Magnetotransport in Cleaved-Edge-Overgrown F e/GaAs-based and Rare-Earth-Doped GaN-based Heterostructures

Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften in der Fakultat fur Physik und Astronomie der Ruhr-Universitat Bochum

vorgelegt von Fang-Yuh Lo

geboren in Taipei, Taiwan

Lehrstuhl fur Angewandte Festkorperphysik

2007 Der erste Gutachter: Prof. Dr. Andreas D. Wieck

Der zweite Gutachter: Prof. Dr. Daniel Hagele

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 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

4 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 Summary 72

5 Summary and outlook 73 5.1 Magnetotransport in cleaved-edge-overgrown Fe/GaAs-based

heterostructures 73 5.2 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 ALGa^As

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 In xGa1-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 H Hamiltonian h Planck constant h 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 ke 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 Y voltage v, v velocity w width X a certain physical quantity Y sputtering yield Z atomic number

Y gyromagnetic ratio

€ electric field

e permitivity (dielectric constant) ^0 permeability in vacuum

^B Bohr magneton q electro-chemical potential p resistivity G conductivity

G± left (+) and right (-) circularly polarized light, respectively

T relaxation time 0 electrical potential

X susceptibility to (angular) frequency 7

1 Introduction

Spintronics is an exciting and up and coming field in both scientific researches and the applicati­ ons 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 in ­ jected 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 magnetoresi­ stance (TMR). Spintronics exploiting GMR and/or TMR can be called metal-based spintronics or magnetoelectronics [2, 3]. Unfortunately, spin injection from ferromagnetic metals into semicon ­ ductors 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 interdis ­ ciplinary 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, semicon ­ ductor 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. Julliere in 1975 [6], and GMR was observed inde ­ pendently 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 commer­ cially available spintronic devices. 8

Semiconductor spintronics attracted great interest since S. Datta and B. Das proposed the prototy­ pe 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 elec­ trons flowing from source to drain can be controlled by the gate voltage. The first GaAs-based dilu ­ ted 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. Jaffres, and others. Due to the conductivity mismatch [13] and spin-related properties of the me­ tal-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 Event Contributor Source First observation of the anisotropic magnetore­ 1856 Lord Kelvin [5] sistance, AMR 1879 Discovery of the Hall effect E. C. Hall 1921 Discovery of (atomic) spins O. Stern and W. Gerlach First observation of the tunneling magnetoresi­ 1975 M. Julliere [6] stance, TMR First theoretical work on electrical spin injecti ­ 1976 A. G. Aronov and G. E. Pikus [12] on 1985 First observation of electrical spin injection M. Johnson and R. H. Silsbee [1] M. N. Baibich et al. [7] 1988 Discovery of the giant magnetoresistance, GMR G. Binasch et al. [8] 1990 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 End of Commercial magnetoresistive read/write head 1990s First commercial magnetoresistive random ac­ 2005 Freescale Semiconductor [19] cess 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 pos­ sible devices in spintronics. Most recently, spin noise spectroscopy was applied to study spin dyna ­ mics 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-overgrow- th (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 unconta ­ minated 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-edge- overgrown 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 ferro­ magnetic 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 ferroma­ gnetic 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 GaAs- and GaN-based heterostructures, magnetism, magnetoresistances in material, electrical spin injec ­ tion, 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 dis ­ cussed. 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 out­ look of the works in this thesis. 11

2 Theoretical Background

In this chapter, the underlying background knowledge to this work will be discussed. The discus ­ sion begins with a brief description of the GaAs- and GaN-based heterostructures, which is follo­ wed by the discussions of magnetism, the magnetotransport and the theory of spin injection, the di ­ luted magnetic semiconductors, and finally, the focused ion beam.

2.1 Introduction to GaAs- and GaN-based heterostruc­ tures

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 heterostruc­ tures are the layer structures fabricated by molecular beam epitaxy (MBE) or by metal-organic che­ mical 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 impuri­ ties, 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 mi­ grate to another. For example, an n-type Si-doped Al0.35 Ga0.65As 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 schematical­ ly-

(a) eeeeee ©0000®

w-AIGaAs

Fig. 2.1 Schematic depiction of the conduction band around a heterojunction between /7-AlGaAs and undoped GaAs, noted as /-GaAs, (a) before and (b) after the charge migration.

An alternative doping technique is called d-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 con ­ centration.

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 hete­ rostructure. The physical properties of the heterostructure can be directly derived from each compo­ nent. (ii) There are fewer technical challenges for the fabrication. As mentioned above, the lattice- matched semiconductor heterostructures have generated great interest in physics and applications. However for certain applications, for example the In xGai_xAs (InGaAs) in fiber optics communicati ­ ons and GaN for the blue laser diode [41], the lattice-mismatched materials are needed. The lattice- mismatched systems such as InAs/GaAs-, Si/Ge-, and AlN/GaN-heterostructures, are of great im­ portance 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, AIN, and their al­ 13 loys, the 2DEG is formed at the interface between Al,Gau,N (AlGaN) and GaN even without do ­ ping. 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 ari­ ses 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 /i-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].

Fig. 2.2 Room temperature conduction (red) and valence (blue) band edge profiles of (a) a 5-doped HEMT structure and (b) a bulk ;?-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 yel­

low; the intrinsic Alo.35Gao.s5As are in dark purple; the light blue lines represents the Si 5-doping, and the n- GaAs 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 hete­ rostructures applied in this work: a 5-doped HEMT and an %-GaAs (n 3D = 1 x 1017 cm-3). The calcu­ lations were carried out with a lDPoisson program written by Prof. Gregory Snider at the Universi ­ ty of Notre Dame, USA [46].

2.2 Magnetism

The effect of magnets have been known to human beings for several thousand years, but its mi­ croscopic origin was not understood until the observation of current-induced magnetic field by H. C. Oersted in 1821 and the discovery of the atomic spin by O. Stern and W. Gerlach a century la­ ter. 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 induc ­ tion), B, is described by the Biot-Savart law, m r d / x r _ m I (v % r) B = 4 ^J r 3 4 n / ' ^ where go 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 x r)-term. The magnetic (dipole) moment, m, is then written as, m = IJ 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 = yJ = y(L + S) , (2.3) where y is the gyromagnetic ratio of the atom, L and S are the total orbital and spin angular momen ­ ta 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, H, e 2 H — H o + m(L + g S )B + E( Bx r, )2 (2.4) 8m„

Z e h where H0 — ^ (——+ Vi) is the original Hamiltonian, V b — 2^ is the Bohr magneton, V is 2m„ i — 1 2m 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 ex­ change, 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 separa­ ting the response of spin-up and spin-down electrons. This is the molecular field theory, which ass­ umes that all spins are subjected to an identical average exchange field, XM, 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 mo­ lecular field. Such a positive feedback can, under the Stoner criterion, lead to spontaneous ferroma­ gnetism.

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 ±SE from the Fermi energy, EF. Then the num ­ bers of the spin-up (spin-down) electrons and the total energy difference, AEdos, are therefore

Nt — 1 N + D(Ef)5E , (2.5)

N,— 1N - D(Ef)S E , (2.6) and AEDOS — 2 D(EF)(5E)2 , (2.7) where Nis 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 — mb (Nt - Ni) — 2mBD(e f)5E (2.8) by assuming an electron has the magnetic moment 1 Ub, and the energy reduction, AEmb, from the molecular field is

J m0(AM') dM' — -2m0AM2 — -2m0mBA(D(EF)5 E)2 A EMB (2.9) o 2 Writing U — m0mB A , the total energy, AE, is 17

AE = AEdos + AEMB = 2 D{EP) {5E)2 (1 - U D{EP)) . (2.10)

When AE < 0, i.e., UD(EP) > 1, spontaneous ferromagnetism is possible, and this is the aforemen ­ tioned Stoner criterion.

AE

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 Fenni energy and the spin-down electrons have lower energy. The energy difference from the Fenni level is ±8E.

D(E) D(E)

It is also possible to study the magnetism by first-principle ab-initio electronic band structure cal­ culations. 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 in ­ teractions 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 homo­ geneous 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 (EDA). 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 exam-

i pie, a function, f(x) = 1 -x2, maps 1 to 0, and a functional, F[f(x)] — J f(x) , maps the function,

f(x) = 1 -x2, to 4/3. 18 electron and the spin densities are taken into consideration, the spin density functional theory to­ gether with the local spin density approximation (LSDA) are applied [47]. Fig. 2.4 shows the spin- resolved DOS of Cu, Co, and Fe from the ab-initio calculation [48].

- Cu(up) - Fe(up)

-l -

Cu(dn) Fe(dn)

ENERGY

Fig. 2.4 Spin-resolved density of states of copper, cobalt, and iron, where up and dn denote the up- and down-spins, re­ spectively. The dash lines mark the position of the Fermi level [48].

2223 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 magne­ tic 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 ali­ gned by the external field. When the magnetic field decreases, the magnetization decreases accor­ dingly. The overall paramagnetic behavior can be semi-classically described by the Langevin func ­ tion. The saturated magnetization decreases rapidly as the temperature increases, and the susceptibi­ lity, x, obeys the Curie's law, / = Cc 1\ where / is given by M — XH , (2.11) and H is also called the magnetic field,

B = ia0{H + M) = p0(l + X)H . (2.12)

Fig. 2.5 shows the field(a) and temperature(b) dependences of a paramagnetic material described by Langevin function.

0.0 0.5 1.0 .5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Fig. 2.5 (a) Magnetic field and (b) temperature dependence of the magnetization of a paramagnet according to the Lan ­ gevin 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 beco­ mes zero at the coercive field, Hc. This is the hysteresis loop of ferromagnetic materials. The satura­ ted 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 susceptibi­ lity of a ferromagnet is orders of magnitudes larger that of a paramagnet, and it obeys the Curie- Weiss law, / = 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 M/b). 20

^ 0.5 -

T/Tc

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 con ­ centration 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 ma­ gnetic 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 depen ­ dence, 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, B:, and the charge carriers experience the Lorentz force, FL, (2.13) 21 and gain additional momentum along the y-direction. This induces a potential difference, Vv, 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 magnetoresi­ stance (MR) effect, and the former is the well-known Hall effect, where Vv can be easily calculated by balancing the Lorentz force and the induced electrostatic field in y-direction, I,B, V (2.14) 1 nm e d W2D S 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 /, flows in the x-direction, the magnetic field B points along the z-direction - denoted as Bz in the text, and the Vy = IThis figure is adopted from / the National Institute of Standards and Technolo­ gy. USA [49].

V ■ V,H

Analyzing the phenomenon by the equation of motion with the effective mass, m*, and relaxation time, t„, , approach [50],

= cl(e + vXBz) , (2.15) Gl Tm the current densities, for electrons, along x- and y-directions are given by crn 6T — (J.... 6". J X = -n3D e i;.v = (2.16) and

Jy = ""3D ^ Vv - / 2 2 €x = O'.™ , (2.17) 1+01CT,„ where o 0 is the conductivity in zerot magnetic field,

(2.18 ) m and coc is the cyclotron frequency, 22

eB, "c _ (2.19) m In terms of resistivity, the results are

1 i 2 2 e^T m 1 1 +Wc Tm _Pc (1 ^^fB2) (2.20) P xx _ m* Vo and the magnetoresistance (MR) is written as

MR _ Ap_ R(B)- R(0) _ (2.21) P R(0) m Z where p0 = 1 / a0, is the resistivity without magnetic field, and the MR ratio is defined as _ Ap_ R (B)- R (0)_ e2 T 2 MR _~p R(0) ~m:TB- • (2.22) which is proportional to B/. The Hall resistivity, pH, is given by

1 ^c Tm 1 (2.23) Ph _ P _ -P0 Wc Tm _ ■B, . ar n3D e

2.3.2 Magnetoresistance in ferromagnetic materials

For ferromagnetic materials, the magnetoresistances have additional features due to their sponta ­ neous magnetization. These are the well-known anomalous Hall effect and the anisotropic magneto­ resistance (AMR) effect.

The discussion of the anomalous Hall effect can be treated qualitatively by substituting BZ with ^o (H, + M,) into equation 2.23,

1 1 P0 PH B, _ — P0 (H , + Mz) _ B-Z.ex,, ^M" z . (2.24) '3D ^ "3D e n 3D e n 3D e 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, B,, is smaller than the saturation field, the second term is the dominating effect. After B, 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

Ph _ RoB + P0 RaM , (2.25) 23 where Ra 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.

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 pxx in B:, and the longitudinal MR represents pxx in Bx [51]. Qualitatively, a transverse magnetic field rotates the magnetization of a ferromagnet about the easy axis, and there­ fore from zero field to the transversal saturation field, the magnetization of the ferromagnet beco­ mes aligned as the magnetic field increases. This leads to a decrease in the resistance, for the spin- dependent 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 ^-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

(I))1™

1.000 CD I 0.996

0.992

Fig. 2.9 Magnetoresistances of a ferromagnet, wliich 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 x B)-term is zero. However, a fer­ romagnet 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 follo­ wing. 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 in ­ creases until the so-called switching field, and at the switching field, the resistance increases sud ­ denly to the saturation value of the resistance. The values of both the switching field and the resi­ stance 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 magne­ toresistance (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 polarizati­ on, Px, of a physical quantity, Z, as

P x ^A + (2.26) A 25 where X is 1 or f for up-spins, and -X is -1 or j for down-spins, respectively. For example, the spin polarization of the DOS, D(E), and of the current density, j, are

P — D (E)T~ D (E )j j t - j i and P j — . . D (E) D (E )T + D (E X /T 1 VT'J T + VIJ i respectively. PX > 0 means that there is larger contribution to Xfrom f than j , 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 trans ­ port is described by the Ohm's Law, and the spin-dependent diffusion equation and the electro-che­ mical potential, p.x, are written as j'A^VF, , (2.27) and eD, Fa-" 5 n,— V (2.28) O, where o X is the conductivity, DX is the diffusion constant, 5 nA — na — nA0 is the non-equilibrium spin, and V is the electrical potential. At the steady state, the equation of continuity for the degene ­ rate electron gas is given by

2 / NaN —a \ Fa F—a , 2/ Na N —a \ Fs V-jA—Ae ^( ) — Ae (- ) (2.29) N A + N—A T„ N A + N—A T.

ta,—at—a,a where Ts — is the spin relaxation time, and Fs=Fa— F—a ta,—a + t—a,a

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,

F s;N ( 0 ) ——2 rNjPj , (2.30) which can be called the spin accumulation,

Fs;N ( 0) — Fs;F ( 0) — 2 rcj (Pj — Po;c) , (2.31) which describes the spin injection ( PO;c is the spin polarization of the contact conductivity), and the spin polarization of the current density in the N-region is

rcP o-c+rpP o P — ^ O;c^r F1 o;F — — P J rN+rc+r " (2.32) cF 26 where P a:P is the spin polarization of the F-electrode conductivity [3],

(a) (b) N 1 F (: N rN

rF t"r t rF « rN Pa.F P,,-c Pr.e Pn;F

L,:F |1 II Kr 4 J k——► ls:F •*—► 4------► 1------► ------k. -V2 V2

Fig. 2.10 Schematic depiction of a (a) semi-infinite F/N-junction and (b) F/N/F-stmcture. 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 rc — 0 , and the current-density spin polarization is

p _rFPv:F (2 33) ■’ r N+r F

For GMR, rN is comparable to />, Pj can be measured, but when rN is much larger than />, 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 de ­ cisive role when TMR or spin injection into semiconductors is investigated [54].

To detect P} 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 mea­ surements 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 val ­ ve. The measurements, similar to its optical counterpart, are to read out the current (or the resistan ­ ce) 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, d N, 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 = Ar = Rn - Rtt = AR p R# RTT ' (2^4) where and ft represent that magnetizations of the two F-electrodes are antiparallel or parallel to each other, respectively. The values after A. Fert and H. Jaffres [55] are

2 (rcPD(Ef);c + rFPD(EF);f ) A R = (2.35) (rc + rF) cosh() + Ln [ 1 + (^)] sinh () ’

Ls;N 2 rN Ls;N and - 2 N + 2 rc (1-PD(EF),c) Rtt = 2 rF (1 - PD (EF) ,F. + rN L N -N r F rc ( P D ( Ef) ,F PD ( Ef ) ,c) + rN ( r FP D (E f) ,F + r c P D ( Ef ) ,c) tanh ( ) 2L ;N +2 , (2.36) -N (rF + rc) + rN tanh ( ) 2 Ls;N where P d(e f) is the spin polarization of the density of states at the Fermi level. Significant MR ap­ pears when rc falls in the following range

r« ( Ll- )< rc < rN (LLs;‘f-) . Ls ; N d N (2.37)

d For r c

L r rate observable MR, and for rc » rN(-——) (or equivalently, dN » (—)Ls;N ), the spin pola- -N rc rization of configuration is completely relaxed by the spin flip in the N-region, i.e., Rn ~R tt , and thus no MR.

By applying Fe for both of the ferromagnetic electrodes ( P d(e „) = 0.45, p = 9.71 x 10-6 Q-cm,

Ls;F = 12 nm [56] ), %-GaAs with the longest spin life time in magnetic field (n 3D = 1 x 1016 cm-3, rN ~ 4x 10-5 Q-cm2, and LS;n = 2 pm [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 x 1 pm2 junction calculated for dN = 2 pm, 200 nm, and 20 nm is shown in Fig. 2.11. 28

Fig. 2.11 MR calculated after A. Fert and H. Jaffres. Both of the ferromagnetic electrodes are made of = 2 pm ------

0.12 - time in magnetic field is chosen as the nonma­

0.08 - gnet: n 3D = lx1016 cm"3, rY~ 4/ KG Q-cnr , and /.,v = 2 pm. The PD {Er) of the spin-selective con ­ tact is assumed to be 0.5. The contact area is lxl pm2.

The theory of optical measurement is simpler than the MR measurement, for that the optical tran ­ sitions 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 o+, 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 pro­ bability ratio 3:1:2. The emission of the right circularly-polarized light, denoted as o“, 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 //+ and //_, respectively, and then the spin polarization of the electron density, Pm is given by

P - (2 38) n+ + //

Since all the holes have very short spin life time, we can treat them as unpolarized. Then for a bulk­ like sample, the circular polarization of the luminescence, PI:cir, is calculated to be P =I+~F (//+ + 3// ) — (3//+ + // Pn I :cir 7+ (2 39) I + / (//+ + 3//J + (3//+ + n 2 ’ where P is the light intensity for o+ and o , respectively. In a quantum well, where the hh-lh dege neracy is lifted, P =I+~F 3/7 — 3 77 + - -P. (2.40) I'c,r I+ + / 3 //_ + 3 //, 29

e, -1/2 e, +1/2 Fig. 2.12 Optical transitions of the left-circularly po­ larized (o. solid lines) and the right-circu-

larly polarized light (o . dashed lines) of bulk GaAs. The ground states of the elec­ trons and holes are denoted by their names and the projection of the total angular mo­ mentum along the z-direction. The num ­ bers in circles represent the ratio of the transition probabilities. so,-1/2 so, +1/2

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 di ­ rectly 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 reverse- bias [14 - 17]. Spin injection in forward-bias were reported as well [58, 59]. Spin injection in re- mant state is required for optical device applications in spintronics, and was observed by Ger- hardt etal [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 GaiJVhhAs has the following characteristics, 1) /i-type semiconductor for that the Mn is an acceptor in GaAs, 2) charge-mediated ferromagnetism via the RKKY interaction, 3) gate-bias controlled fer­ romagnetism [64], which is the direct consequence from 2), 4) low solubility of Mn in GaAs, maxi­ mum 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 Gai_.x.TMxupN while in the spin-glass-like state, the magnetic moments of

TMs have two components, which are anti-parallel, and noted as Gai-x-TMx./2upTMx./2down N.

AE = TE(Gai_x.TMx./2upTM.x./2down N) - TE(Gai _.xTM.xupN) 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 fer­ romagnetic state is stable for Gai.xVxN and Gau,Crv N while Gai.xFexN, Gai.xCoxN, and Gai_xNixN are stable in the spin-glass-like state. For Gai.xMn xN, it is stable in ferromagnetic state for low Mn con ­ centrations 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. Kataya­ ma-Yoshida and K. Sato as well and depicted in Fig. 2.14. The valence band consists mainly of N- 2p 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 ex­ change splitting, which leads to high spin configurations. Considering the local symmetry, the five-

Up spin fa) V; 5% Up spin (b) Cr: 5% Up spin (c) Mn; 5%

----- Total -----Total ----- Total Down spin Down spin Cr-3d Down spin

Up spin id) Fe; 5%_ Up spin Up spin

Down spin Down spin Co-3d Down spin Ni 3d -4 -2 Energy relative to the Fermi energy (eV)

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 3dy states and threefold degene ­ rate 3ds states. The 3ds orbitals, having the symmetry of the functions xy, yz, and zx, hybridize well with p orbitals of valence bands and make the bonding (tb) and the anti-bonding (ta) states. The

3dy orbitals, having the symmetry of the functions 3z2-r and x 2-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 so­ mewhere between the Fermi level and the conduction band edge, and the e states, due to the non ­ bonding 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 Gau,TIVf N has ferromagnetic ground state, which is the case for Ga0.95Cr0.05N and Ga0.95Mn 0.05N. The ferroma­ gnetic 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 Ga, _.VTMVN

Substitutional Site (S-site) Energy >1

Conduction Band anti-bonding state Fig. 2.14 Schematic depiction of the electronic struc­ ture of TM at a substitutional site in GaN. d(3z -r ), d(xV)l [ d(xy), d(yz), d(zx) The anti-bonding ta states and the non-bon­ x non-bonding state ding e states appear in the band gap [67].

bonding state

Valence Band

For the GaN doped with rare-earth (RE) elements, due to the localized nature of their 4f states, the theoretical results from LSD A, except for Gd, deviate significantly from the experimental obser­ vations. In the case of Gd, due to its half-filled 4f-shell and the large exchange splitting, LSD A pro­ vides a reasonably accurate description.

A. Svane etal 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 mini ­ mum (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 GaiJVhtiNi 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 «-type, G. M. Dalpian and S.-H. Wei investigated the intrinsic and n- type Gd-doped ZB GaN theoretically with LSDA. Their investigations show as well that the intrin ­ sic Gai_/jd*N 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 Gai./jdJM, shown in Fig. 2.15. Therefore, it is possible to stabilize the ferromagnetic phase of ZB Gai./jdJM by introducing free electrons with co-doping [69].

-6 -4 -2 0 2 4 6

Total Fig. 2.15 Density of states for ZB Gai-v Gd v N 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 summa­ rized by Pearton et al. in 2003 [70] and Liu et al. in 2005 [71] are not consistent and depend strong­ ly 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 sur­ face. 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 pm 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

Fig. 2.16 (a) A photo and (b) a sketch of an empty liquid metal ion source. The capillary is made of tungsten spirals, which will later be filled with a metal or metal alloy. The photo is courtesy of FEI.

needle 34 and Si are nonmetals, and except Bi, Ga, In and Sn, the other elements can only be prepared in eu­ tectic (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 pm. 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 6 x 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 accele­ ration 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 6 x 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 app­ lied 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

Liquid Metal Ion Source

Extraction Lens

Condenser Lens

Condenser Lens Apertun

Wien-Filter

Objective Lens Apertures

Blanking

Faraday-Cup

Scan-Deflectors

Objective Lens

Ion Beam

Sample

Fig. 2.17 Schematic depiction of a Canion 31 Plus FIB column from Orsay Physics. All the electrical potentials deno ­ ted 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 electrosta­ tic field, are applied. An ion after acceleration has the kinetic energy,

^ = = (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 = At a certain value for each field, respectively, the Lorentz and the electrostatic 36 forces on the ion counterbalance each other, i.e.,

F L =qvB = q £ = F £ , (2.42)

£ 2 q and the ions having the velocities other than v = — = will be deflected and blocked B \ 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 57 Fe and Fe+ from Fe2+ as well. However, technically, gre­ at 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 diffi ­ cult 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 structu­ res 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 afore­ mentioned 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 pro­ cess 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

10- 25- 20krV Oi* 25keVCa* 8- Bombardment 20- Bombardment of Sj A*lh 6 V 15- 4- 10- ¥

2- 5- < 0- T"" ~r~ i 0-. 20 40 —r- 1 I 60 20 40 60

nfx A (Degree*.) ArvJle fDeCTAe*!

Fig. 2.18 Angle dependence of the sputtering yield of Ga+ ions on Si (left) and GaAs (right).

Crow et al. and Kaito el 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 maxi­ mum 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).

.$ .....f-—* | *-l .--i i...... i—---- { I ^

™r™ 15 10 15 20 25 30 Energy QteV) Energy (keV)

Fig. 2.19 Energy dependence of the sputtering yield of Ga+ ions on Si (left) and GaAs (right).

2.S.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 repea­ tedly 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. Amorphizati­ on 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 im­ plantation. 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 de ­ fects 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 bet­ ween the swellings on both sides of the milled line is denoted ® -20 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 trian ­ gle-like, and the swelling is clearly observed. The rate of FIB milling is usually written as the mil­ led volume per unit charge, and the typical scale is pm3/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 pm for the depth and cm 2 for the dose, respectively. 39

3 Magnetotransport in cleaved-edge-over- grown Fe/GaAs-based heterostructures

In this chapter, the considerations for as well as the film and the contact properties of the cleaved- edge 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 im­ portant 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 prepa­ red 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 pm.

Fig. 3.1 (a) Sample holder and the process of sample mounting, (b) Schema­ tic depiction of the UHV cleavage process [77].

shutter Cleaved edge

The heterostructures applied in this work were grown by semiconductor molecular beam epitaxy (MBE) on semi-insulated GaAs(OOl) substrates, and the overgrowth of the metal thin films was car­ ried out on the freshly-cleaved (HO)-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 Jn-sitit UHV cleava ­ ge, the Fe and the capping layers were grown at room temperature (RT). The low-energy electron diffraction (FEED) 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 FEED pattern of (a) GaAs (llO)-surface, (b) epitaxially grown Fe layer, and (c) the superposition of (a) and (b). The FEED pattern of Fe has the periodicity twice as large as that of GaAs for that GaAs has the lattice constant twi­ ce 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 [00Indirection, 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

a) [001] b) [110]

8 0-

-15 -10 -15 -10 Feld [mT] Feld [mT]

Fig. 3.4 MOKE measurements on the Fe thin films overgrown on the cleaved (llO)-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 //-GaAs, 5-doped //-HEMT, and an //-type pseudomorphic HEMT, consisting a InAs quantum well sandwiched by a series of strained InGaAs layers, are applied. The contact between bulk //-doped semiconductors and metal is known as the Schottky contact, and can be described using Shockley theorem by treating the contact as one-sided abruptp+-n contact [79]. The I-V characteristic is therefore written as

/ = A*T2w d exp(~-y b’T°) [exP(^y) ~ 1] , and the depletion zone width, ho, is written as

1,0 = j7T7~v~ TT* ' where A* is the effective Richardson constant, Tis the temperature, w and d are the width and the thickness of the conducting channel, respectively, 17,,// is the zero-field built-in potential, His the ap­ plied voltage, e 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

/ = 5.36 A*T2w d exp(-^ [exp(J-y) ~ 1] , and the depletion zone width, /, is then written as

j _ 2££o Vbi, o

2D

Fig. 3.5 show the I-V characteristics measured between ±5 V at both 300 K and 4.2 K. The bulk «-GaAs and 5-doped //-HEMT have the diode-like I-V characteristics. The reason that the 5-doped //-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.

V| V| VI V|

(b) 8

7 Fig. 3.5 I-V characteristics measured between ±5 V at

6 300 K (solid symbols) and 4.2 K (open symbols) — S for (a) a bulk ;?-GaAs, (b) a 5-doped //-HEMT. and (c) an //-type pseudomorphic HEMT.

-5 -4 -3 -2 -1 0 1 2 3 4 5 V| V| 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 1016 cm-2, the sputte­ ring 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 val ­ ve in this work. First, the 130-pm 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 %-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 1pm-wide rectangle with different doses ranging from 3x10 16 cm-2 to

1x10 18 cm-2. Then the depth profiles of the milling were measured with a Park Scientific atomic for­ ce microscope (AFM), and the I-V characteristics across the milled lines or rectangles were measu­ red with a Hewlett-Packard semiconductor parameter analyzer at both RT and 4.2 K. 45

------4 x 10 cm 5 x 10" cm ------6 x 10 * cm 100 -

------8 % 10 * cm 9 % I0U cm 1 % 10 cm 2 x 10 cm 3x10 cm

— 6x10 cm ------7 x 10 cm 8 x 10 cm ------9x 10 cm ------I x 10 " cm scaning range | pm | scanning range | pm

600 -

Fig. 3.6 (a) Depth profiles of all the milled rectangles, and 500 - (b) the depth profile of the rectangle milled with 400 - the dose 3 x 1016 cm"2. The milled-line width ver ­ sus milling dose is plotted in (c), and the red line is the linear fit of the half-logarithmic plot.

dose | cm |

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 x 1016 cm 2. For a dosage higher than 2x 1017 cm 2, the depth pro­ file 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 x 1017 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 x 1015 cm 2, where the milled-line width is extrapolated to be zero. 46

(a) (c) io’ 10* 0 1 ° °o°o 0 _ f cP o o o 0 0 0 10* o 10* r d° ° ■ ■ ■ 10* r G 'o’ r 6 ■ , pi nf ioJ r . "o° ■ ■ « 0 ■ o ■ ■ 10* r o uf r oo" ’

10' i(i,r 10 10 (lose | cm" | dose | cm " |

o oo io" I o'" 10* 10* io7 G G 10* io5 pi pi IO* in' io2 io1 B0eS 10" 10 10 dose | cm | dose | cm |

Fig. 3.7 Resistances versus milling dose measured across a milled rectangle at (a) room temperature and (b) 4.2 K. Re­ sistances 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 HC1.

Fig. 3.7 show the dose dependence of the resistance across the milled lines and the rectangles, re­ spectively, 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+ im­ plantation makes «-GaAs become/t-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 HC1 (~ 4%) for 1 minute to remove the amorphous /t-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 HC1 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 HC1 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 re­ sults 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 dilu ­ ted HC1, and the range of the over-etching is around 10 pm.

Fig. 3.8 Image of a milled structure after dipping in HC1. 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 x 1017 cm"2 was chosen. No dipping in HC1 was per­ formed 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 pm, 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-pm long Fe wire [53]. For a clear observati ­ on of the magnetoresistance for a spin valve made of Fe nanowires, one of the electrodes should be at most 500 mn wide, and the width of the other should be several micrometers.

0 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.

Fig. 3.10 (a) Schematic depiction of a spin valve structure fabricated by FIB milling in the cleaved-edge-overgrowth geometry. The GaAs(OOl) 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 77 -GaAs or the 2DEG. (b) SEM image of the middle part of the spin valve structure. The widths of the structure are 500 mn - 200 mn - 4.3 pm.

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 charac­ teristics measured from the CEO spin valve structures fabricated on the Fe/GaAs-based heterostruc­ tures show the metal-like temperature dependence of the resistances for the bulk «-GaAs and the 49

??-type pseudomorphic HEMT or at the threshold to become semiconductor-like for the 5-doped

77- 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.

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 V| V| VI V|

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,

-1.5 - (b) a 5-doped n-HEMT, and (c) an /7-type pseu­ -3.0 - domorphic HEMT.

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 V| V|

3.3.2 Magnetoresistances of the spin valves

All of the magnetoresistances (MRs) for the CEO spin-valve structures were measured in a ma­ gnetic field between ±100 mT or ±50 mT along the (00Indirection 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. The­ re 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 featu­ res 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 «-GaAs. The additional feature matches the switching fields of the Fe electrodes estimated from Ref. 53, which seems to be the electrical obser­ vation of the spin injection. However, the following MR measurements on the same structure wi­ thout time delay show a increase in resistance and without the additional feature - shown in

Fig. 3.12(c).

52.315 - 52.310 Fig. 3.12 Magnetoresistance for the spin valves fabricated on the cleaved edge of a bulk n-GaAs. Red cur­ ves 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.

-100 -80 -60 -40 -20 0 20 40 60 80 100 B | mT |

(b) (c)

156.0 - 36.5 -

136.4 - 155.8 -

d 136.3 - 155.6 - 136.2 -

155.4 -

155.2 -

-50 -40 -30 -20 -10 0 10 20 30 40 50 -50 -40 -30 -20 -10 0 10 20 30 40 50 B | mT | B | mT |

The MRs for the spin valves on the 5-doped w-FLEMT - shown in Fig. 3.13 - are as inconsistent as those for the bulk «-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 oppo­ site direction. The transverse MR of the semiconductor could be assumed to be one possible rea­ son. Another possible reason could be the anisotropic magnetoresistance (AMR) effect of the L-sha- pe contacts, where the current flow perpendicular to the applied magnetic field has a different field dependence than its parallel counterpart.

(a) 87.48

87.46

87.44

— 87.42 05 87.40

87.38

87.36 182.465 -

-100 -80 -60 -40 -20 0 20 40 60 80 100 -100 -80 -60 -40 -20 0 20 40 60 80 100 B | mT | B | mT |

Fig. 3.13 Magnetoresistance for the spin valves fabricated on the cleaved edge of a 5-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 «-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 ].

195.58 - Fig. 3.14 Magnetoresistance for the spin valves fabrica­

ted on the cleaved edge of an 77 -type pseudo ­ morphic HEMT. Red curves are the first part 195.54 - of the measurements, i.e., from -100 mT) to +100 mT, and the blue curves are the second part of the measurements. -100 -80 -60 -40 -20 20 40 60 80 100 B | mT | 52

All the observed MR ratios calculated with equation 2.34 are between 0.5 % and 0.7 % for the bulk «-GaAs and between 0.014 % and 0.057 % for the 5-doped //-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 ferro- magnet in order to avoid additional influence from the electrodes. For this CEO geometry, the desi ­ re 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 investiga ­ te 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-

Fig. 3.15 The layout of the structures for the longitudinal magnetoresistance measurements. The An con ­ tacts are in green and the L-shaped metal thin films are in yellow. The width of thin arm of the L-shaped metals varies from 500 mn to 5 pm. 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. 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 tech­ nique.

192.9 -

1664 -

1663 - a 192.7 -

192.6 - 1661 - 192.5 -

-100 -80 -60 -40 -20 0 20 40 60 80 100 -100 -80 -60 -40 -20 0 20 40 60 80 100 B | niT | B | mT |

Fig. 3.16 Longitudinal magnetoresistances of structures whose width is (a) 500 mn and (b) 5.2 pm. 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-pm wide structures were shown in Fig. 3.16, respectively. The decrease in resistance be­ fore the field changes its direction was seen for the width up to around 3 pm. Such a behavior is as­ sumed 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 ex­ pected due to the shape anisotropy. The MR ratios are clearly separated into two groups - one group (b) 0.30 h M ■ % 0.25 -

— 0.20 - as — 0.15 - 36 o.io -

0.05 -

0.00 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 width | pm width | pm |

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 depositi ­ on method of the Fe/Au thin films. The MBE grown thin films have lower MR ration than the elec­ tron 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 anisotro ­ py is rather weak. The reasons for the weak anisotropy can be attributed to the 1.4 % lattice mis­ match 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 3M016 cm-2 and around 1M017 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 hete­ rostructures shows the Schottky-like behavior, and this agrees with the theory. Due to the FIB-indu ­ ced parallel conducting channel, the I-V characteristics of the spin valve structures showed no con ­ sistence 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 sam­ ple 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 %-GaAs and between 0.014 % and 0.057 % for the 5- doped w-HEMT structures, respectively. These values are comparable to the longitudinal MRs mea­ sured 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 infor ­ mation 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 for­ med 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 main ­ ly 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 applicati­ ons 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 sym­ metry, ZB GaN has more isotropic properties and no spontaneous electric polarization, it has smal­ ler 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 stu­ died, 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...... se­ quence, 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 order ­ ing temperature (Curie temperature) Tc above 300 K incorporated by MBE [38] and by FIB implan ­ tation [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, petY (peff = M(50 kOe) / n Ga), was found for MBE-dop- ing to be as high as 4000 pB at 2 K and 2000 pB at 300 K, respectively, and those for FIB implanta ­ tion were found to be even larger, lxlO 5 pB at 2 K and 1 / 104 pB at 300 K. These values are signifi­ cant compared to the atomic magnetic moment of Gd, 8 pB. 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 «-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 /10IS cm 3 [95]. The 58 sample was then cut into four pieces of the same size (5x5 mm2) and labelled numerically. Among them, Sample 4 was kept unimplanted as a reference, and the others were implanted with Gd 3+ ions by using a 100-kV FIB facility (EIKO-lOO). The implantations were carried out at room tempera­ ture (RT) with a constant ion energy of 300 keV. The implantation doses for Samples 1 and 2 were lxlO 13 cnr 2 and lxlO 15 cm 2, respectively, while Sample 3 was first implanted with a dose lxlO 12 cm 2, and after magnetic measurements, it was subsequently implanted with a dose of lxlO 14 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 integrat­ ing the ion distribution over the implantation profile and then dividing by the projected range, which yields the corresponding Gd concentrations, from lxlO 17 cnr 3, lxlO 18 cnr 3, lxlO 19 cnr 3, to lxlO 20 cm"3, respectively. The Gd concentration of lxlO 20 cnr 3 is equivalent to x = 0.0023 in the GaUvGdvN notation.

2.0

'a u o S 2 12

gS 0.8 ■d U 0.4

0.0 0 10 20 30 40 50 60 70 80 90 100110120130 depth | nm |

Fig. 4.2 Schematic sketch of the zinc-blende GaN sample structures. The growth direction is to the left. The implantati ­ on profile for the dose of 1 x 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 co-29 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 28 is observed in the XRD pattern, a WZ GaN (0002) peak at 34.5° in 28 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 incorpora ­ tion of Gd into ZB GaN matrix and that the nuclcation of the WZ phase occurred at the interface be­ tween 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 inter ­ ference 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 investig ­ ated 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 un ­ der 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.

ZB GaN(002)

ref x 5

sample 2

20 | deg | 20 | deg |

Fig. 4.3 X-ray diffraction co-20 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 measure­ ments 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 DIO14 cm2), and Gd-implanted 60

Sample 2 (dose lxlO 15 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 dis ­ tinguishable 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 mag­ netization is not saturated up to the highest field of 50 kOe, indicating a strong paramagnetic contri ­ bution 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 pB, 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 behavi ­ or 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]. ____

(c) » X \

■ — Sample 4 —• — Sample 3 ll Vl R H

Sample 3 — Sample 2 \ X [ / \y

•s/r... i — i — i — i — -50 -40 -30 -20 -10 0 10 20 30 40 50 -50 -40 -30 -20 -10 0 10 20 30 40 50 H | kOe 1 H | kOe 1

— • — Sample 4 —•—Sample 3

— ° — Sample 3 —°—Sample 2 Fig. 4.4 Magnetization loops obtained from Samples 2, 3,

and 4 at (a) 5 K and (b) 300 K. (c) The 5 K hyster­ esis loop of Gd-implanted sample 2 after the dia ­ magnetic background was subtracted. The unim ­ planted and Gd-implanted curves are with solid and open symbols, respectively.

-50 -40 -30 -20 -10 0 10 20 30 40 50 H | kOe 1 61

All implanted samples but Sample 2 show the same temperature-dependent behavior as the refer­ ence 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 de ­ picted 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 behavi ­ or, the FC curve of Sample 2 has a weak temperature dependence between 10 K and 60 K, indicat ­ ive 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 temper­ ature 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) 12 : H = 100 Oe 10 . ■ —■— —o— Sample 4 — Sample 3 I —A— —A— Sample 2 — Sample 2 = s 1 T 6 O _ 4 ■^^dpDDHb0°arftoaaprfPDD~flDD s

0

0 50 100 ISO 200 250 300 T1K|

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 wanning up (open symbols).

Although the magnetic ordering phase of Sample 2 has the ferromagnetic-like temperature de ­ pendence, 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 Gai.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( 1x 1Q16 cm-3) for WZ Ga^GdxN, 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-de- fect 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 interac ­ tion 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.xGd xN, 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 coex­ isting 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 (QQQ1) substrate / 25 nm GaN buffer (43Q °C) / 8 Q nm AlN (85Q °C ramping to 9QQ °C) / 2 pm AlQ.44GaQ.56N (84Q °C) / 1.96 pm GaN (8 QQ °C). The sample was then cut into four pieces of the same size (4x5 mm2) and labelled numerically. Among them, Sample 4 was kept unimplanted as a reference, and the others were implanted with Eu2+ ions using a lQQ-kV FIB facility (EIKO-1QQ). The implantations were carried out at RT with a constant ion energy of

2QQ keV. The implantation doses for Samples 1, 2, and 3 were 1x 1Q15 cm-2, 3.5x 1Q15 cm-2 and 63 lxio 14 cm 2, respectively. None of samples were subjected to annealing treatment.

depth | nni |

Fig. 4.6 Schematic sketch of the wurtzite GaN sample structures. The growth direction is towards the left. The Eu-im- plantation profile for the dose of 1 x 1015 cm"2.

The SRIM-calculated projected range for the 200-keV Eu ions is 80 nm and plotted in Fig. 4.6 to­ gether 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* 102u cm 3, and 4.38><10 2u cm 3, respectively. The Eu concen ­ tration of 1 xl0 2u cm"3 is equivalent to x = 0.01 in the Gau.Eu.N 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 peu at 5 K for the highest dose is around 1 pB, which is larger than the reported value from the MBE-grown WZ Ga0.9sEu0.02N [98] and indicates the defect-enhanced magnetic moment as observed from Gd-FIB-implanted WZ Ga,_,Gd.,N [39]. The temperature-de- pendent measurements show no remanent magnetic moment and no magnetic ordering for all doses, shown in Fig. 4.7(b). 64

T-SK —■— unimplanted —o—Eu, n - lxl<

S 4 - —C— Eu. n = 3.5xlOls cm

-50 -40 -30 -20 -10 0 10 20 30 40 SO H | kOe |

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 wanning up (open symbols).

Comparing this work to the MBE-grown WZ Gai_xEuxN reported by Hashimoto el al. [98] and the Gd-FIB-implanted WZ GaN reported by Dhar etal. [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 pB, which does not induce the spin-splitting re­ quired to set the essential spontaneous electric polarization into yielding the ferromagnetic ordering.

4.3 Magnetotransport in Gd-implanted GaN-based he­ terostructures

Since the WZ Gai-.xGd xN 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 pm GaN / 1 nm AIN / 21 nm Alo.2sGao.72 N / 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 de ­ picted in Fig. 5.8(b). For the magnetotransport measurements, the z-axis is parallel to the growth di- 65 recti on, or perpendicular to the sample surface, and the x-axis is along the longer edge of the trans ­ mission line (TML) structure.

depth | nm |

van der Pauw structures

transmission line structures

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 5x190 pm2 rectangle, the pink rectangle in Fig. 4.8(b), was implanted with 300-keV 66

Gd 3+ ions at the position A - 35 x 160 pm- area between ohmic contacts - of each row from the TML structures with different doses, ranging from 1x10" cm - to 1x10" cm -, and the implantation pro­ file 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 1x10" cm -, and it is completely depleted from the dose of 1x10" cm - and onwards.

8 : • no FIB

$10 cm

< 0 ...... < (I

-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 -2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8

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: 3x10" cm" and 3x10" cm". The implantation patterns are a 5x190 pm- rectangle for the position A of TML structures, and a 130x130 pm- 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 3x10" cm", which matches the previous implantation test. The magnetotransport was studied by Hall effect and magnet ore si stance (MR) measurements only for the structures implanted with the dose of 3x10" cm". 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 ar­ rangement 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 fi/T, was subtracted, a ferro- magnetic-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 fi/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: 6.25x10'- cm-. 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 fi/T over the whole magnetic field range and the two-dimensional electron concentration is calculated to be 8.22x10'- cm -. The sheet resistances measured from the unimplanted and the Gd-implanted structures are 50.6 fi/D and 1025.5 fi/D, re­ spectively, and the calculated (Hall) electron mobilities are 15026.5 cm-/Vs and 975.1 cm-/Vs, re­ spectively. 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 param­ agnetic defects. 68

200 -

-100 :

-200 - -400 -

-400 j -5 -4 -3 -2 -1 -4 -3 -2 BIT] B|T]

“ -40 - r -2 :

-4 -3 -2 -5 -4 -3 -2 B | T | B | T | (0 . 85 H a 80 | 75

! 100 - |=7»

65 -5 -4 -3 -2 -1 -5-4-3-2-10 I 2 3 4 5 B | T | B | T |

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 derivati ­ ve of (a), (d) As-measured Hall effect curve at 4.2 K from a unimplanted van der Pauw structure, (e) The cur­ ve 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, B- 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 distri ­ butions 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-

600 - 600 - ■ R - R

a 400 - a 4oo -

-5 -4 -3 -2 -1 -5 -4 -3 -2 -1

-60 -200 20 60 (d) -80 -60 -20-10-5 0 5

10 15 20 30 40 60 80

-10 -5 0 5 10 5 10 20 40 60 80

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 R^ and Rvx in Bz is 200%, and that for Rxx and R in Bv is only 7%. Note that the very small MR ratio for R in Br 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 Br (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 R in B)h respectively. All the neg­ ative MR shows the typical feature of the transverse MR [51].

4.20 -

4.15 -

4.10 -

4.05 -

-5 -4 -3 -2 -1 -5 -4 -3 -2 -1 B | T | B | T |

Fig. 4.12 Rxx and Ryy measured at 4.2 K for the Gd-implanted vdP structure in (a) B:, (b) B,.

4.3.2.3 Magnetoresistance of transmission line structures

Magnetoresistances of the TML structures were studied by measuring the resistance in the x-di- rection, noted as Rxx , in magnetic fields, Bz and Bv. 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 R in /L, and 24.24% for Rxx in B)h respectively.

The Rxx at zero field is twice as large as the unimplanted one, which results from the defects in ­ duced by Gd-implantation. The Rxx in Bz from the implanted structures has, at a first glance, a posi­ tive 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 approxi­ mation 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%.

unimplanted Fig. 4.13 Rxx measured at 4.2 K for unimplanted (solid symbols) and Gd-implanted (open symbols) in (a) II and (b) Bt. and (c) the difference bet­ ween Gd-implanted and unimplanted curves in (a).

-5 -4 -3 -2 B | T | 72

4.4 Summary

In this work, the 300-keV Gd 3+ ions were successfully incorporated in zinc-blende GaN by room temperature FIB implantation, whose doses range from 1x10 12 cm-2 to 1x10 15 cm-2. The XRD pat­ tern 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 superparam- agnetic-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 1x10 14 cm-2 to 3.5x10 15 cm-2. All of the samples show only paramagnetic behavior with­ out 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 Gd 3+ ions for the ion dose lower than 1x10 12 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 mo­ bility 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 op­ posed 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 3x10 16 cm-2 and around 1x10 17 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 FIB- induced 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 %-GaAs and between 0.014 % and 0.057 % for the 5- doped M-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 «-type Schottky contact of the spin injection.

A study of the optical polarization of lateral p-n diodes realized by overcompensating a /Mype 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 thep-n junction.

9 8 Fig. 5.1 Intensity versus polarization plot of the emitted light from a lateral p-n diode on a p-type 7 ■ Nr. 9, 15V, 12mA pseudomorphic HEMT structure by locally 6 - Nr. 6, 19V, 11mA = ------Nr. 3, 20V, 11mA overcompensation with FIB-implanted Si ions. Cl 5 . The rotation angle of the 1/4-plate represents the 4 - different polarization of the light, e.g., ±45 ° are

3 for the left- and right-circular polarization, 0 45 90 135 180 225 270 315 360 rotation angle of A/4-plate respectively.

5.2 Magnetotransport in rare-earth-doped GaN-based heterostructures

The 300-keV Gd 3+ ions were successfully incorporated in zinc-blende GaN by room temperature 75

FIB implantation, whose doses range from 1*10 12 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 U1014 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 Ga^E^N.

The 2DEG of a GaN-based HEMT structure was not depleted by the 300-keV FIB-implantation of Gd 3+ ions for the ion dose lower than 1*10 12 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 fur Angewandte Festkorperphysik 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 Universitat Duisburg-Essen, Christian Urban, Sani Noor, Carsten Godde and Prof. Dr. U. Kohler of EPIV at Ruhr- Universitat Bochum, for the semiconductor and metal MBE growth for the cleaved-edge-overgrown heterostructures and beneficial discussions.

Dr. S. Potthast, J. Schormann, Prof. Dr. As, and Prof. Dr. Lischka at Universitat 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. 85

Dr. Dorina Diaconescu, Dr. Peter Schafmeister, Dr. Andre 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 Gok 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. 86

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 Bi^-J^O^ 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 fur Angewandte Festkorperphysik, Ruhr-Universitat Bochum, Germany

Topic: Magnetotransport in cleaved-edge-overgrown Fe/GaAs-based and rare-earth-doped GaN-based heterostructures Supervisor: Prof. Dr. A. D. Wieck 87

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 Bi^Fefl^,

Jpn. J. Appl. Phys. 38, 6687 (1999). [2] N.C. Gerhardt, S. Hovel, 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. Hovel, 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/PtjvMultilayer 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. Schormann, S. Potthast, D. J. As, K. Lischka, Magnetic and structural properties of Gd- implantedzinc-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-HEMTstructures, 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). 88

[2] N. C. Gerhardt, S. Hovel, 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. Hovel, 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. Kohler, 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. Schormann, D. J. As, K. Lischka, S. Pezzagna, Y. Cordier, J.-Y. Duboz, and A. D. Wieck, Gd- andEu-implanted GaN, Regensburg, 2007.