the calculation is the density functional theory2.
In the density functional theory, the ground state energy of a many-electron system is written as a
functional of the electron density, n(r), and the functional has three contributions, a kinetic energy,
a Coulomb energy due to the electrostatic interactions between the charged particles in the system,
and a term called the exchange-correlation energy that captures all the many-body interactions.
Even though, certain approximation is still needed because the exchange-correlation energy is not
know in detail. One approach is to use the known results of many-electron interactions in a homogeneous electron gas for n(r), integrate the contributions over space and then sum up all the three
terms, which is called the local density approximation (LDA). For the magnetic systems, where the
2 A function maps a number to another number, and a functional maps a function to a number. For exam1
ple, a function, f(x) = 1 -x2, maps 1 to 0, and a functional, F [ f  x] =
∫ f x
−1
f(x) = 1 -x2, to 4/3.
, maps the function,
18
electron and the spin densities are taken into consideration, the spin density functional theory together with the local spin density approximation (LSDA) are applied [47]. Fig. 2.4 shows the spinresolved DOS of Cu, Co, and Fe from the ab-initio calculation [48].
Fig. 2.4 Spin-resolved density of states of copper, cobalt, and iron, where up and dn denote the up- and down-spins, respectively. The dash lines mark the position of the Fermi level [48].
2.2.2.3 Magnetic materials
Although in daily life, magnetic materials mainly refer to ferromagnetic materials while the
others are called non-magnetic, all materials are categorized, according to their response in magnetic field, to be paramagnetic, diamagnetic, ferromagnetic, anti-ferromagnetic, and ferrimagnetic. In
this section, the paramagnetic and ferromagnetic behaviors will be briefly discussed.
The magnetic moment of the paramagnetic materials will align along the same direction as that of
the external field. The magnetization loop has a positive linear response for small magnetic field,
19
and then it will slowly become saturated because all the magnetic moments in the material are aligned by the external field. When the magnetic field decreases, the magnetization decreases accordingly. The overall paramagnetic behavior can be semi-classically described by the Langevin function. The saturated magnetization decreases rapidly as the temperature increases, and the susceptibility, χ, obeys the Curie's law, χ = Cc / T, where χ is given by
M = H ,
(2.11)
and H is also called the magnetic field,
B = 0  H  M  = 0 1   H .
(2.12)
Fig. 2.5 shows the field(a) and temperature(b) dependences of a paramagnetic material described by
Langevin function.
(a)
(b)
Fig. 2.5 (a) Magnetic field and (b) temperature dependence of the magnetization of a paramagnet according to the Langevin function.
The ferromagnetic materials have spontaneous magnetization in the absence external magnetic
field. When an external magnetic field is applied, the magnetization increases as the field increases
until the saturation value, Ms, is reached. When the magnetic field decreases from the saturation
field to zero, the magnetization reduces rather slightly to the remanent magnetization, Mr. When the
magnetic field decreases further, or say increases in the opposite direction, the magnetization becomes zero at the coercive field, Hc. This is the hysteresis loop of ferromagnetic materials. The saturated magnetization decreases slightly as the temperature increases until the temperature reaches the
neighborhood of the Curie temperature, Tc, Ms decreases rapidly and vanishes at Tc. The susceptibility of a ferromagnet is orders of magnitudes larger that of a paramagnet, and it obeys the CurieWeiss law, χ = C / (T -Tc). At temperature beyond Tc, ferromagnetic materials behave as the same
as paramagnetic ones. Fig. 2.6 shows the hysteresis loop(a) and the temperature dependence of
Ms(b).
20
(a)
(b)
Mr
Hc
Fig. 2.6 (a) The hysteresis loop and (b) the temperature dependence of the magnetization of a ferromagnet. The curve
from zero magnetization at zero field to the saturated magnetization at high field is called the virgin curve of a
ferromagnet.
If there are ferromagnetic impurities distributed in a nonmagnetic material and the impurity concentration is low, where the exchange interactions between any two ferromagnetic particles can be
neglected, the material behaves like a paramagnet, and the ferromagnetic impurities are called the
paramagnetic centers. The independent magnetic moment in this system is no longer the atomic magnetic moments of the impurity but large groups of moments, each group inside a ferromagnetic
particle and therefore, the system is called a superparamagnet. Because the moments of the groups
are able to fluctuate rapidly at high temperature, in addition to the paramagnetic temperature dependence, the total magnetic moment will decrease or vanish „suddenly“ at a certain temperature for a
certain measurement technique. This temperature is called the blocking temperature.
2.3 Magnetotransport and electrical spin injection
2.3.1 Magnetoresistance in nonmagnetic materials
As depicted in Fig. 2.7, a current, Ix, flowing in a nonmagnetic material subjected to a transverse
magnetic field, Bz, and the charge carriers experience the Lorentz force, FL,
F L = qv× B z  ,
(2.13)
21
and gain additional momentum along the y-direction. This induces a potential difference, Vy, along
the y-direction, and this additional momentum in turn induces another additional momentum along
the x-direction. The latter will induce an increase in the resistance – called the positive magnetoresistance (MR) effect, and the former is the well-known Hall effect, where Vy can be easily calculated
by balancing the Lorentz force and the induced electrostatic field in y-direction,
Vy=
I x Bz
I B
= x z ,
n3D e d
n2D e
(2.14)
where n3D and n2D are the three- and two-dimensional charge concentrations, respectively, and d is
the thickness of the sample.
Fig. 2.7 Schematic sketch of the Hall effect along a long,
thin bar of conducting material. The current Ix
flows in the x-direction, the magnetic field B
points along the z-direction – denoted as Bz in the
text, and the Vy = VH. This figure is adopted from
Ix
the National Institute of Standards and Technology, USA [49].
Analyzing the phenomenon by the equation of motion with the effective mass, m*, and relaxation
time, τm , approach [50],
∗
m 
dv v
  = q    v× B z  ,
dt m
(2.15)
the current densities, for electrons, along x- and y-directions are given by
j x = −n3D e v x =
0
2
2
1c m
 x =  xx  x
,
(2.16)
 x =  yx  x
,
(2.17)
and
j y = −n 3D e v y =
 0 c m
2
2
1c m
where σ0 is the conductivity in zerot magnetic field,
0 =
n3D e 2 m
m∗
,
and ωc is the cyclotron frequency,
(2.18)
22
c =
e Bz
m
.
∗
(2.19)
In terms of resistivity, the results are
2
2
2
1c m
e2  m 2
1
 xx =
=
= 0 1  ∗2 B z  ,
 xx
0
m
(2.20)
and the magnetoresistance (MR) is written as
2
2
  R B − R0  e m 2
MR =
=
= ∗2 B z ,

R0
m
(2.21)
where ρ0 = 1 / σ0, is the resistivity without magnetic field, and the MR ratio is defined as
2
MR =
2
  R B − R0  e m 2
=
= ∗2 B z ,

R0
m
(2.22)
which is proportional to Bz2. The Hall resistivity, ρH, is given by
 H =  yx =
y
jx
=−
 
1
1
B .
= − c m = − 0 c m = −
 xy
0
n 3D e z
(2.23)
2.3.2 Magnetoresistance in ferromagnetic materials
For ferromagnetic materials, the magnetoresistances have additional features due to their spontaneous magnetization. These are the well-known anomalous Hall effect and the anisotropic magnetoresistance (AMR) effect.
The discussion of the anomalous Hall effect can be treated qualitatively by substituting Bz with
μ0 ( Hz + Mz ) into equation 2.23,
H = −
1
n3D e
Bz =−
1
n 3D e
0 H z  M z  = −
1
n3D e
B z , ext −
0
n3D e
Mz .
(2.24)
The first term is the ordinary Hall effect and the second term is the anomalous Hall effect. Fig. 2.8
shows the Hall resistivity in a ferromagnet, and there is a change in slope of the curve at a magnetic
field, Bs – the saturation field. When the external magnetic field, Bz, is smaller than the saturation
field, the second term is the dominating effect. After Bz reaches the saturation field, the second term
stays constant, the major effect is the ordinary Hall effect. Certainly, the second term is never that
straightforward because possible spin-dependent scattering processes are involved, and so that the
Hall resistivity is written empirically as
 H = R o B  0 R a M ,
(2.25)
23
where Ro is the ordinary Hall coefficient, which gives us the information about carrier density, and
Ra is the anomalous Hall coefficient, which is strongly temperature-dependent.
Fig. 2.8 Schematic depiction of the Hall resistivity in
a ferromagnet.
The AMR is the effect that MR of a ferromagnet depends on the direction of the electric current
with respect to the orientation of its magnetization, which can be changed by applying an external
magnetic field. It was first discovered in 1856 by Lord Kelvin when he measured the resistance of
an iron sample – he found a +0.2% MR when a longitudinal magnetic field was applied and a -0.4%
MR when a transverse magnetic field was applied [5, 47]. The value of MR can be either positive or
negative before the magnetization is saturated.
Assuming the spontaneous magnetization of a ferromagnet has the preference to aligned along
the x-direction, which is called the easy axis of the ferromagnet. The transverse MR – shown in
Fig. 2.9 – represents ρxx in Bz, and the longitudinal MR represents ρxx in Bx [51]. Qualitatively, a
transverse magnetic field rotates the magnetization of a ferromagnet about the easy axis, and therefore from zero field to the transversal saturation field, the magnetization of the ferromagnet becomes aligned as the magnetic field increases. This leads to a decrease in the resistance, for the spindependent scattering decreases accordingly in this range. For the magnetic field higher than the
transversal saturation field, the influence of the magnetic field in a bulk-like ferromagnet is the
same as in a nonmagnet, and the resistance increases following the positive B2-dependence as the
field increases. For a very thin film, whose thickness is smaller or comparable to the mean free path
of the charge carriers, only negative MR is observed above the saturation field.
24
(a)
(b)
Fig. 2.9 Magnetoresistances of a ferromagnet, which is (a) bulk-like or (b) very thin, i.e., two-dimensional-like [51].
No longitudinal MR is expected in a nonmagnet because the (v × B)-term is zero. However, a ferromagnet has a hysteresis loop of the magnetization, and the longitudinal MR is observed due to
different scattering properties of up- and down-spins, and the MR behavior is described as the following. By decreasing the magnetic field from a field stronger than Bs, the resistance stays constant or
has a small increase until zero field. The magnetic field then increases in the other direction and
starts to switch the magnetization in the opposite direction. The resistance decreases as the field increases until the so-called switching field, and at the switching field, the resistance increases suddenly to the saturation value of the resistance. The values of both the switching field and the resistance at the switching field vary slightly from measurement to measurement, and this is attributed
to the change in domain formation during the demagnetization processes [52, 53].
2.3.3 Electrical spin injection
Spin injection is a phenomenon that the transport of the nonequilibrium spin polarization from a
ferromagnet (F) to a nonmagnet (N). The giant magnetoresistance (GMR) and the tunneling magnetoresistance (TMR) are two of the most famous effects related to spin injection.
In order to make the discussion of spin injection clear, it is necessary to define the spin polarization, PX, of a physical quantity, X, as
PX =
X  − X −
X   X − ,
(2.26)
25
where λ is 1 or ↑ for up-spins, and -λ is -1 or ↓ for down-spins, respectively. For example, the spin
polarization of the DOS, D(E), and of the current density, j, are
P DE  =
D  E  − D E 
j  − j
and P j =
,
D  E   D E 
j   j
respectively. P X  0 means that there is larger contribution to X from ↑ than ↓ , and vice versa.
To describe the electrical spin injection theoretically, the approach to describe CPP-GMR (the
current perpendicular to the plane GMR) is adopted and generalized. As depicted in Fig. 2.10(a), a
single F/N junction is considered. The characteristic resistances per unit area of the F-, N-regions
and the contact are denoted as rF, rN, and rc, respectively. In the diffusive regime, the charge transport is described by the Ohm's Law, and the spin-dependent diffusion equation and the electro-chemical potential, μλ, are written as
j =  ∇  ,
(2.27)
and
 =
e D
 n−V ,

(2.28)
where σλ is the conductivity, Dλ is the diffusion constant,  n = n  − n0 is the non-equilibrium
spin, and V is the electrical potential. At the steady state, the equation of continuity for the degenerate electron gas is given by
∇⋅ j=e 2 
where s=
N  N − −−
N N


=e 2   −  s ,
N  N −
s
N  N − s
(2.29)
,− − ,
is the spin relaxation time, and  s=−− .
 ,−−,
Considered that the properties of the up-spins and down-spins are different in F but the same in
N, together with the boundary conditions at the F/N junction and at infinity, the electro-chemical
potential at the N-side of the junction is written as,
 s ; N 0=−2 r N jP j ,
(2.30)
which can be called the spin accumulation,
 s ; N 0− s ; F 0=2 r c j  P j − P  ;c  ,
(2.31)
which describes the spin injection ( P  ;c is the spin polarization of the contact conductivity), and
the spin polarization of the current density in the N-region is
P j=
r c P  ;c r F P  ; F
=− P R ,
r N r c r F
(2.32)
26
where P  ; F is the spin polarization of the F-electrode conductivity [3].
(b)
(a)
-dn/2 dn/2
Fig. 2.10 Schematic depiction of a (a) semi-infinite F/N-junction and (b) F/N/F-structure. After Ref. 55.
The results tell us, for large spin accumulation at the N-side of the junction, rN should be large.
For spin injection, the large spin polarization of the ferromagnet does not itself lead to strong spin
injection, which happens only when r c = 0 , and the current-density spin polarization is
P j=
r F P ; F
.
r N r F
(2.33)
For GMR, rN is comparable to rF, Pj can be measured, but when rN is much larger than rF, which is
the case for spin injection into semiconductors, Pj will be too small to be observed. This is called
the conductivity mismatch problem, which was first pointed out by Schmidt et al. [13]. Thus, the
spin-selective contact having rc at least comparable to rN, first suggested by E. I. Rashba, plays a decisive role when TMR or spin injection into semiconductors is investigated [54].
To detect Pj in the N-region, both optical and electrical methods are available. If the nonmagnet
has current-induced light emission, it is possible to use the optical method to analyze the left- and
right-circularly polarization of the emitted light, and hence, to determine Pj. For the electrical measurements of Pj, we have to bring in another ferromagnet at the other side of the nonmagnet to form
the second F/N-junction to analyze it. Such an simple F/N/F-structure is generally called a spin valve. The measurements, similar to its optical counterpart, are to read out the current (or the resistance) for different spin polarization of the second ferromagnet. In other words, we measure the MR of
the spin valve, and then we can determine Pj.
For the electrical measurement to be possible, the spin polarization cannot be lost during the
spins travel through the nonmagnet. Therefore, the thickness of the nonmagnet, dN, should be smal-
27
ler than the spin diffusion length in the nonmagnet, Ls;N . Considering the structure shown in
Fig. 2.10(b), we can write down similar equations for both F/N-junctions and solve for the MR of
the spin valve. The MR is defined as
MR =
R − R   R

= 
=
,

R 
R 
(2.34)
where ↑↓ and ↑↑ represent that magnetizations of the two F-electrodes are antiparallel or parallel to
each other, respectively. The values after A. Fert and H. Jaffrès [55] are
2 r c P D  E
R=
r c  r F  cosh 
F
 r F P DE
 ;c
F
; F
2
2
,
r
dN
r
d
  N [1   c  ] sinh N 
L s; N
2
rN
Ls ; N
(2.35)
and
R   = 2 r F 1 − P 2D  E
r F rc  P DE
F
F
, F
,F
− P DE
2
where P D  E
F

dN
 2 r c 1− P 2D  E
Ls ; N
  rN
F
 ,c
2  r N r F P 2D  E
F
F
,F
 ,c

 r c P D2  E
F
 ,c
 tanh 
dN

2 L s; N
dN
r F  r c   r N tanh 

2 Ls ; N
, (2.36)
is the spin polarization of the density of states at the Fermi level. Significant MR ap-
pears when rc falls in the following range
rN 
dN
L
  r c  r N  s; N  .
Ls ; N
dN
For r c ≪ r N 
(2.37)
dN
 , the spin accumulation at the first F/N-junction is not strong enough to geneLs ; N
rate observable MR, and for r c ≫ r N 
Ls ; N
r
 (or equivalently, d N ≫  N  L s ; N ), the spin poladN
rc
rization of ↑↓ configuration is completely relaxed by the spin flip in the N-region, i.e., R   ~ R  ,
and thus no MR.
By applying Fe for both of the ferromagnetic electrodes ( P D  E
F

= 0.45, ρ = 9.71 × 10-6 Ω·cm,
Ls;F = 12 nm [56] ), n-GaAs with the longest spin life time in magnetic field (n3D = 1 × 1016 cm-3,
rN ~ 4× 10-5 Ω·cm2, and Ls;N = 2 μm [28, 55] ) for the nonmagnet, and assuming P D  E
F

= 0.5 for
the spin-selective contact, the MR versus rc for a 1 × 1 μm2 junction calculated for dN = 2 μm,
200 nm, and 20 nm is shown in Fig. 2.11.
28
Fig. 2.11 MR calculated after A. Fert and H. Jaffrès. Both
of the ferromagnetic electrodes are made of
Fe: P D E  = 0.45,
F
ρ = 9.71×10-6 Ω·cm,
and
Ls;F = 12 nm. The n-GaAs with longest spin life
time in magnetic field is chosen as the nonmagnet: n3D = 1×1016 cm-3, rN ~ 4×10-5 Ω·cm2 , and
Ls;N = 2 μm. The P D E  of the spin-selective conF
tact is assumed to be 0.5. The contact area is
1×1 μm2.
The theory of optical measurement is simpler than the MR measurement, for that the optical transitions only relates to the optical selection rule. Take GaAs, band structure shown in Fig. 2.12, as an
example, and this is representative of a large class of III-V and II-VI zinc-blende semiconductors.
The emission of the left circularly-polarized light, denoted as σ+, is attributed to the recombinations
between (1) a spin-down electron and a spin-down heavy hole (hh), (2) a spin-up electron and a
spin-down light hole (lh), or (3) a spin-up electron and a spin-down split-off hole (so) with the probability ratio 3:1:2. The emission of the right circularly-polarized light, denoted as σ –, is attributed
to the recombinations between (1) a spin-up electron and a spin-up heavy hole (hh), (2) a spin-down
electron and a spin-up light hole (lh), or (3) a spin-down electron and a spin-up split-off hole (so)
with the probability ratio 3:1:2 [57]. By denoting the density of the electrons spin-polarized for
spin-up and spin-down direction as n+ and n-, respectively, and then the spin polarization of the
electron density, Pn, is given by
Pn =
n − n−
.
n  n−
(2.38)
Since all the holes have very short spin life time, we can treat them as unpolarized. Then for a bulklike sample, the circular polarization of the luminescence, PI;cir, is calculated to be
P I ;cir =

−
n  3 n− − 3n  n− 
P
I −I
= 
=− n ,

−
n  3 n−  3n  n− 
2
I I
(2.39)
where I± is the light intensity for σ+ and σ –, respectively. In a quantum well, where the hh-lh degeneracy is lifted,
P I ;cir =

−
3 n − 3 n
I −I
= −
= −P n .

−
3 n−  3 n
I I
(2.40)
29
Fig. 2.12 Optical transitions of the left-circularly polarized (σ+, solid lines) and the right-circularly polarized light (σ–, dashed lines) of
bulk GaAs. The ground states of the electrons and holes are denoted by their names
and the projection of the total angular momentum along the z-direction. The numbers in circles represent the ratio of the
transition probabilities.
Though the electrical spin injection from a ferromagnetic metal into a semiconductor requires a
spin-selective resistive contact, optical observation relates the degree of the optical polarization directly to the spin polarization of the carrier density. It is the reason that optical investigations of the
electrical spin injection with a semiconductor light emitting device (LED) are quite successful. The
spin-selective resistive contact can be the native Schottky contact or an insulating tunneling contact
between a metal and a semiconductor, and both proved to be adequate for spin injection in reversebias [14 – 17]. Spin injection in forward-bias were reported as well [58, 59]. Spin injection in remant state is required for optical device applications in spintronics, and was observed by Gerhardt et al. [16, 17]. Spin-polarized laser was also studied for spintronic applications [60 – 62].
2.4 GaN-based diluted magnetic semiconductors
Diluted magnetic semiconductors (DMSs) are semiconducting alloys, whose lattice is made up in
part of substitutional magnetic atoms, and they are extensively studied for the last three decades.
Before the middle 1990s, the II-VI type DMSs were majorly studied [63], and since H. Ohno et al.
successfully incorporated Mn into GaAs to fabricate the first GaAs-based DMS in 1996 [11], the
III-V type DMSs attracted great attention due to their great potential applications in spintronics. The
Ga1-xMnxAs has the following characteristics, 1) p-type semiconductor for that the Mn is an acceptor
in GaAs, 2) charge-mediated ferromagnetism via the RKKY interaction, 3) gate-bias controlled ferromagnetism [64], which is the direct consequence from 2), 4) low solubility of Mn in GaAs, maximum is about 8% [65], and 5) low Curie temperature, the highest Tc is 172 K [66]. In search for fer-
30
romagnetic Mn-incorporated DMS above 300 K, theoretical calculations based on Zener model and
the RKKY interaction for 5 % Mn in some selected cubic semiconductors were carried out and
show that GaN and ZnO are the only candidates among them [33, 34].
To understand the microscopic origin of GaN-based DMS, ab-initio electronic calculations were
carried out by using LSDA. H. Katayama-Yoshida and K. Sato studied the 3d transition metal (TM)
doped GaN by the difference in total energy (TE) in two possible magnetic states: the ferromagnetic
and the spin-glass-like. In the ferromagnetic state, the magnetic moments of TMs are parallel to
each other and noted as Ga1-xTMxupN while in the spin-glass-like state, the magnetic moments of
TMs have two components, which are anti-parallel, and noted as Ga1-xTMx/2upTMx/2downN.
ΔE = TE(Ga1-xTMx/2upTMx/2downN) – TE(Ga1-xTMxupN) are calculated for V, Cr, Mn, Fe, Co, and Ni
with x = 0.05, 0.10, 0.15,0.20, and 0.25 and depicted in Fig. 2.13. For all the concentrations, the ferromagnetic state is stable for Ga1-xVxN and Ga1-xCrxN while Ga1-xFexN, Ga1-xCoxN, and Ga1-xNixN are
stable in the spin-glass-like state. For Ga1-xMnxN, it is stable in ferromagnetic state for low Mn concentrations but has spin-glass-like ground state for high Mn concentration [67].
Spin-resolved density of states (DOS) of 5 % TM-doped GaN were calculated by H. Katayama-Yoshida and K. Sato as well and depicted in Fig. 2.14. The valence band consists mainly of N2p states, and the impurity-d states appear near the Fermi level. As shown in Fig. 2.13 by the dotted
lines, these impurity-3d states show substantial hybridization with the valence p-states and large exchange splitting, which leads to high spin configurations. Considering the local symmetry, the five-
Fe
ferromagnetic state
Fig. 2.13 Stability of the ferromagnetic states
of GaN-based diluted magnetic semiconductors doped with transition
spin-glass state
metals, such as V, Cr, Mn, Fe, Co,
and Ni. The energy difference is
calculated by subtracting the total
energy of the ferromagnetic state
from the total energy of the spinglass state.
Fig. 2.13 Spin-resolved density of states calculated by H. Katayama-Yoshida and K. Sato for 5 % TM-doped WZ GaN
[67].
31
fold degenerate impurity-3d states are split into doubly degenerate 3dγ states and threefold degenerate 3dε states. The 3dε orbitals, having the symmetry of the functions xy, yz, and zx, hybridize
well with p orbitals of valence bands and make the bonding (t b) and the anti-bonding (ta) states. The
3dγ orbitals, having the symmetry of the functions 3z2-r2 and x2-y2, extend to the interstitial region
to make the non-bonding (e) states. The tb states appear in the valence bands, the ta states appear somewhere between the Fermi level and the conduction band edge, and the e states, due to the nonbonding nature, appear just below the Fermi level, shown in Fig. 2.14. For that electrons in e states
are less itinerant than in ta states, as long as the ta states are neither empty nor full, the Ga1-xTMxN
has ferromagnetic ground state, which is the case for Ga0.95Cr0.05N and Ga0.95Mn0.05N. The ferromagnetic ground states of Ga0.95V0.05N is, therefore, meta-stable from, and by doing the co-doping to
bring electrons into the ta states enables us to stabilize the ferromagnetic ground state of Ga1-xTMxN.
Fig. 2.14 Schematic depiction of the electronic structure of TM at a substitutional site in GaN.
The anti-bonding ta states and the non-bonding e states appear in the band gap [67].
For the GaN doped with rare-earth (RE) elements, due to the localized nature of their 4f states,
the theoretical results from LSDA, except for Gd, deviate significantly from the experimental observations. In the case of Gd, due to its half-filled 4f-shell and the large exchange splitting, LSDA provides a reasonably accurate description.
A. Svane et al. performed the theoretical calculations of the electronic structure of RE dopants in
zinc-blende (ZB) GaN and GaAs by using the self-interaction corrected (SIC) LSDA. As for the
electronic properties, their studies show that the trivalent state of RE dopants is preferred when RE
elements are incorporated into GaN, indicating the substitution of Ga and no released charge carrier
from RE dopants. For the magnetic properties, the induced exchange splitting between the up and
down spins of 4f states at both the valence band maximum (VBM) and the conduction band minimum (CBM) are quite small, ranging between 6 meV and 45 meV for VBM and between 100 meV
32
and 150 meV for CBM, respectively. These values are two orders of magnitudes smaller than those
for Ga1-xMnxN by using the same method. Additionally, For Eu, Gd, Tb, Dy, and Ho, the exchange
interaction at CBM is anti-ferromagnetic. From these results, it looks very unlikely that the isolated
RE dopants by themselves can lead to room temperature (RT) ferromagnetism, and these dopants
have to interact with certain defects, either native or external [68].
For that GaN is normally n-type, G. M. Dalpian and S.-H. Wei investigated the intrinsic and ntype Gd-doped ZB GaN theoretically with LSDA. Their investigations show as well that the intrinsic Ga1-xGdxN has the anti-ferromagnetic ground state, but the unoccupied spin-down 4f states of Gd
appear not only above but also close to CBM, resulting in the bounding f-s character of spin-down
CBM of Ga1-xGdxN, shown in Fig. 2.15. Therefore, it is possible to stabilize the ferromagnetic phase
of ZB Ga1-xGdxN by introducing free electrons with co-doping [69].
Fig. 2.15 Density of states for ZB Ga1-xGdxN with
x = 0.0625. The blue dashed and red lines
are the partial DOS of Gd f and d levels,
respectively. The DOS of the Gd d levels
was multiplied by 3.
Theoretical and experimental studies on GaN doped with various transition metals (TMs) and
rare-earth (RE) elements are performed extensively since 2000. The experimental results summarized by Pearton et al. in 2003 [70] and Liu et al. in 2005 [71] are not consistent and depend strongly on the preparation methods.
2.5 Focused ion beam
For the lightest ion (H+, proton) having the same energy as an electron, its momentum is roughly
two orders of magnitude larger than the electron's. This means that we could improve the resolution
33
for at least two orders of magnitude in microscopy if we use ions instead of electrons. On the other
hand, this means that the incoming ions will transfer a large amount momentum to the target atoms
when the ions meet the target surface. During the collision process, a certain amount of ions will be
stopped and trapped inside the target and some target atoms will be ejected from and near the surface. Thus, we will have a multifunctional apparatus when we modify a scanning electron beam
(SEM) column into a focused ion beam (FIB) column. Using FIB, we can perform microscopy, ion
lithography, ion implantation, milling, etc.. It is also worthy to note that the ion beam microscopy,
unlike electron beam microscopy, is destructive even at the possibly lowest ion density at the target
surface. In this work, FIB with Ga source was exploited for ion implantation and milling.
2.5.1 Focused ion beam system
A focused ion beam system consists of a ion source, a ion beam optics, a deflector system, and a
specimen stage, which are all mounted into a vacuum chamber.
2.5.1.1 Liquid metal ion source
For high resolution FIB systems, which have the focused beam or probe size smaller than 1 μm
and the current density of the order of 1 A/cm-2 [72], the filed emission types of sources are applied.
Among them, the liquid metal ion sources (LMIS) are the most popular, for their high brightness
and the advantage that almost all metals having relatively low melting point and low reactivity
could be made into sources. The available LMISs in our Lehrstuhl include the elements: As, Au, B,
Be, Bi, Co, Cr, Cu, Dy, Er, Fe, Ga, Ge, Gd, Ho, In, Mn, Ni, P, Pd, Pt, Si, Sn, and Tb, where B, P
(a)
(b)
Fig. 2.16 (a) A photo and (b) a sketch of an empty
liquid metal ion source. The capillary is
Heater contact
made of tungsten spirals, which will later
be filled with a metal or metal alloy. The
capillary
needle
photo is courtesy of FEI.
34
and Si are nonmetals, and except Bi, Ga, In and Sn, the other elements can only be prepared in eutectic (alloy) form. As, B, Be, Ga and Si LMIS are important for semiconductor technology because
they are the dopant elements. Bi, Fe, Mn, to name a few, attract growing interest from scientists and
engineers working on semiconductor and/or magnetism, for that the ions can bring magnetization
into semiconductors.
A LMIS consists of a capillary tube with a needle through it, an extraction electrode and a shield
(Fig. 2.16). The capillary tube serves as the reservoir of the metals, and the tip of the needle has the
radius between 1 and 10 μm. To extract the ions, the capillary tube is heated to the melting point of
the metal and meanwhile a high positive voltage, relative to the extraction electrode, is applied to
the needle. The liquid metal flows then to the tip of the needle and forms a cone, called Taylor cone,
by the balance of the electrostatic and the surface tension forces acting on it. The apex of the Taylor
cone is believed to have the radius of only about 5 nm, and due to this small radius, the high electric
field on it results in the field evaporation and field ionization of the atoms in vapor state.
2.5.1.2 Focused ion beam column
The FIB column employed in this work is the Canion 31 Plus from Orsay Physics, depicted in
Fig. 2.17, and consists of (from top to down) a stigmator (not shown), a condenser lens, a set of
condenser lens apertures, an

× B filter, a set of objective lens apertures, a beam blanker, beam
deflector, and a objective lens. This column operates between 5 kV and 30 kV, which is the acceleration voltage of the ions, denoted as Vacc. The condenser lens is used to collimate the beam, or to
form a beam cross-over at the center of the

× B filter (Wien-filter) or of the center of a objective
lens aperture, which is then imaged onto the specimen by the objective lens. The stigmator is applied to eliminate the ions that are not directed vertically, and the condenser lens apertures (current
regulator) are applied to cut off the beam, and thus to regulate the beam current and to decrease to
lens aberrations. The electrostatic beam deflector controls the landing location of the ions on the
specimen.
35
Fig. 2.17 Schematic depiction of a Canion 31 Plus FIB column from Orsay Physics. All the electrical potentials denoted by U instead of V as in the text.
A Wien-filter is a velocity selector serving as a mass filter for choosing a certain ion isotope with
a certain energy to go through the ion bema column. The principle is the following. Orthogonal to
the optical axis, an electrostatic field and a magnetic field, which is perpendicular to the electrostatic field, are applied. An ion after acceleration has the kinetic energy,
Ek =
1
2
m v = q V acc ,
2
(2.41)
where m is the mass and q is the charge of the ion, and the velocity of the ion is then expressed as
v=

2 q V acc
. At a certain value for each field, respectively, the Lorentz and the electrostatic
m
36
forces on the ion counterbalance each other, i.e.,
FL= q v B= q
 = F
,
and the ions having the velocities other than v =
(2.42)

B
=

2 q V acc
will be deflected and blocked
m
by the objective lens aperture (mass selector) beneath. The Wien filter selects, in fact, the ions with
a certain charge-to-mass ratio, so that we are able not only to separate, e.g., Fe from Au and Ge of
the Au-Fe-Ge alloy source, but 56Fe from 57Fe and Fe+ from Fe2+ as well. However, technically, great consideration was taken to separate the isotopes of an element for the small difference in the
charge-to-mass ratio, and also due to the difference in natural abundance of the isotopes, it is difficult to resolve the isotopes for some elements.
2.5.2 Focused ion beam milling
Ordinary mechanical means of milling are capable of producing structures with dimensions of the
order of 10-3 inch (25 mm) and a precision of the order of 10-4 inch [72]. For smaller structures, we
have to use other techniques, and FIB is one of them, which has the advantage to write the structures on the specimen directly, i.e., maskless. Essentially, FIB milling is a process combing (physical)
sputtering, material redeposition, implantation and amorphization [73]. In this section, the aforementioned processes are discussed and followed by the results of my milling work.
2.5.2.1 Sputtering
The sputtering process involves the transfer of momentum to surface or near-surface atoms from
the incident ion beam through a series of collisions with the solid target [74]. Since the transfer of
the vertical component of the incident momentum is the major mechanism of the sputter, the process depends on the angle of incidence of the beam. Besides, the sputter yield, Y, defined as the
number of ejected atoms from the target per incident ion, is also dependent on the mass and energy
of the ions, the mass of the target atoms and nature of the target atomic structure. The range of Y is
typically between 0 and 20.
37
Fig. 2.18 Angle dependence of the sputtering yield of Ga+ ions on Si (left) and GaAs (right).
Crow et al. and Kaito et al. studied the sputter yield of Ga+ ions on Si (Crow and Kaito) and
GaAs (Crow) [75]. The important observation from them is that the sputter yield reaches a maximum when the incident angle is near 80 ° and the decreases as the incident angle approaches 90 °
(Fig. 2.18). An additional information from Crow's measurements is that the sputter yield flattens
out at around 30 keV, so that little is gained by going to higher energies (Fig. 2.19).
Fig. 2.19 Energy dependence of the sputtering yield of Ga+ ions on Si (left) and GaAs (right).
2.5.2.2 Redeposition
Redeposition is generally the process that the ejected atoms from the target surface, which are in
gas phase and normally not at thermodynamic equilibrium, condense back into solid phase upon
collision with a nearby surface. It can also indicate only the condensation of the out-splashed atoms
on the already sputtered surface. Redeposition can be greatly reduced by writing the structure repeatedly instead of once, but in the end, with the same total amount of ions, namely the same total ion
dose. By writing repeatedly, each successive writing removes the redeposited materials from the
previous writing; although the milling rate is somewhat reduced, the uniformity of the milled struc-
38
ture is improved.
2.5.2.3 Implantation and amorphization
Looking at the cross section of any FIB milled structure, there is always swellings at the edges.
This is not an artifact from the measurements but the FIB-amorphized target material. Amorphization happens when the energy or the dose level of the incident ions is not high enough for sputtering,
and the incident ions are in most cases buried in the bombarded target material, which is called implantation. The implantation profile of an ion to a material can be simulated by a SRIM (stopping
and range of ions in matter) program[76]. At very low dose, the density of implantation-induced defects is rather low, and the swelling profile is not seen. Usually, the swelling starts to show when
the dose level reaches around 1015 ions per square centimeter. During the milling process, the low
dose level comes from the extended tail in the ion distribution of the FIB, called side dose, which is
the nature of FIBs [77]. The magnitude of the swelling due to amorphization can be as high as tens
of nanometers, and therefore, amorphization diminishes the dimensional accuracy of milling and is
an important consideration in nanofabrication.
Fig. 2.20 A typical FIB milled line pattern adapted from Ref. 73, and this
pattern was measured by an AFM. In this figure, the width between the swellings on both sides of the milled line is denoted
as A. The width of the milled line, the milled depth, and the
height of the swelling are denoted as B, C, D, respectively.
Fig. 2.20 shows a typical milled line pattern measured by an AFM. The line pattern looks triangle-like, and the swelling is clearly observed. The rate of FIB milling is usually written as the milled volume per unit charge, and the typical scale is μm3/nC. If the milling pattern is an area instead
of a line, then the milling rate can be written as depth per unit dose, and the typical scales are nm or
μm for the depth and cm-2 for the dose, respectively.
39
3 Magnetotransport in cleaved-edge-overgrown Fe/GaAs-based heterostructures
In this chapter, the considerations for as well as the film and the contact properties of the cleavededge overgrown Fe on GaAs-based heterostructures are first discussed. The magnetoresistances
measured from the spin valve structure fabricated on such samples are then presented. Some important magnetoresistances involved in the magnetotransport of the spin valve are discussed at the
end.
3.1 Cleaved-edge overgrowth
From the previous chapter, we learned that the spin injection phenomenon is highly sensitive to
the interface properties, which can be represented by the contact resistivity, rc. It is desirable to have
a uncontaminated and atomic smooth interface between the metal thin films and the semiconductor
heterostructures in order to avoid the undesired scatterings from the unwanted impurities and the
rough interface. For such an ideal interface, the surface for the metal epitaxy must be freshly prepared in a ultra-high vacuum (UHV) chamber shortly before the thin film deposition, which is carried
out by the „ in-situ “ UHV sample cleavage.
To cut the sample, a line will be first marked at the expected cutting position on the substrate side
of the sample by using a diamond tip, and then the sample will be mounted on the sample holder in
the manner that the line-marker aligned at the edge of the sample holder, which is shown in
Fig. 3.1(a). During transferring the sample into the proper position in the main chamber, the tail part
of the sample extending outside the sample holder is sent to meet the shutter for the sample holder,
and the sample will break itself into two pieces along the line-marker. The process is schematically
depicted in Fig. 3.1(b). Another possibility to make the UHV cleavage easier is to polish the sample
from the substrate side mechanically, and some of samples studied in this work was polished to the
40
thickness of 130 μm.
(a)
buffer
buffer
Fig. 3.1 (a) Sample holder and the process of sample mounting. (b) Schematic depiction of the UHV cleavage process [77].
sample
(b)
line mark
shutter
Cleaved edge
The heterostructures applied in this work were grown by semiconductor molecular beam epitaxy
(MBE) on semi-insulated GaAs(001) substrates, and the overgrowth of the metal thin films was carried out on the freshly-cleaved (110)-surface with the metal MBE. The thin films consist of 20-nm
thick Fe and a capping layer consisting of 4-nm Pt, 5-nm Au, or 5-nm Ag/ 5-nm Au. The metal
MBE enables us to have single-crystalline metal thin films, which reduces the unwanted scattering
inside the metal thin films.
Fig. 3.2 Images of the cleaved edge of a GaAs substrate tanken
with a scanning electron microscope. The terrace
structures and the stepwise edge profiles are clearly
visible in the pictures [78].
41
3.1.1 Properties of the interface and the metal thin films
The surface of the cleaved edge is unfortunately not smooth throughout the sample, and there
exists the so-called „terrace structures“ on the surface. The terrace structures consist of some flat
plateaus extending from some hundred micrometers to some millimeters, and their images taken
with a scanning electron microscope (SEM) are shown in Fig. 3.2. After the „in-situ“ UHV cleavage, the Fe and the capping layers were grown at room temperature (RT). The low-energy electron
diffraction (LEED) was performed during the deposition is shown in Fig. 3.3, and the overgrowth
of the metal thin film with the metal MBE was epitaxial in spite of the terrace structures [78].
Fig. 3.3 LEED pattern of (a) GaAs (110)-surface, (b) epitaxially grown Fe layer, and (c) the superposition of (a) and
(b). The LEED pattern of Fe has the periodicity twice as large as that of GaAs for that GaAs has the lattice constant twice as large as that of Fe [78].
After the overgrowth, the magnetic properties of the metal thin film were investigated with the
magneto-optical Kerr effect (MOKE) magnetometry. The magnetic field was aligned along both the
[001]- and [110]-direction for the MOKE measurements. The results, depicted in Fig. 3.4, show
that, the magnetic hard axis lay, as expected from the shape anisotropy, along the [001]-direction,
which is in the plane of the metal thin films. However the magnetic anisotropy is not pronounced,
which can be attributed to the 1.4 % lattice mismatch between Fe and GaAs, the terrace structures
and its step-like edge profiles [78].
42
Fig. 3.4 MOKE measurements on the Fe thin films overgrown on the cleaved (110)-GaAs for the external magnetic
field apllied along (a) [001]- and (b) [110]-direction, respectively [78].
3.1.2 Properties of the metal-semiconductor contacts
Although the total thickness of the metal thin films is between 20 nm to 30 nm, but due to the
contact area to the semiconductor heterostructures, it can be treated as the bulk type conductor –
called the three-dimensional electron gas (3DEG). In this work, bulk n-GaAs, δ-doped n-HEMT,
and an n-type pseudomorphic HEMT, consisting a InAs quantum well sandwiched by a series of
strained InGaAs layers, are applied. The contact between bulk n-doped semiconductors and metal is
known as the Schottky contact, and can be described using Shockley theorem by treating the contact
as one-sided abrupt p+-n contact [79]. The I-V characteristic is therefore written as
I = A∗ T 2 w d exp −
e V bi ,0
eV
 [exp 
 − 1] ,
kB T
kB T
and the depletion zone width, l3D, is written as
l 3D =

k T
2  0
V bi ,0 − V − B  ,
eND
e
where A* is the effective Richardson constant, T is the temperature, w and d are the width and the
thickness of the conducting channel, respectively, Vbi,0 is the zero-field built-in potential, V is the applied voltage,  is the dielectric constant, and ND is the donor concentration.
Since the 2DEG and the 3DEG have different energy spectra, the abrupt contact between them is
strongly non-ohmic, and a depletion zone forms in the 2DEG. Theoretical investigations on such
43
contacts were carried out by S. G. Petrosyan et al. [80, 81], and the I-V characteristic was found to
differ from 3D Schottky contact only with a numerical factor, and it is then written as
I = 5.36 A∗ T 2 w d exp −
e V bi ,0
eV
 [exp 
 − 1] ,
kB T
kB T
and the depletion zone width, l, is then written as
l=
2  0 V bi , 0
.
e n2D
Fig. 3.5 show the I-V characteristics measured between ±5 V at both 300 K and 4.2 K. The bulk
n-GaAs and δ-doped n-HEMT have the diode-like I-V characteristics. The reason that the δ-doped
n-HEMT has higher current at 4.2 K than at 300 K is due to the much higher electron mobility of
the heterostructures at 4.2 K. Because of the small band gap of InAs, 0.36 eV at 300 K and 0.42 eV
at 4.2 K, the I-V characteristics of the pseudomorphic HEMT looks ohmic-like at 300 K and shows
only a little diode-like behavior at 4.2 K.
(a)
(c)
(b)
Fig. 3.5
I-V characteristics measured between ±5 V at
300 K (solid symbols) and 4.2 K (open symbols)
for (a) a bulk n-GaAs, (b) a δ-doped n-HEMT,
and (c) an n-type pseudomorphic HEMT.
44
3.2 Focused ion beam milling
As mentioned in Chap. 2.5, any focused ion beam (FIB) process involves with implantation,
amorphization, sputtering, and redeposition. There are two characteristic doses for the FIB process,
1015 cm-2 and 1016 cm-2. When the dose is higher than 1015 cm-2, the ion-induced defects in the target
material are no more local but over the whole sample. When the dose exceeds 10 16 cm-2, the sputtering effect is stronger than the implantation. Therefore, we can apply FIB for different purposes by
selecting the suitable dosage: typically 1010 cm-2 to 1014 cm-2 for implantation and > 1016 cm-2 for
sputtering.
FIB milling is one of the physical etching processes, and it operates in the sputtering dose range.
For that the diameter of the ion beam can be focused to around 100 nm with a high-resolution FIB
column, the milling process is to scan the beam over the area we want to etch away the material.
Therefore, FIB milling has the advantages that neither mask and nor lithography process is needed
to define the structure and that it is possible to perform micro- or nano-machining.
There are two major reasons to apply FIB milling by using 30-keV Ga+ ions to fabricate spin valve in this work. First, the 130-μm thin sample is fragile and thus, the FIB milling is more suitable
than the standard lithography process due to its maskless advantage and no necessity for thermal
treatment. Secondly, the implanted Ga ions make the n-GaAs-heterostructures insulated as known
from the in-plane-gate (IPG) transistor, which was first fabricated by A. D. Wieck and K. Ploog in
1989 [82, 83]. This serves the purpose very well that the spin-polarized current injected from one of
the Fe-contacts will „be forced“ to go through the semiconductor and then come out from the other
Fe-contact of the spin valve.
In order to know the necessary dose for milling away the 25-nm thick metal films, a milling test
was performed on a 50-nm thick Au film on a semi-isolated GaAs substrate. The Au films were
milled by writing a line or a 1μm-wide rectangle with different doses ranging from 3×1016 cm-2 to
1×1018 cm-2. Then the depth profiles of the milling were measured with a Park Scientific atomic force microscope (AFM), and the I-V characteristics across the milled lines or rectangles were measured with a Hewlett-Packard semiconductor parameter analyzer at both RT and 4.2 K.
45
(a)
(b)
(c)
Fig. 3.6 (a) Depth profiles of all the milled rectangles, and
(b) the depth profile of the rectangle milled with
the dose 3 × 1016 cm-2. The milled-line width versus milling dose is plotted in (c), and the red line
is the linear fit of the half-logarithmic plot.
Fig. 3.6(a) shows the depth profiles of the milled rectangles, and the dose to mill through the
50-nm Au was found to be around 3×1016 cm-2. For a dosage higher than 2×1017 cm-2, the depth profile is no longer a rectangle, and this can be attributed to the dependences of the sputtering rate of
the angle of incidence and the crystal directions. Fig. 3.6(b) depicts the depth profile for the dose
3×1016 cm-2, and the swelling of the amorphization was observed at the milled edge. However, the
bottom of the milled area is not smooth, which might influence the insulation across the rectangle.
The milled-through dose for writing a line was found to be higher, around 1×10 17 cm-2 (not shown),
and this can be understood from the different depth profiles – rectangular for writing a rectangle
versus triangular for writing a line. Fig. 3.6(c) shows the half-logarithmic plot for the milled-line
width versus milling dose, and with the linear fit, the threshold dosage for sputtering is estimated to
be 6.5×1015 cm-2, where the milled-line width is extrapolated to be zero.
46
(a)
(c)
(b)
(d)
Fig. 3.7 Resistances versus milling dose measured across a milled rectangle at (a) room temperature and (b) 4.2 K. Resistances versus milling dose measured across a milled line at (c) room temperature and (d) 4.2 K. The solid
and open symbols represent the resistances before and after dipping the samples in HCl.
Fig. 3.7 show the dose dependence of the resistance across the milled lines and the rectangles, respectively, at RT and 4.2 K, and for the milled-through dose, the film is not insulated across the
milled line or rectangle. This could be explained by existing a parallel conducting channel and
could be possibly attributed to what Y. Hirayama and H. Okamoto observed in 1985 that Ga+ implantation makes n-GaAs become p-type [84]. Another possible reason is the redeposited Au, which
was not removed by the repeated scan of the ion beam. The samples were then dipped in a diluted
HCl (~ 4%) for 1 minute to remove the amorphous p-GaAs, its oxides as well as the redeposited
materials, and the I-V characteristics were measured again. It is seen clearly that the resistance after
HCl dipping was increased, and from the milled-through dose on, the Au films are insulated across
the milled lines or rectangles. The inconsistence between the resistances measured at 300 K
(Fig. 3.7(c)) and 4.2 K (Fig. 3.7(d)) across the milled line after HCl dipping is attributed to some
nano-particles fallen into the milled line between these measurements, which was observed later by
47
a scanning electron microscope (SEM).
Another milling test was carried out on a 20-nm Fe film capped with 5-nm Au film, and the results are quite similar to those shown in Fig. 3.7, for that the sputter yield for Au is a bit more than
twice as that for Fe [75]. However, as depicted in Fig. 3.8, over-etching of the Fe film under the Au
cap was clearly observed under optical microscope after dipping the sample for 1 minute in the diluted HCl, and the range of the over-etching is around 10 μm.
Fig. 3.8 Image of a milled structure after dipping in HCl. The
four contacts on the edge are made of Au, and the
rectangle in the middle is made of 20-nm Fe capped
with 5-nm Au. The dark area of the middle rectangle
represents the unetched Fe film.
Considered the sufficient milled depth and the required milling time, which should be less than
eight hours per structure, the milling dose of 1 × 1017 cm-2 was chosen. No dipping in HCl was performed for any of the samples to avoid the over-etching of Fe thin film, which results in no contact
between metal thin films and the conducting channel of the heterostructures. The widths of the two
electrodes for the spin valve were chosen as 500 nm and 4 to 5 μm, respectively, according to the
switching fields of the Fe nanowires measured with Hall magnetometry – shown in Fig. 3.9 [53,
85]. A milled line was chosen as the separation of the two Fe electrodes. Fig. 3.10 shows a schema-
Fig. 3.9 The width dependence of the switching field of a
100-μm long Fe wire [53]. For a clear observation of the magnetoresistance for a spin valve
made of Fe nanowires, one of the electrodes
should be at most 500 nm wide, and the width of
the other should be several micrometers.
48
tic depiction of a spin valve structure fabricated by FIB milling in the cleaved-edge-overgrowth
(CEO) geometry and a SEM image of a milled structure. The edges of the terraces are seen clearly
on the image.
(a)
(b)
(001)
Fig. 3.10 (a) Schematic depiction of a spin valve structure fabricated by FIB milling in the cleaved-edge-overgrowth
geometry. The GaAs(001) direction is denoted with an arrow. Milled areas are in black, gray squares are the
ohmic contact to the semiconductor heterostructure, and the blue dotted line represents the position of the
bulk n-GaAs or the 2DEG. (b) SEM image of the middle part of the spin valve structure. The widths of the
structure are 500 nm – 200 nm – 4.3 μm.
3.3 Electrical properties and magnetoresistances of the
spin valves
3.3.1 Electrical properties of the spin valves
Despite the geometrical separation, the metal films are not insulated across a milled or a rectangle
for the chosen milling dose from the insulation test of the FIB milling. Accordingly, the I-V characteristics measured from the CEO spin valve structures fabricated on the Fe/GaAs-based heterostructures show the metal-like temperature dependence of the resistances for the bulk n-GaAs and the
49
n-type pseudomorphic HEMT or at the threshold to become semiconductor-like for the δ-doped
n-HEMT (shown in Fig. 3.11). However, the resistances of the spin valves were inconsistent, either.
The terrace-structure-induced difference in FIB milling was assumed to be a major reason.
(a)
(c)
(b)
Fig. 3.11 I-V characteristics of a CEO spin valve structure
measured at room temperature (solid symbols)
and 4.2 K (open symbols) of (a) a bulk n-GaAs,
(b) a δ-doped n-HEMT, and (c) an n-type pseudomorphic HEMT.
3.3.2 Magnetoresistances of the spin valves
All of the magnetoresistances (MRs) for the CEO spin-valve structures were measured in a magnetic field between ±100 mT or ±50 mT along the (001)-direction of the heterostructures with
Lock-In technique, but only at 4.2 K due to the longer spin life time in semiconductors [28]. The
measurements started from the magnetic field of -100 mT to +100 mT and then back to -100 mT,
and the same for ±50-mT measurements.
50
Fig. 3.11 show the MR curves for two selected pieces of the spin valve on the bulk n-GaAs. There was no MR at all for the lower-resistance piece – shown in Fig. 3.12(a). For the higher-resistance
one, the MR curves show, surprisingly, the transverse MR of a semiconductor with additional features between the switching fields of the two Fe electrodes – depicted in Fig. 3.12(b). The transverse
MR indicates that the current flows through the bulk n-GaAs. The additional feature matches the
switching fields of the Fe electrodes estimated from Ref. 53, which seems to be the electrical observation of the spin injection. However, the following MR measurements on the same structure without time delay show a increase in resistance and without the additional feature – shown in
Fig. 3.12(c).
(a)
Fig. 3.12 Magnetoresistance for the spin valves fabricated
on the cleaved edge of a bulk n-GaAs. Red curves are the first part of the measurements, i.e.,
from -100 mT (or -50 mT) to +100 mT (or
+50 mT), and the blue curves are the second part
of the measurements.
(b)
(c)
The MRs for the spin valves on the δ-doped n-HEMT – shown in Fig. 3.13 – are as inconsistent
as those for the bulk n-GaAs. For the lower-resistance pieces, there was no MR observed, and for
the higher-resistance pieces, spin-valve-like effect was observed. Though the position of of the peak
in the spin-valve-like MR curves agrees with the switching fields, it looks rather unusual that the
51
MR – instead of staying constant – starts to increase before the magnetic field changes to the opposite direction. The transverse MR of the semiconductor could be assumed to be one possible reason. Another possible reason could be the anisotropic magnetoresistance (AMR) effect of the L-shape contacts, where the current flow perpendicular to the applied magnetic field has a different field
dependence than its parallel counterpart.
(a)
(b)
Fig. 3.13 Magnetoresistance for the spin valves fabricated on the cleaved edge of a δ-doped n-HEMT. Red curves are
the first part of the measurements, i.e., from -100 mT) to +100 mT, and the blue curves are the second part of
the measurements.
The only consistent results are obtained from the n-type pseudomorphic HEMT, where no MR
was ever observed, shown in Fig. 3.14. The possible reason for no MR could be attributed to the
much shorter spin relaxation time of the InAs [86].
Fig. 3.14 Magnetoresistance for the spin valves fabricated on the cleaved edge of an n-type pseudomorphic HEMT. Red curves are the first part
of the measurements, i.e., from -100 mT) to
+100 mT, and the blue curves are the second
part of the measurements.
52
All the observed MR ratios calculated with equation 2.34 are between 0.5 % and 0.7 % for the
bulk n-GaAs and between 0.014 % and 0.057 % for the δ-doped n-HEMT structures, respectively.
These values are very small.
3.4 Longitudinal magnetoresistances of the electrodes
Usually, the nonmagnetic electrodes are employed to measure the MR of a spin valve or a ferromagnet in order to avoid additional influence from the electrodes. For this CEO geometry, the desire to employ single crystalline spin-injecting electrodes makes it impossible to deposit some area
with a ferromagnetic material and the other with a nonmagnetic material. Therefore, the electrodes
are now ferromagnetic, and the MRs of the electrodes are involved when we measure the MR of a
spin valve in CEO geometry. Secondly, the electrodes is L-shape in this case and no longer a single
wire as in Refs. 52 and 53, so that the switching fields might deviate from our estimate based on the
two references. Furthermore, the MR ratios obtained from the the CEO spin valves are in the range
of the longitudinal MR of a ferromagnetic single wire. Given the above, it is important to investigate the longitudinal MR of the electrodes.
The structures for the longitudinal MR measurements were fabricated combining the optical and
electron beam lithography and the Lift-off techniques. Fig. 3.15 shows the layout and the measure-
V-
I
Fig. 3.15 The layout of the structures for the longitudinal
magnetoresistance measurements. The Au contacts are in green and the L-shaped metal thin
130μm
films are in yellow. The width of thin arm of
B
the L-shaped metals varies from 500 nm to
5 μm. The measurements are carried out at
4.2 K with the standard 4-point technique, and
the connections are shown in the figure. The
magnetic field were applied along the orange
arrow.
I
V+
53
ment geometry of the structures. The contacts are made of Au and the L-shaped metal are 20-nm Fe
capped with 5-nm Au. The measurements were carried out at 4.2 K using the standard 4-point technique.
(a)
(b)
Fig. 3.16 Longitudinal magnetoresistances of structures whose width is (a) 500 nm and (b) 5.2 μm. Red curves are the
first part of the measurements, i.e., from -100 mT to +100 mT, and the blue curves are the second part of the
measurements.
The negative MR were clearly observed for all the structures, and those obtained from a 500-nm
and a 5.2-μm wide structures were shown in Fig. 3.16, respectively. The decrease in resistance before the field changes its direction was seen for the width up to around 3 μm. Such a behavior is assumed the AMR effect from the L-shaped electrodes. Fig. 3.17 shows the switching field and the
MR ratio versus width. The switching field strength decreases as the width increases, which is expected due to the shape anisotropy. The MR ratios are clearly separated into two groups – one group
(a)
(b)
Fig. 3.17 (a) The relation of the switching field versus the width. The curve with open symbols is the calculation using
the model from Ref. 53. (b) The relation of MR ratio versus width.
54
has 0.05 % of MR and the other has around 0.3 % of MR. Both values are comparable to the MR
ratio observed from the spin valve structures. The difference between the two groups is the deposition method of the Fe/Au thin films. The MBE grown thin films have lower MR ration than the electron beam assisted evaporation. The thin films grown by the MBE have smaller grains.
3.5 Summary and Discussion
In this work, the epitaxial Fe thin films were successful overgrown on the UHV-cleaved (110)surface of the GaAs-based heterostructures. The MOKE magnetometry showed that the overgrown
Fe thin films having the easy axis long the (001)-direction of the heterostructures, but the anisotropy is rather weak. The reasons for the weak anisotropy can be attributed to the 1.4 % lattice mismatch between Fe and GaAs and/or the terrace structures on the cleaved edge.
Successful FIB milling was carried out with 30-keV Ga+ ions. It takes the doses of 3×1016 cm-2
and around 1×1017 cm-2 to mill through the 20-nm thick Fe film capped with a 5-nm thick Au film.
The I-V characteristics show that the FIB milling induces a parallel conducting channel, and the
channel can be removed by diluted HCl. However, there is over-etching for the Fe thin film in the
diluted HCl, and the fabrication of the spin valve was carried out without dipping in HCl.
The contacts between the cleaved-edge-overgrown metal thin films and the GaAs-based heterostructures shows the Schottky-like behavior, and this agrees with the theory. Due to the FIB-induced parallel conducting channel, the I-V characteristics of the spin valve structures showed no consistence from sample to sample and has the metal-like temperature dependence of resistances.
The MR measurements on the spin valve structures showed the inconsistence not only from sample to sample, but from measurement to measurement as well. The MR ratios, if MR was observed,
ranges between 0.5 % and 0.7 % for the bulk n-GaAs and between 0.014 % and 0.057 % for the δdoped n-HEMT structures, respectively. These values are comparable to the longitudinal MRs measured from the lithography-made L-shaped contacts. The observed MR curves have the switching
field agreed with the model from Ref. 53 and the longitudinal MR measurement.
In addition to what mentioned above, the contact resistance might not in the range to make MR
55
appear though optical observation proved the Schottky contact adequate for spin injection. The
long, „circling path“ that the injected electrons have to travel will makes them lose their spin information as well.
FIB-induced domain wall pinning both by implantation and sputtering in ferromagnetic thin films
were reported by M. Brands, C. Hassel and co-workers [87 – 89]. This FIB-induced domain pinning
might also play a role in the MR of the CEO spin valve fabricated by FIB milling.
It is important to note that even for a ferromagnet, whose magnetization is completely aligned
along its easy axis, magnetic domains having magnetization perpendicular to the easy axis are formed at both ends of the easy axis in order to reduce the energy. For the heterostructures employed
in this work, the spin-polarized current was injected from the end of the ferromagnetic electrode, so
that the majority of the injected electrons carry the spin orientaion of the end domain. The external
magnetic field as well as the stray magnetic field at the end of the ferromagnetic electrodes, which
has gradients in both its strength and its direction, will right away make the spins to precess. This
spin precession can not be separated from individual measurements, such as the longitudinal MR,
Hall effect, etc. [53, 85, 90], and it will decrease the spin life time and the spin coherence, which in
turn might make the spin valve effect unobservable. This is the biggest disadvantage in this work
even without all the aforementioned factors.
56
4 Magnetic properties in rare-earth elements
doped GaN and its heterostructures
The strong interest in studying the incorporation of rare-earth (RE) elements into GaN was mainly driven by the potential for electronic and optoelectronic applications, for example, to develop
blue, green, and red light emitting devices [91, 92]. RE elements have unfilled 4f shells and thus the
strong atomic magnetic moment, so that the RE-doped GaN has an ample potential for the applications in spintronics, as well.
In its natural state, GaN has the wurtzite (WZ) crystal structure with hexagonal symmetry. Due to
the local tetrahedral arrangement of the Ga and N atoms and the strong electron affinity of the N
atom, WZ GaN has a spontaneous electric polarization. The cubic zinc-blende (ZB) structure is very
similar to the WZ structure: both have the same local tetrahedral environment, but start to differ
only from their third-nearest-neighbor atomic arrangement on (Fig. 4.1), and hence, it is possible to
stabilize the ZB phase of GaN by doping with certain impurities [93]. Because of the higher symmetry, ZB GaN has more isotropic properties and no spontaneous electric polarization, it has smaller effective masses, higher carrier mobility, and doping efficiency. Given the above, ZB GaN and
its diluted magnetic semiconductors (DMSs) are expected to be more suitable for certain electronic
device and spintronic applications, respectively [94].
This chapter begins with the investigation of Gd-implanted ZB GaN with focused ion beam (FIB)
and then compared with the similar work on WZ GaN. The Eu-FIB-implanted WZ GaN was studied, and followed by the study of magnetotransport in WZ GaN-based heterostructure to complete
this chapter.
57
Fig. 4.1 The atomic arrangement of the wurtzite and the zinc-blende structures. Each circle is an atom, and the plane,
where the green circles are lying, is noted as B. The arbitrarily chosen center atoms are colored in yellow. The
A-arrangement is in red, and the C-arrangement is in purple. The wurtzite structure has the ABABAB…… sequence, and the zinc-blende structure has the ABCABC…… sequence.
4.1 Gd-doped zinc-blende GaN with focused ion beam
Recently, very diluted Gd-doped WZ GaN was reported to exhibit ferromagnetism with an ordering temperature (Curie temperature) Tc above 300 K incorporated by MBE [38] and by FIB implantation [39]. The magnetic easy axis is parallel to the sample surface. The ferromagnetic behavior
was present in the aforementioned works for the Gd concentration as low as 1×1016 cm-3. Moreover,
the effective magnetic moment per Gd atom, peff (peff = M(50 kOe) / nGd), was found for MBE-doping to be as high as 4000 μB at 2 K and 2000 μB at 300 K, respectively, and those for FIB implantation were found to be even larger, 1×105 μB at 2 K and 1×104 μB at 300 K. These values are significant compared to the atomic magnetic moment of Gd, 8 μB. Therefore, it was postulated that defects
contribute to the interaction between Gd atoms in the WZ GaN matrix and strongly enhance the
magnetic moment, but the microscopic origin of these effects is not yet understood, especially since
all these sample are highly resistive.
The sample studied in this work was an n-type 700-nm thick ZB GaN layer grown by MBE on a
3C-SiC (001) substrate at 720 °C, and the doping concentration is around 1×1018 cm-3 [95]. The
58
sample was then cut into four pieces of the same size (5×5 mm2) and labelled numerically. Among
them, Sample 4 was kept unimplanted as a reference, and the others were implanted with Gd3+ ions
by using a 100-kV FIB facility (EIKO-100). The implantations were carried out at room temperature (RT) with a constant ion energy of 300 keV. The implantation doses for Samples 1 and 2 were
1×1013 cm-2 and 1×1015 cm-2, respectively, while Sample 3 was first implanted with a dose
1×1012 cm-2, and after magnetic measurements, it was subsequently implanted with a dose of
1×1014 cm-2. No samples were subjected to annealing treatment.
The projected range of the 300-keV Gd ion into GaN was calculated to be 100 nm by using the
SRIM (stopping and range of ions in matter) program [76] and the implantation profile is plotted in
Fig. 4.2 together with the sample structure. The Gd concentration in GaN was estimated by integrating the ion distribution over the implantation profile and then dividing by the projected range,
which yields the corresponding Gd concentrations, from 1×1017 cm-3, 1×1018 cm-3, 1×1019 cm-3, to
1×1020 cm-3, respectively. The Gd concentration of 1×1020 cm-3 is equivalent to x = 0.0023 in the
Ga1-xGdxN notation.
Fig. 4.2 Schematic sketch of the zinc-blende GaN sample structures. The growth direction is to the left. The implantation profile for the dose of 1×1015 cm-2 is plotted as well.
The structural properties were investigated by X-ray diffraction (XRD) with a Phillips X'Pert
MRD diffractometer after crystal growth and FIB implantation. Fig. 4.3(a) shows the X-ray ω-2θ
scan, which was performed in a double axis configuration right after the film growth. Though a
clear ZB GaN (002) peak at 39.9° in 2θ is observed in the XRD pattern, a WZ GaN (0002) peak at
34.5° in 2θ was registered. From the ratio of the integrated intensity between both peaks, more than
59
99.5% of the GaN layer was found in the ZB phase. XRD patterns taken after FIB implantation are
shown in Fig. 4.3(b), where a clear Gd-related broadening of the ZB GaN (002) peak was observed,
which is known from the WZ Gd-implanted GaN. No segregated GdN or other mixed phase could
be identified from the XRD pattern after Gd implantation. These indicate the successful incorporation of Gd into ZB GaN matrix and that the nucleation of the WZ phase occurred at the interface between GaN and the 3C-SiC substrate during the initial growth process, which did not extend to the
sample surface.
The magnetic properties were measured with a Quantum Design superconducting quantum interference device (SQUID) magnetometer. For all the SQUID measurements, the magnetic field was
applied parallel to the sample surface. The magnetization loops were recorded at 5 K and 300 K for
magnetic fields between ±50 kOe. The temperature dependence of the magnetization was investigated by the field-cooled (FC), zero-field-cooled (ZFC), and the temperature-dependent remanent
(TR) magnetization curves measured between 2 K and 300 K. The samples were cooled either under a saturation magnetic field of 50 kOe (FC) or zero field (ZFC), and then the magnetization was
measured at a magnetic field of 100 Oe during a warm-up process. For the TR curves, a 30 kOe
magnetic field was applied to the samples prior to the cooling and warming-up processes, and then
the samples were cooled down or warmed up in zero field while the remanence was measured.
(a)
(b)
Fig. 4.3 X-ray diffraction ω-2θ scans of (a) the as-grown sample, and (b) the implanted sample 2 and the reference
sample. The arrow indicates the Gd-related broadening after FIB implantation.
All samples including the unimplanted reference piece 4 were subjected to magnetic measurements before Gd implantation. Fig. 4.4(a) shows the as-measured hysteresis loops at 5 K for
Sample 4, Sample 3 before and after Gd implantation (dose 1×1014 cm-2), and Gd-implanted
60
Sample 2 (dose 1×1015 cm-2). The reference sample shows the expected diamagnetic behavior
between ±50 kOe. The hysteresis loops of the three lower Gd concentrations show no difference
from the reference curves, and only Sample 2 implanted with the highest concentration shows a distinguishable but very small additional signal. After the diamagnetic background was subtracted, the
magnetization loop of Sample 2 shows only weak hysteretic behavior at 5 K,and therefore, the magnetization is not saturated up to the highest field of 50 kOe, indicating a strong paramagnetic contribution to the overall signal (shown in Fig. 4.4(c)). The total magnetization of the sample is around
18.5 emu/cm-3 at 50 kOe, and the peff is around 20 μB, which is roughly one half of that observed at
2 K in Gd-implanted epitaxially grown WZ GaN layers of the same dose [39]. For the as-measured
hysteresis loops at 300 K, shown in Fig. 4.4(b), all the samples exhibit only the diamagnetic behavior between ±50 kOe which is in strong contrast to WZ GaN, where a clear magnetic hysteresis
could be recorded up to 300 K for all implantation doses [39].
(a)
(c)
(b)
Fig. 4.4 Magnetization loops obtained from Samples 2, 3,
and 4 at (a) 5 K and (b) 300 K. (c) The 5 K hysteresis loop of Gd-implanted sample 2 after the diamagnetic background was subtracted. The unimplanted and Gd-implanted curves are with solid
and open symbols, respectively.
61
All implanted samples but Sample 2 show the same temperature-dependent behavior as the reference sample (Sample 4). The comparison of FC and ZFC curves between Sample 4 and Sample 2 is
depicted in Fig. 4.5(a), and the comparison of the TR curves between Sample 3 and Sample 2 is depicted in Fig. 4.5(b). Qualitatively, FC and ZFC curves of the three lower Gd concentrations and the
reference sample have only a strong temperature dependence below 10 K as well as the ZFC curve
of Sample 2, and this dependence is paramagnetic-like. In addition to the paramagnetic-like behavior, the FC curve of Sample 2 has a weak temperature dependence between 10 K and 60 K, indicative of long range magnetic ordering. The warming-up TR curves other than that of Sample 2 have
no magnetic signal beyond the small value recorded for the reference sample which is presumably a
fitting artefact from the SQUID. For Sample 2, a very small finite remanence is visible up to about
60 K having a weak temperature dependency, which means that a low-temperature magnetically
ordered phase may exist for the highest implantation dose up to about 60 K. Note, that this temperature roughly coincides with the order temperature of rocksalt GdN, which is ferromagnetic up to
about 60 K [96]. However, we have no indications of phase segregated GdN by means of XRD.
(a)
(b)
Fig. 4.5 Temperature dependence of the magnetizations at (a) field-cooled (solid symbols) and zero-field-cooled (open
symbols) conditions at a magnetic field of 100 Oe, and (b) remanence during cooling (solid symbols) and
warming up (open symbols).
Although the magnetic ordering phase of Sample 2 has the ferromagnetic-like temperature dependence, the rounded magnetization loop together with the FC/ZFC behaviour suggests that this
sample is more superparamagnetic-like rather than ferromagnetic. One reason that none of the
samples show no or – in the case of the highest dose – only low temperature ferromagnetic ordering
can be attributed to the low Gd and donor concentrations, which are orders of magnitudes smaller
than the theoretical calculation [69]. Also, the highly localized character of the f orbitals of Gd lead-
62
ing only to a weak electron-mediated interaction may account for that. In other words, to have ZB
Ga1-xGdxN featuring RT ferromagnetism, higher Gd and electron concentrations are needed.
Comparing the results for ZB GaN presented here to the ones on WZ GaN reported by
S. Dhar et al. [39], there are two major differences: (i) RT ferromagnetic ordering and the colossal
magnetic moment at very low Gd concentration(1×1016 cm-3) for WZ Ga1-xGdxN, and (ii) their
highly resistive property, which is less favorable of ferromagnetic ordering. The former indicates
that there exists a very strong long-range interaction between the Gd atoms and/or between Gd
atoms and defects in the WZ GaN matrix, and the latter suggests that all the Gd-Gd and the Gd-defect interactions are highly localized. As mentioned in Chapter 2.5, rare-earth dopants are unlikely
to induce RT ferromagnetism and the colossal magnetic moment by themselves. Thus, the Gd has to
interact via certain defects, either native or external [68]. In the view of our present experiments it
seems imperative to suggest that the spontaneous electric polarization – the only long-range interaction in the undoped WZ GaN – seem to be essential in yielding the long-range magnetic order in
WZ GaN.
4.2 Eu-doped wurtzite GaN with focused ion beam
For the success of magnetic WZ Ga1-xGdxN, it seems intuitive that Eu and/or Tb would be the
second-best candidates for fabricating WZ GaN-based DMS because they have one fewer half-filled
4f-shell than Gd. Theoretical calculations showed that Ce-, Nd-, Sm-, Eu-, Ho-, and Er-doped WZ
GaN has stable ferromagnetic state [97]. Experimental studies showed that Eu(2%)-, Tb(1.6%)-,
and Er(2.2%)-doped WZ GaN during MBE film growth exhibited paramagnetic behavior but coexisting ferromagnetic order was also present in Eu(2%)- and Er(2.2%)-doped WZ GaN [98, 99].
The sample studied in this work was grown by NH3-MBE and has the following structure –
shown in Fig. 4.6: sapphire (0001) substrate / 25 nm GaN buffer (430 °C) / 80 nm AlN (850 °C
ramping to 900 °C) / 2 μm Al0.44Ga0.56N (840 °C) / 1.96 μm GaN (800 °C). The sample was then cut
into four pieces of the same size (4×5 mm2) and labelled numerically. Among them, Sample 4 was
kept unimplanted as a reference, and the others were implanted with Eu2+ ions using a 100-kV FIB
facility (EIKO-100). The implantations were carried out at RT with a constant ion energy of
200 keV. The implantation doses for Samples 1, 2, and 3 were 1×1015 cm-2, 3.5×1015 cm-2 and
63
1×1014 cm-2, respectively. None of samples were subjected to annealing treatment.
Fig. 4.6 Schematic sketch of the wurtzite GaN sample structures. The growth direction is towards the left. The Eu-implantation profile for the dose of 1×1015 cm-2.
The SRIM-calculated projected range for the 200-keV Eu ions is 80 nm and plotted in Fig. 4.6 together with the sample structure, and the Eu concentrations for the samples were estimated to be,
from low to high, 1.25×1019 cm-3, 1.25×1020 cm-3, and 4.38×1020 cm-3, respectively. The Eu concentration of 1×1020 cm-3 is equivalent to x = 0.01 in the Ga1-xEuxN notation.
No structural investigation was carried out for these samples, and the magnetic properties were
measured with a SQUID magnetometer. Other than applying the magnetic field perpendicular to the
sample surface, the parameters for SQUID measurements are the same as the Gd-implanted ZB
GaN.
From the as-measured hysteresis loops, all the implanted samples show almost no variation from
the reference sample at both 5 K and 300 K. After the diamagnetic background was subtracted, the
samples showed only at 5 K the paramagnetic-like hysteretic behavior without saturation up to
50 kOe, shown in Fig. 4.7(a). The peff at 5 K for the highest dose is around 1 μB, which is larger than
the reported value from the MBE-grown WZ Ga0.98Eu0.02N [98] and indicates the defect-enhanced
magnetic moment as observed from Gd-FIB-implanted WZ Ga1-xGdxN [39]. The temperature-dependent measurements show no remanent magnetic moment and no magnetic ordering for all doses,
shown in Fig. 4.7(b).
64
(a)
(b)
Fig. 4.7 (a) Magnetization loops obtained at 5 K from all samples after the diamagnetic background was subtracted.
(b) The temperature dependence of the magnetizations at remanance during cooling (solid symbols) and
warming up (open symbols).
Comparing this work to the MBE-grown WZ Ga1-xEuxN reported by Hashimoto et al. [98] and
the Gd-FIB-implanted WZ GaN reported by Dhar et al. [39], the defect-enhanced magnetic moment
was observed but no the ferromagnetic phase even for the sample with the highest dose and at low
temperature. The reasons might be that the 4f orbitals are more localized and thus, despite the 1% of
Eu, the atomic magnetic moment of Eu is only 4 μB, which does not induce the spin-splitting required to set the essential spontaneous electric polarization into yielding the ferromagnetic ordering.
4.3 Magnetotransport in Gd-implanted GaN-based heterostructures
Since the WZ Ga1-xGdxN is ferromagnetic above 300 K and has the easy axis parallel to the
sample surface, it is only natural to study the magnetotransport in the Gd-incorporated GaN-based
heterostructures in conjunction. The MBE-grown GaN-based high electron mobility transistor
(HEMT) structures studied in this work, shown in Fig. 4.8(a), has the following layer sequence:
Si (111) substrate / 1.7 μm GaN / 1 nm AlN / 21 nm Al0.28Ga0.72N / 5 nm GaN. After the growth, the
mesa structures, the ohmic contacts, and the gates were brought onto the structure by standard
lithography, etching, lift-off, and the alloying processes. The final look of the the structures are depicted in Fig. 5.8(b). For the magnetotransport measurements, the z-axis is parallel to the growth di-
65
rection, or perpendicular to the sample surface, and the x-axis is along the longer edge of the transmission line (TML) structure.
(a)
(b)
(c)
van der Pauw
structures
y
D C B A
z
transmission
line structures
x
Fig. 4.8 (a) A schematic sketch of the wurtzite GaN-based HEMT structure. The growth direction is towards the left.
(b) The final look of a single structure along with the coordinates. (c) The implantation patterns.
4.3.1 I-V characteristics after Gd implantation
The defects induced by the ion implantation will deplete the two-dimensional electron gas
(2DEG), and therefore, it is important to ascertain the dose range where the 2DEG is not depleted
by FIB implantation without having to resort to any annealing to recover the compromised crystal
structure. A 5×190 μm2 rectangle, the pink rectangle in Fig. 4.8(b), was implanted with 300-keV
66
Gd3+ ions at the position A – 35×160 μm2 area between ohmic contacts – of each row from the TML
structures with different doses, ranging from 1×1011 cm-2 to 1×1014 cm-2, and the implantation profile is depicted in Fig. 4.8(a).
The I-V characteristics were measured at 300 K, shown in Fig. 4.9(a), and at 4.2 K, shown in
Fig. 4.9(b). The I-V characteristics tell us that 2DEG shows ohmic characteristics up to the dose of
1×1012 cm-2, and it is completely depleted from the dose of 1×1013 cm-2 and onwards.
(a)
(b)
Fig. 4.9 I-V characteristics measured from position A of the transmission line structures at (a) 300 K and (b) 4.2 K.
The unimplanted and Gd-implanted curves are plotted with solid and open symbols, respectively.
4.3.2 Magnetotransport in Gd-implanted GaN-based HEMT
structures
Knowing the suitable dose range, the next step is to study the magnetotransport in Gd-implanted
structures. The 300-keV Gd implantations were carried out with two different doses: 3×10 11 cm-2
and 3×1012 cm-2. The implantation patterns are a 5×190 μm2 rectangle for the position A of TML
structures, and a 130×130 μm2 square for the van der Pauw (vdP) structures, respectively (shown in
Fig. 4.8(c)). The I-V characteristics show that the 2DEG is completely depleted at a dosage of
3×1012 cm-2, which matches the previous implantation test. The magnetotransport was studied by
Hall effect and magnetoresistance (MR) measurements only for the structures implanted with the
dose of 3×1011 cm-2.
67
4.3.2.1 Hall effect
The Hall effect was studied with the vdP structures by applying Bz between ±5 T at 4.2 K. Note
that the electrons gives rise to positive Hall voltage under positive magnetic field for the contact arrangement in this work. For the implanted structure, the slope of the as-measured Hall resistance, at
a first glance, seems to change around ±1 T, where the arrows point at in Fig. 4.10(a). After a line
extrapolated from the values between 4 T and 5 T, whose slope is 100 Ω/T, was subtracted, a ferromagnetic-hard-axis-like hysteresis loop was observed, and the saturation magnetic field is around
1.2 T (Fig. 4.10(b)). The slope of the as-measured curve can also be extracted by calculating the
first-order derivative of the as-measured curve, and it stays constant at 100 Ω/T after the magnetic
field reaches 1.2 T (Fig. 4.10(c)). This is the well-known anomalous Hall effect, and the high-field
slope, gives us the two-dimensional electron concentration of the structure: 6.25×1012 cm-2. The
Hall effect measured from the unimplanted structures are plotted in Fig. 4.10(d)-(e). The slope of
the curve stays at the constant value of around 76 Ω/T over the whole magnetic field range and the
two-dimensional electron concentration is calculated to be 8.22×1012 cm-2. The sheet resistances
measured from the unimplanted and the Gd-implanted structures are 50.6 Ω/ and 1025.5 Ω/, respectively, and the calculated (Hall) electron mobilities are 15026.5 cm2/Vs and 975.1 cm2/Vs, respectively. The reduction in both the electron concentration and the mobility is due to implantation
induced defects, which not only might deplete the 2DEG but damage the crystal structure. The
residual Hall resistance is not saturated until 4 T, which could be attributed to certain native paramagnetic defects.
68
(a)
(d)
(b)
(e)
(c)
(f)
Fig. 4.10 (a) As-measured Hall effect curve at 4.2 K from a Gd-implanted van der Pauw structure. The arrows indicate
a change in slope. (b) The curve after high-field values were subtracted from (a). (c) The first-order derivative of (a). (d) As-measured Hall effect curve at 4.2 K from a unimplanted van der Pauw structure. (e) The curve after high-field values were subtracted from (d). (f) The first-order derivative of (d).
69
4.3.2.2 Magnetoresistances of van der Pauw structures
Magnetoresistances (MRs) of the vdP structures were studied by measuring the resistances in
both x- and y-directions, noted as Rxx and Ryy, respectively, with the ordinary two-point technique in
magnetic fields, Bz and By, between ±5 T at 4.2 K. For the unimplanted vdP structures, Rxx and Ryy
in magnetic fields, both Bz and By, have a typical positive MR with a B2-dependence (shown in
Fig. 4.11(a) and (b)), described in Chapter 2.3. Ryy in the magnetic field, By, has the same positive
MR with a B2-dependence, plotted in Fig. 4.11(b), and this could be attributed to the current distributions both in the x-direction and the small tilt angle from the y-direction of the external magnetic
field. The current distribution along the x-direction is due to the electric field distribution, plotted in
Fig. 4.11(c) and (d) [100], which looks substantial. The small tilt angle from the y-direction of the
magnetic field comes from the employed 90°-adaptor for the sample holder, which is not perpendic-
(a)
(b)
(c)
(d)
Fig. 4.11 Rxx and Ryy measured at 4.2 K for the unimplanted vdP structure in (a) Bz, (b) By. The equi-potential lines for
the vdP structure when the current flows along the (c) top edge and (d) the top-right-to-bottom-left diagonal
[100].
70
ular to the z-direction. The MR ratio between 0 T and ±5 T for Rxx and Ryy in Bz is 200%, and that
for Rxx and Ryy in By is only 7%. Note that the very small MR ratio for Rxx in By could result from
the current distribution along y-direction caused by the field distribution.
Instead of the positive MR, the Gd-implanted vdP structures have negative MR for both Rxx and
Ryy in magnetic fields, both Bz and By (in Fig. 4.12). The MR ratios between 0 T and ±5 T are
-12.90% for both Rxx and Ryy in Bz, and -4.76% for both Rxx and Ryy in By, respectively. All the negative MR shows the typical feature of the transverse MR [51].
(a)
(b)
Fig. 4.12 Rxx and Ryy measured at 4.2 K for the Gd-implanted vdP structure in (a) Bz, (b) By.
4.3.2.3 Magnetoresistance of transmission line structures
Magnetoresistances of the TML structures were studied by measuring the resistance in the x-direction, noted as Rxx, in magnetic fields, Bz and By, between ±5 T at 4.2 K. All the measurements
were performed only at the position A from the TML structures. For the unimplanted structures, the
MR curves show the same typical positive B2-dependence as from vdP structures (in Fig. 4.13(a)
and (b)), and the MR ratios between 0 T and ±5 T are 700% for Rxx in Bz, and 24.24% for Rxx in By,
respectively.
The Rxx at zero field is twice as large as the unimplanted one, which results from the defects induced by Gd-implantation. The Rxx in Bz from the implanted structures has, at a first glance, a positive B2-dependence as well, but when plotted together with the unimplanted curve, the dependence
71
is obviously weaker for the Gd-implanted curve for the magnetic fields between 0 T and ±4 T. The
overall positive MR with B2-dependence is reasonable, for that the implantation pattern is smaller
than the area of the structure, and we can use the series resistance model as the first-order approximation for the contribution of the implanted part. The influence of the Gd-implantation can be then
estimated by subtracting the unimplanted value from the implanted ones, and the typical negative
MR was observed (in Fig. 4.13(c)) with the MR ratio, -89.47%, between 0 T and ±5 T. The Rxx in
By first decreases as the field increases to a value between 0.2 T and 0.6 T, which is the saturation
field along the easy axis, and then it increases with the B2-dependence as the field increase to 5 T in
both directions (in Fig. 4.13(b)). This is, as mentioned previously, the typical transverse MR curve,
and the MR ratio between the zero-field and the saturation field is around -4.22%.
(a)
(c)
(b)
Fig. 4.13 Rxx measured at 4.2 K for unimplanted (solid
symbols) and Gd-implanted (open symbols) in
(a) Bz and (b) By, and (c) the difference between Gd-implanted and unimplanted curves in
(a).
72
4.4 Summary
In this work, the 300-keV Gd3+ ions were successfully incorporated in zinc-blende GaN by room
temperature FIB implantation, whose doses range from 1×1012 cm-2 to 1×1015 cm-2. The XRD pattern revealed no indications of phase segregated GdN. The magnetic measurements found out that
only the sample implanted with highest dose exhibits certain magnetic ordering at low temperatures.
Due to its paramagnetic-like hysteresis loop, the magnetic ordering is suggested to be superparamagnetic-like. The temperature of the magnetic ordering is 60 K. Comparing the results to Ref. 39,
the spontaneous electric polarization in the wurtzite GaN is thought to be essential in yielding the
long-range magnetic order.
The 200-eV Eu2+ ions were FIB-implanted at room temperature into wurtzite GaN, and the doses
range from 1×1014 cm-2 to 3.5×1015 cm-2. All of the samples show only paramagnetic behavior without any magnetic ordering at low temperatures. The small spin splitting of Eu in GaN is thought to
be the deciding factor for these nonmagnetic Ga1-xEuxN.
The 2DEG of a GaN-based HEMT structure was not depleted by the 300-keV FIB-implantation
of Gd3+ ions for the ion dose lower than 1×1012 cm-2 at both 300 K and 4.2 K. The anomalous Hall
effect was observed from the Gd-implanted vdP structures, and the saturation field in z-direction
was found to be around 1.2 T. The carrier concentration has the reduction around 25 % and the mobility was decreased to 1/15 of the value prior to the implantation, due to the defects introduced by
Gd-implantation. The negative transverse MR was observed from the Gd-implanted vdP and TML
structures. The MR ratio is smaller when the magnetic field is applied along the y-direction as opposed to along the z-direction.
73
5 Summary and Outlook
5.1 Magnetotransport in cleaved-edge-overgrown
Fe/GaAs-based heterostructures
The epitaxial Fe thin films were successful overgrown on the UHV-cleaved (110)-surface of the
GaAs-based heterostructures. The MOKE magnetometry showed that the overgrown Fe thin films
having the easy axis long the (001)-direction of the heterostructures, but the anisotropy is rather
weak. The reasons for the weak anisotropy cab be attributed to the 1.4 % lattice mismatch between
Fe and GaAs and/or the terrace structures on the cleaved edge.
Successful FIB milling was then carried out with 30-keV Ga+ ions. It takes the doses of
3×1016 cm-2 and around 1×1017 cm-2 to mill through the 20-nm thick Fe film capped with a 5-nm
thick Au film, which revealed by the AFM measurement. The I-V characteristics show that the FIB
milling induces a parallel conducting channel, and the channel can be removed by diluted HCl.
However, there is over-etching for the Fe thin film in the diluted HCl, and the fabrication of the
spin valve was carried out without dipping in HCl.
The contacts between the cleaved-edge-overgrown (CEO) metal thin films and the GaAs-based
heterostructures shows the Schottky-like behavior, and this agrees with the theory. Due to the FIBinduced parallel conducting channel, the I-V characteristics of the spin valve structures showed no
consistency from sample to sample and has the metal-like temperature dependence of resistances.
The MR measurements on the spin valve structures showed inconsistence not only from sample
to sample, but from measurement to measurement as well. The MR ratios, if MR was observed,
ranges between 0.5 % and 0.7 % for the bulk n-GaAs and between 0.014 % and 0.057 % for the δdoped n-HEMT structures, respectively. These values are comparable to the longitudinal MRs
measured from the lithography-made L-shape contacts. The observed MR curves have the
74
switching field well agreed with the model from Ref. 53 and the longitudinal MR measurement.
Since 1) the Schottky contact is known as one kind of the required spin-selective contact from the
optical observations of electrical spin injection, and 2) these optical measurements do not have the
dependence of the contact resistance, it is possible for us to perform the optical investigation in this
cleave-edge-overgrowth geometry. A lateral light emitting device (LED) is required for the optical
study, and such an device can be realized by local doping or overcompensation of the charge
carriers in the semiconductor heterostructures with FIB implantation [101, 102]. The ferromagnetic
metals are then overgrown on the cleaved edge as the n-type Schottky contact of the spin injection.
A study of the optical polarization of lateral p-n diodes realized by overcompensating a p-type
pseudomorphic HEMT locally with FIB implantation of Si, and it showed that there is no optical
polarization from such kind of diode – shown in Fig. 5.1 [103]. It is also possible to study optically
the spin relaxation in the CEO lateral diode to study when we variate the distances between the
cleaved edge and the p-n junction.
Fig. 5.1 Intensity versus polarization plot of the emitted
light from a lateral p-n diode on a p-type
pseudomorphic HEMT structure by locally
overcompensation with FIB-implanted Si ions.
The rotation angle of the λ/4-plate represents the
different polarization of the light, e.g., ±45 ° are
for the left- and right-circular polarization,
respectively.
5.2 Magnetotransport in rare-earth-doped GaN-based
heterostructures
The 300-keV Gd3+ ions were successfully incorporated in zinc-blende GaN by room temperature
75
FIB implantation, whose doses range from 1×1012 cm-2 to 1×1015 cm-2. The XRD pattern revealed no
indications of phase segregated GdN. The magnetic measurements with SQUID found out that only
the sample implanted with highest dose exhibits certain magnetic ordering at low temperatures. Due
to its paramagnetic-like hysteresis loop, the magnetic ordering is suggested to be
superparamagnetic-like. The temperature of the magnetic ordering is 60 K. Comparing the results to
Ref. 39, the spontaneous electric polarization in the wurtzite GaN is thought to be essential in
yielding the long-range magnetic order.
The 200-eV Eu2+ ions were FIB-implanted at room temperature into wurtzite GaN, and the doses
range from 1×1014 cm-2 to 3.5×1015 cm-2. All of the samples show only paramagnetic behavior
without any magnetic ordering at low temperatures. The small spin splitting of Eu in GaN is
thought to be the deciding factor for these nonmagnetic Ga1-xEuxN.
The 2DEG of a GaN-based HEMT structure was not depleted by the 300-keV FIB-implantation
of Gd3+ ions for the ion dose lower than 1×1012 cm-2 at both 300 K and 4.2 K. The anomalous Hall
effect was observed from the Gd-implanted vdP structures, and the saturation field in z-direction
was found to be around 1.2 T. The carrier concentration has the reduction around 25 % and the
mobility was decreased to 1/15 of the value prior to the implantation, due to the defects introduced
by Gd-implantation. The negative transverse MR was observed from the Gd-implanted vdP and
TML structures. The MR ratio is smaller when the magnetic field is applied along the y-direction as
opposed to along the z-direction.
For the unannealed Gd- and Eu-implanted GaN films, the FIB-induced defects were assumed
contributing to the large effective magnetic moment per Gd atom, but they might reduce the
strength magnetic interaction, which is responsible for the magnetic ordering. It is, therefore,
important to anneal the samples and study their magnetic properties again. This will increase our
knowledge about the GaN-based diluted magnetic semiconductors (DMSs) realized by
incorporations of the rare-earth elements. Investigations for the degree of the optical polarization of
the photoluminescence from these samples are also useful for both understanding the GaN-based
DMSs and the applications in optoelectronics and spintronics.
As mentioned in Cahpter 4.2, Ce-, Nd-, Sm-, Eu-, Ho-, and Er-doped wurtzite GaN has stable
ferromagnetic state [97], and to the author's knowledge, there is surprisingly no reports on the
magnetic properties of Ce-, Nd-, Sm-, and Ho-doped wurtzite GaN. Incorporation of Ce, Sm, Nd,
76
and Ho into wurtzite GaN is worthy of studying, and the study of the Ho-implanted wurtzite GaN is
already underway by the time the author finished this thesis.
For the magnetotransport in the Gd-implanted GaN-based HEMT structures, it is important to
measurement the quantum Hall effect (QHE) to see if there exists the zero-field spin splitting in the
Shubnikov-de Haas oscillations as well as at high magnetic fields. The measurements shall also be
carried out on the annealed HEMT structures after Gd-implantation.
77
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Acknowledgement
It is impossible for me alone to finish this work, and I am greatly indebted to and appreciate for
all the help from everyone along the way. Especially, I want to thank the following people:
Prof. Dr. A. D. Wieck for offering me the opportunity and the topic in pursuit of my Ph.D in
Lehrstuhl für Angewandte Festkörperphysik and the continuous support.
Dr. D. Reuter for supervising my work, offering exciting and beneficial discussions and critical
review about my work, sharing his research and teaching experiences, and the timely hints and
pushes, which benefited me greatly throughout the whole work.
Dr. A. Melnikov for the fabrication of all the ion sources, the technical help with the FIB columns,
sharing his experiences, and the great mood and tolerance.
Dr. A. Ney for the SQUID and XRD measurements, and beneficial discussions on magnetism.
Additionally, I learned from the aforementioned four persons how to conduct myself in a
collaborative project, and how to plan and proceed a work carefully and critically, which makes me
mature and, hopefully, a better physicist.
Dr. J. Yang,
Ellen Schuster
and
Prof. Dr. W. Keune
at
Universität
Duisburg-Essen,
Christian Urban, Sani Noor, Carsten Godde and Prof. Dr. U. Köhler of EPIV at RuhrUniversität Bochum, for the semiconductor and metal MBE growth for the cleaved-edge-overgrown
heterostructures and beneficial discussions.
Dr. S. Potthast, J. Schörmann, Prof. Dr. As, and Prof. Dr. Lischka at Universität Paderborn,
Dr. S. Pezzagna, and Dr. Y. Cordier at CRHEA, CNRS, France, for the semiconductor MBE
growth of the GaN samples applied in this work.
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Dr. Dorina Diaconescu,
Dr. Peter Schafmeister,
Dr. Andrè Ebbers,
Dr. Sascha Hoch,
Dr. Christof Riedesel, and Dr. Peter Kailuweit, for introducing me the techniques and apparatus
applied in the Lehrstuhl, useful discussions in Physics, and sharing and having some fun together
after work.
Rolf Werndardt and Georg Kortenbruck for helping getting accommodated in Germany, the
technical help, trouble-shooting experiences, and some funny jokes.
Dr. Safak Gök for AFM measurements, useful discussions on spintronics, and exchange of life
experiences. Dr. Mihai Draghici for helpful discussions and informations and the help of FIB
implantation. Mirja Richter, Christian Werner, and Nadine Viteritti for helpful discussions and
technical support. Dr. Mario Brands and Christoph Hassel for the electron beam lithography.
K.-S. Wu and Prof. Dr. M.-Y. Chen of Thin Film Physics Laboratory at National Taiwan
University, Taiwan, for AFM measurements.
All the AFP members for the support, and the friendly working atmosphere.
Yuan-Juhn Chiao for the English corrections of the thesis.
Yin-Zu Chen, my girlfriend, for her support and encouragement to keep me going.
The last, but never the least, I thank my parents for the upbringing, love, care, and support, which
made it possible for me to finish the Ph.D work.
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Curriculum Vitae
Fang-Yuh Lo born on 18.03.1975 in Taipei City, Taiwan.
09/1981 – 06/1987
Taipei Mandarin Experimental Elementary School, Taipei City, Taiwan
09/1987 – 06/1990
Taipei Municipal Nanmen Junior High School, Taipei City, Taiwan
09/1990 – 06/1993
Taipei Municipal Chien-Kuo Senior High School, Taipei City, Taiwan
10/1993 – 06/1997
Bachelor Studium, Department of Physics, National Taiwan University,
Taipei City, Taiwan
07/1995 – 06/1996
Chairman, Student Society of the Department of Physics, National Taiwan
University, Taipei City, Taiwan
09/1997 – 06/1999
Master Studium, Graduate Institute of Physics, National Taiwan University,
Taipei City, Taiwan
Topic: Faraday Magneto-optical Spectroscopy of BixY3-xFe5O12 Thin Films
Supervisor: Prof. Dr. Ming-Yau Chern
09/1997 – 06/1999
Teaching assistant, Department of Physics, National Taiwan University,
Taipei City, Taiwan
Lecture: Quantum Physics
Lecturer: Prof. Dr. Yih-Yuh Chen
09/1997 – 06/1999
Student representative and board member, Consumer's Cooperative, National
Taiwan University, Taipei City, Taiwan
07/1999 – 03/2001
Military Service
04/2001 – 06/2002
Research assistant, Thin Film Physics Laboratory
Topic: Pulsed Laser Deposition of Single Crystalline ZnO Thin Films
Laboratory leader: Prof. Dr. Ming-Yau Chern
08/2002 – present
Doktorand and wissenschaftlicher Mitarbeiter, Lehrstuhl für Angewandte
Festkörperphysik, Ruhr-Universität Bochum, Germany
Topic: Magnetotransport in cleaved-edge-overgrown Fe/GaAs-based and
rare-earth-doped GaN-based heterostructures
Supervisor: Prof. Dr. A. D. Wieck
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List of Publications
Peer Reviewed Journals
[1] Ming-Yau Chern, Fang-Yuh Lo, Da-Ren Liu, Kuang Yang and Juin-Sen Liaw, Red Shift of
Faraday Rotation in Thin Films of Completely Bismuth-Substituted Iron Garnet Bi3Fe5O12,
Jpn. J. Appl. Phys. 38, 6687 (1999).
[2] N.C. Gerhardt, S. Hövel, C. Brenner, M. R. Hofmann, F.-Y. Lo, D. Reuter, A. D. Wieck,
E. Schuster, W. Keune, and K. Westerholt, Electron spin injection into GaAs from
ferromagnetic contacts in remanence, Appl. Phys. Lett. 87, 032502 (2005).
[3] N. C. Gerhardt, S. Hövel, C. Brenner, M. R. Hofmann, F.-Y. Lo, D. Reuter, A. D. Wieck,
E. Schuster, W. Keune, S. Halm, G. Bacher, and K. Westerholt, Spin injection light-emitting
diode with vertically magnetized ferromagnetic metal contacts, J. Appl. Phys. 99, 073907
(2006).
[4] C. Hassel, M. Brands, F. Y. Lo, A. D. Wieck, and G. Dumpich, Resistance of a Single Domain
Wall in (Co/Pt)7 Multilayer Nanowires, Phys. Rev. Lett. 97, 226805 (2006).
[5] F.-Y. Lo, A. Melnikov, D. Reuter, A. D. Wieck, V. Ney, T. Kammermeier, A. Ney,
J. Schörmann, S. Potthast, D. J. As, K. Lischka, Magnetic and structural properties of Gdimplanted zinc-blende GaN, Submitted to Appl. Phys. Lett. 90, 262505 (2007).
[6] F.-Y. Lo, A. Melnikov, D. Reuter, Y. Cordier, J.-Y. Duboz, and A. D. Wieck,
Magnetotransport in Gd-implanted wurtzite GaN-HEMT structures, in preparation.
Conference Papers
[1] E. Schuster, W. Keune, F.-Y. Lo, D. Reuter, A. Wieck, K. Westerholt, Preparation and
characterization of epitaxial Fe(001) thin films on GaAs(001)-based LED for spin injection,
Superlattices Microstruct. 37, 313 (2005).
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[2] N. C. Gerhardt, S. Hövel, C. Brenner, M. R. Hofmann, F. Lo, D. Reuter, A. D. Wieck,
E. Schuster, and W. Keune, Spin-controlled LEDs and VCSELs, Proc. SPIE, 5722, Physics and
Simulation of Optoelectronic Devices XIII, 221 (2005).
[3] S. Hövel, N. C. Gerhardt, C. Brenner, M. R. Hofmann, F.-Y. Lo, D. Reuter, A. D. Wieck,
E. Schuster, and W. Keune, Spin-controlled LEDs and VCSELs, phys. stat. sol. (a) 204, 500
(2007).
DPG-Tagung Posters
[1] Fang-Yuh Lo, D. Reuter, A. Dremin,M. Bayer, E. Schuster, W. Keune, and A. D. Wieck,
Optical and electrical observations of spin injection from Fe into GaAs-based heterostructures,
Regensburg, 2004.
[2] Fang-Yuh Lo, D. Reuter, E. Schuster, W. Keune, and A. D. Wieck, Electrical searches of spin
injection from Fe into GaAs-based heterostructures, Berlin, 2005.
[3] Fang-Yuh Lo, D. Reuter, E. Schuster, W. Keune, C. Urban, U. Köhler, and A. D. Wieck,
Electrical properties of Fe/GaAs-heterostructures in cleaved-edge-overgrowth geometry,
Dresden, 2006.
[4] Fang-Yuh Lo, A. Ney, A. Melnikov, D. Reuter, S. Potthast, J. Schörmann, D. J. As, K. Lischka,
S. Pezzagna, Y. Cordier, J.-Y. Duboz, and A. D. Wieck, Gd- and Eu-implanted GaN,
Regensburg, 2007.