final thesis - diva portalliu.diva-portal.org/smash/get/diva2:224551/fulltext01.pdf · 2009. 6....

55
1 Final Thesis Spin Dependent recombination in GaNAs Yuttapoom Puttisong LITH-IFM-A-EX--09/2187SE Examiner: Irina Buyanova, Linköping University Division of Functional Electronic Materials Department of Physics, Chemistry and Biology Linköping University, Sweden Linköping 2009

Upload: others

Post on 17-Aug-2020

7 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

1

Final Thesis

Spin Dependent recombination in GaNAs

Yuttapoom Puttisong

LITH-IFM-A-EX--09/2187—SE

Examiner: Irina Buyanova, Linköping University

Division of Functional Electronic Materials

Department of Physics, Chemistry and Biology

Linköping University, Sweden

Linköping 2009

Page 2: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

2

Upphovsrätt

Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare – under 25 år

från publiceringsdatum under förutsättning att inga extraordinära omständigheter uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner, skriva

ut enstaka kopior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning

och för undervisning. Överföring av upphovsrätten vid en senare tidpunkt kan inte upphäva

detta tillstånd. All annan användning av dokumentet kräver upphovsmannens medgivande.

För att garantera äktheten, säkerheten och tillgängligheten finns lösningar av teknisk och

administrativ art.

Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman i den

omfattning som god sed kräver vid användning av dokumentet på ovan beskrivna sätt samt

skydd mot att dokumentet ändras eller presenteras i sådan form eller i sådant sammanhang

som är kränkande för upphovsmannens litterära eller konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press se förlagets

hemsida http://www.ep.liu.se/.

Copyright

The publishers will keep this document online on the Internet – or its possible

replacement – for a period of 25 years starting from the date of publication barring

exceptional circumstances.

The online availability of the document implies permanent permission for anyone to read,

to download, or to print out single copies for his/her own use and to use it unchanged for non-

commercial research and educational purposes. Subsequent transfers of copyright cannot

revoke this permission. All other uses of the document are conditional upon the consent of the

copyright owner. The publisher has taken technical and administrative measures to assure

authenticity, security and accessibility.

According to intellectual property law the author has the right to be mentioned when

his/her work is accessed as described above and to be protected against infringement.

For additional information about Linköping University Electronic Press and its

procedures for publication and for assurance of document integrity, please refer to its

www home page: http://www.ep.liu.se/.

© Yuttapoom Puttisong

Page 3: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

3

Abstract

Spin filtering properties of novel GaNAs alloys are reported in this thesis. Spin-

dependent recombination (SDR) in GaNAs via a deep paramagnetic defect center is intensively

studied. By using the optical orientation photoluminescence (PL) technique, GaNAs is shown to

be able to spin filter electrons injected from GaAs, which is a useful functional property for

integratition with future electronic devices. The spin filtering ability is found to degrade in

narrow GaNAs quantum well (QW) structures which is attributed to (i) acceleration of band-to-

band recombination competing with the SDR process and to (ii) faster electron spin relaxation in

the narrow QWs. Ga interstitial-related defect centers have been found to be responsible for the

SDR process by using the optically detected magnetic resonance (ODMR) technique. The

defects are found to be the dominant grown-in defects in GaNAs, commonly formed during both

MBE and MOCVD growths. Methods to control the concentration of the Ga interstitials by

varying doping, growth parameters and post-growth treatments are also examined.

Page 4: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

4

“Thanks to the world with uncertainty principle”

Page 5: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

5

Acknowledgement

I grateful to my supervisor, Prof. Irina Buyanova and Prof. Weimin Chen for letting me be a part

of this interesting project, for always opening the door to have fruitful discussions and for their

support and encouragement.

I would like to thank Xingjun Wang for all valuable time we spend in labs, for sharing

the knowledge in semiconductor spintronics as well as for teaching me experimental techniques

during my work on the thesis.

I also would like to thank my opponent, Huan-Hung Yu for intensively discussing my

thesis.

I am also grateful to Shula Chen, Shun-Kyun Lee, Daniel Dagnelund, Jan Beyer and

Deyong Wang for family-like research atmosphere, I am kind of working in a very lovely family.

I further thank Arne Eklund for technical assistance and Lejla Vrazalica for her help with

administrative matters.

Finally, I am grateful to my mother for always supporting me during all her life. I cannot stand

in this place without you.

Yuttapoom Puttisong

.

Page 6: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

6

Tables of contents

Introduction 8

Chapter One: Fundamental electronic structure of GaNAs 9

The empirical band anti-crossing (BAC) model..................................................................9

Pseudopotential LDA calculation......................................................................................10

Band alignment in GaNAs/GaAs hetero-structures...........................................................11

Strain-induced splitting of the valence band......................................................................11

Confinement effect-induced lh-hh splitting in a QW system............................................12

Radiative recombination process in GaNAs......................................................................13

Non-radiative (NR) recombination....................................................................................14

Chapter Two: Spin dynamics 15

Optical orientation and spin polarization...........................................................................15

Spin relaxation...................................................................................................................17

Chapter Three: Spin Dependent Recombination (SDR) 20

General principles of SDR.................................................................................................20

Optical orientation in the presence of a deep paramagnetic center...................................21

SDR ratio...........................................................................................................................22

Two spin pools picture.......................................................................................................23

Physical realization of an efficient spin dependent-recombination process......................24

Chapter Four: Experimental Approach 27

Optical orientation PL spectroscopy..................................................................................27

Magnetic resonance technique...........................................................................................30

Chapter Five: Experimental Results

Defect Engineering for Spin Filtering Effect in GaNAs 37

Defect engineered spin filter from a low dimensional semiconductor structure; spin

filtering effect in QW structures........................................................................................37 Effect of growth temperature and post-growth treatment on the SDR process.................41

Page 7: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

7

Effects of doping on the formation of the Gai-interstitial paramagnetic centers...............46 Effects of growth techniques on the defect formation.......................................................50

Summary 53

Bibliography 54

Page 8: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

8

Introduction

Diluted-nitrides (i.e. N containing III-V ternary and quaternary alloys) have emerged as a

subject of considerable theoretical and experimental research efforts because of their unique and

fascinating electronic properties. Unlike conventional ternary III-V alloys, such as AlGaAs,

GaInAs, etc, where the band gap energy of the alloy can be approximated as a weighted linear

average of the parental compounds, the dilute nitrides exhibit a huge bowing in the band gap

energy. Consequently, GaInNAs has been considered as a key material for long wavelength

lasers emitting at the optical-fiber communication wavelength window (1300-1550 nm) [1].

Unfortunately, from numerous optical studies it has been concluded that the radiative efficiency

of dilute nitrides rapidly degrades with incorporation of nitrogen as a result of N-induced

formation of efficient non radiative (NR) defect centers. This efficient NR recombination

currently prevents efficient utilization of dilute nitrides in light emitting devices. On the other

hand, the recent study by X.J. Wang et al. [2] provides different perspectives on the role of

defect-mediated recombination in GaNAs. It shows a possibility to utilize this material as an

efficient semiconductor spin-filter which operates at room temperature and does not require

using a ferromagnetic metal (or diluted magnetic semiconductors) or applying a magnetic field.

It has been shown that the spin filtering effect in GaNAs relies on existence of a paramagnetic

defect and selective recombination under Pauli exclusion principle. Therefore, the NR defects

decremented in terms of optical properties were found to have an important role in spintronics

application.

The work presented in this thesis focuses on detailed characterization of the SDR process

in GaNAs alloys. The thesis is organized as follows. In the first chapter we attempt to give a

brief review on the present knowledge of electronic properties of GaNAs, mainly from

experimental perspectives. The second chapter is devoted to physical mechanisms which govern

spin relaxation in semiconductors and to optical methods of generating spin polarization. Basic

principles of the spin-dependent recombination (SDR) are introduced in chapter three. Chapter

four describes characterization techniques utilized in this work. Finally, experimental results and

summary are presented in chapter five and in the final part of the thesis, respectively.

Page 9: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

9

Chapter One: Fundamental electronic structure of GaNAs

Early absorption measurements [3] [4] [5] [6] have unambiguously demonstrated that

GaN𝑥As1−𝑥 is a direct band gap semiconductor, similar to parental GaAs and GaN. However,

instead of the expected blue shift from the GaAs band gap with N incorporation, the GaNAs

alloy has shown a considerable red shift in the fundamental absorption edge (see figure 1.1.) This

was accompanied by the splitting of the conduction band (CB) of GaNAs into two subbands, as

demonstrated by the electro- [7] and photo [8] -reflectance measurements. The lower one is

usually denoted as E− and represents the CB edge of the alloys, whereas the upper subband is

denoted by E+. The E− and E+energies depend on the concentration of nitrogen [N]. With

increasing the nitrogen composition, the E− subband shifts towards lower energies while the E+

position increases with [N]. Photo-reflectance measurements have also shown that a spin-orbit

splitting energy (∆0) remains independent of the nitrogen concentration.

Two theoretical approaches, i.e. the so-called band-anti-crossing (BAC) model [9] and

local-density approximation (LDA) calculations [10], [11], [12] are usually considered to

describe the formation of the E+ and E− states under the presence of nitrogen.

The empirical band anti-crossing (BAC) model

According to this model, the formation of the E− and E+ states is induced by an

interaction between the delocalized CB states of the Γ character and the localized nitrogen-

related state EN (EN = 1.65 eV in GaAs.) A magnitude of the splitting is mainly determined by

an inter-band matrix element VMN. The E− sub-band is delocalized, conduction band-like while

the E+ state is derived from the localized EN state. The dispersion relation is then given by:

Figure 1.1: Compositional dependence of

the band gap energy of III-V-N alloys at

room temperature. Lines show result from

model calculation. Local density

approximation and dielectric model is

used.

Page 10: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

10

E± = E𝑔 ± [( E𝑔 − E𝑁 2

+ 4𝑉𝑀𝑁2 )1/2 − |E𝑔 − E𝑁|]/2,

where E𝑔 is the bandgap of the parental III-V compound before alloying it with N. VMN is the

interaction term which depends on nitrogen composition:

𝑉𝑀𝑁 = 𝐶𝑀𝑁𝑥1/2,

Here x refers to nitrogen composition and 𝐶𝑀𝑁 is a constant equal to 𝐶𝑀𝑁 = 2.7eV for GaNAs.

This model is empirical since it only considers the interaction of the CB states with the N

level related to an isolated substitutional N atom. It neglects mixing of the CB states introduced

by nitrogen and also a complexity of formed nitrogen centers. However, the BAC model

provides a simple, analytical expression to describe the GaNAs electronic properties, including

the position of E±, a temperature induced shift of the band-gap, an electron effective mass, etc.

The position of E± as a function of nitrogen concentration is shown in figure 1.2.

Pseudopotential LDA calculation

The more complicated theory based on pseudopotential provides more general physical

explanation of the existence of the sub-bands. It shows that the formation of the E−and E+ states

is induced by a strong perturbation by nitrogen of host states resulting in symmetry breaking.

The degenerate L and X CB minima are now split into a1 and t1 states. Mixing between the

a1(Γ) and a1(L) conduction band states leads to the formation of E−. On the other hand, the

E+ state originates from a weighted average of a1(L) and a1(N) states. According to this model,

the interaction between the CB and EN is small and E+ exhibits the L-like characterer. However

pseudopotential LDA calculations require a substantial effort and the numerical results are

difficult to use.

Figure 1.2; positions of E+ and E− in

GaNAs alloy according to the empirical

band-anti-crossing model. E𝐿 refers to

the position of the L CB minimum relative

to the top of the VB in GaAs.

Page 11: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

11

Band alignment in GaNAs/GaAs hetero-structures

Band alignment in GaNAs/GaAs heterostructures is of importance for optoelectronic and

spintronic applications. Both type-I and type-II band alignment in GaNAs/GaAs quantum wells

(QWs) has been concluded as schematically illustrated in figure 1.3. However, the type-I band

alignment seems to be more probable based on several experimental observations [13]. Firstly,

according to the time-resolve photoluminescence measurements, recombination lifetime of

electron-hole pairs in the GaNAs QWs is of the same order of magnitude as in bulk GaAs. Since

in the type-II structures the recombination lifetime is expected to be longer due to spatial

separation of electron-hole pairs, the GaNAs/GaAs structures have the type-I alignment.

Secondly, it has been found that the lowest energy photoluminescence (PL) originates from the

CB-light hole (lh) transitions, based on the PL polarization measurements in GaNAs/GaAs QWs.

This means that holes participating in the recombination should be located in the GaNAs QW as

the uppermost VB states in GaAs barriers are heavy hole (hh) states.

Strain-induced splitting of the valence band

At the Γ point (k =0) the top VB states has a total angular momentum 𝐽 = 3/2, due to

spin orbit interaction. At this point, the Jz=±3/2 and Jz=±1/2 states are degenerate. But if the

bulk material is subjected to compressive or tensile stain, this degeneracy will be lifted. Indeed,

let us consider the in-plane biaxial strain. In this case the in-plane deformation energy (say in a

xy plane) will be different from that a z-direction. Hence, symmetry of the system is reduced

and the degeneracy is lifted [14]. The result is a splitting between the hh (Jz=±3/2) and the lh

(Jz=±1/2) states. Therefore, if a lattice constant of an epilayer material is smaller than that of a

Figure 1.3; schematics of type I and type

II band alignment in GaNAs/GaAs QW

system. The arrows show dominant

recombination transitions, i.e. direct in

space of the type I transitions (the solid

line) and indirect in space for the type II

transitions (the dashed line).

Recombination rate is higher in the type I

QW which is preferred for optoelectronic

applications in terms of high radiative

efficiency.

Page 12: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

12

substrate, i. e. when the epilayer is under tensile strain, the VB lh states will lie above the hh

states. On the other hand, if the system is under compression, the lh states lie below the hh states

(see figure 1.4.)

GaAs is a common substrate for GaNAs. The lattice constant of GaNAs is smaller than

that of GaAs and biaxial tensile stain dominates. Thus, in the strained GaNAs the lh VB states

usually lie above the hh states.

Figure 1.4; fundamental semiconductor band structure under tensile and compressive strain.The degeneracy of the

VB states is lifte and the, lh and hh states are spit.

Confinement effect-induced lh-hh splitting in a QW system

Due to the confinement effect, energy levels in quantum wells are separated into discrete

levels. The separation between adjacent levels is determined by a size of the quantum well and

by values of effective masses of carriers. By solving the Schrödinger equation for the QW

structure it can be shown that the energy positions of levels in the QW are inversely proportional

to the QW size and also to effective masses of the carriers [14]. Thus, for a fixed size and a

fixed quantum number, the lh VB states, which have the smaller effective mass, will be pulled

further down in energy as compared with the heavy hole states. If the system is unstrained, the

degeneracy between the lh and hh states is lifted and the lh states have higher energy than the hh

states (see figure 1.5.)

lh

hh

so

E(p)

tension

Eg

lh

hh

so

E(p)

unstrained

Eg

lh

hh

so

E(p)

compression

p

Eg

Page 13: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

13

Radiative recombination process in GaNAs

As mentioned above, one of the promising applications of the III-V-N alloys is for the

near-infrared light emitters. Therefore, understanding origin of radiative recombination

processes in these materials is of importance. Previous optical measurements have shown that

introduction of nitrogen induces strong localization effects. As a result, low temperature PL in

these materials is due to localized exciton (LE) recombination [13]. This assignment was based

on several experimental observations. (i) A strong red shift of the PL maximum is observed with

increasing temperature and exhibits the so-called S-shape behavior (see figure 1.6). The physical

explanation of this behavior is as follows. When temperature is increased, carriers in the

localized excitonic states can be excited into the delocalized states in CB. The S-shape point is

the transition from the localized states to the delocalized states. (ii) A blue shift of the PL

maximum is observed when excitation power is increased as a result of filling of higher energy

states within the localized states.

700 750 800 850 900 950 1000 1050 1100 1150

6 K

60 K

120 K

180 K

240 K

300 K

PL

In

ten

sit

y (

No

rmali

zed

)

wavelength (nm)

GaNAs, N = 0.54%

Figure 1.6; PL spectra from GaNAs as a

function of temperature.

Eg

n = 1 n = 2

hh, n = l lh, n = 1

Figure 1.5; quantum size effect. Due to

quantum confinement the lh states have

higher energy than the hh states. Optical

transitions in the well follow selection

rules, ∆n=0, ∆m=±1.

Page 14: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

14

Non-radiative (NR) recombination

The radiative efficiency of III-V-N compounds rapidly degrades when nitrogen

composition is increased. The observed degradation is commonly attributed to poor structural

quality of the N-containing alloys and also to increasing concentrations of non-radiative (NR)

defects [15]. For optoelectronic applications, radiative luminescence has to be utilized.

Fortunately, according to previous studies the radiative efficiency can be improved by post-

growth treatments [13]. Rapid thermal annealing has also been employed to narrow a spectral

width of the PL spectrum and to increase the PL intensity.

Spin-dependent recombination

GaNAs shows fascinating spin dynamics of carriers. Specifically, an apparent spin

relaxation time has been shown to dramatically increase with increasing temperature and is

longer than several ns at room temperature. Long spin polarization life-time in diluted nitrides

can be explained by the spin-dependent recombination (SDR) model initially developed by

Weisbush and Lampel in AlGaAs [16]. As will be discussed later, this unusual spin dynamics is

due to a large concentration of the NR paramagnetic centers induced by the presence of nitrogen.

Page 15: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

15

Chapter Two: Spin dynamics

The success of spintronics relies on the ability to create, control, maintain and manipulate spin

orientation over practical time and length scales. Below we will discuss how spin orientation can

be created and detected in semiconductors by optical means and also physical mechanisms which

govern losses of this orientation.

Optical orientation and spin polarization

During all physical processes a total momentum must be conserved. Therefore, optical

excitation with circularly polarized light can provide spin orientation of carriers in a

semiconductor. The total spin of electron and hole must be equal to the angular momentum of an

absorbed photon. Photons of right or left polarized light have a projection of the angular

momentum on the direction of their propagation (helicity) equal to +1 or −1, respectively.

Linearly polarized photons are in a superposition of these two states. When a circularly polarized

photon is absorbed its angular momentum must be distributed between the photoexcited electron

in the conduction band and hole in the valence band. Probability of optical transitions within the

dipole approximation is described by a transition matrix element [17]:

𝐷𝑖𝑓 = 𝑓 𝐷 𝑖 ,

where 𝐷 is the dipole moment operator and | 𝑖, 𝑓 refer to an initial and final states, respectively.

Wavefunction of the VB holes is p-like whereas the CB electrons have the s-like wavefunction.

Due to these symmetry properties the only matrix elements not equal to zero are:

𝑆 𝐷 𝑥 𝑋 = 𝑆 𝐷 𝑦 𝑌 = 𝑆 𝐷 𝑧 𝑍 ,

where | 𝑆 refers to the conduction band state (S symmetry) and | 𝑋, 𝑌, 𝑍 refers to the p-type

coordinate parts of the Bloch amplitudes, which transforms as the coordinates x, y, z. Matrix

elements for different interband transitions are summarized in table 2.1. Two dipoles rotating

clockwise and counter-clockwise in a plane perpendicular to wave vector k (which is usually

defined as the direction of the wave vector of light propagating perpendicularly to the

semiconductor layer and normally defined to be z-axis) corresponds to hh-c transitions. The lh-c

transitions and SO-c transitions correspond to two dipoles oscillating along k and two dipoles

rotating in the plane perpendicular to k.

Page 16: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

16

Band

Initial (VB)

Final (CB)

½

-1/2

hh

lh

SO

+3/2

−3/2

+1/2

−1/2

+1/2

−1/2

− 1/2(𝑥 + 𝑖𝑦)

0

− 2/3 𝑧

1/6(𝑥 − 𝑖𝑦)

− 1/3 𝑧

− 1/3(𝑥 − 𝑖𝑦)

0

1/2(𝑥 − 𝑖𝑦)

− 1/6(𝑥 + 𝑖𝑦)

− 2/3 𝑧

− 1/3(𝑥 + 𝑖𝑦)

1/3 𝑧

Table 2.1; matrix elements of dipole moment for different interband transitions, x and y are unit vector along a

plane perpendicular to the momentum k, z is a unit vector along k.

Figure 2.1; selection rules and relative intensities of transitions. I+ and I - are the intensities of right-and left

polarized emission, respectively.

Since matrix elements of dipole transitions are not equal for the transitions involving lh

and hh, relative intensities of these transitions are also different. Therefore, optical absorption of

the 100% circularly polarized light in the strain-free material will generate 50% of electron spin

polarization in CB, if only the hh and lh VB states are involved – see Figure 2.1. For example, if

the pumping light is σ+ –polarized the photogenerated electrons in the conduction band will be

preferentially generated in the -1/2 spin state (see figure 2.1) (Note, the two spin states in the

conduction band will be populated equally if the photon energy sufficiently exceeds Eg+Δ,

where Δ is the spin-orbit splitting). If both photo-excited electrons and holes retain their spin

orientations without spin relaxation, the reverse PL process should lead to 100 % σ+polarization

+1/2 -1/2

-3/2 +3/2

-1/2 +1/2

I+

Emission

I - I

+ I -

VB

lh

hh

+1/2 -1/2

-3/2 +3/2

-1/2 +1/2

σ+ σ+

Absorption: σ+ light ∆mj = +𝟏

lh

VB

hh

Page 17: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

17

in optical detection. If complete spin relaxation occurs between the hole states, e.g. due to strong

hh-lh mixing, the polarization degree of optical detection should decrease down to 25 %. The

latter is defined as in equation 2.1

𝑃𝑐= I+ − I –

(I+ + I -)

,

where I+ and I - are the intensities of +- and

--polarized emission, respectively. The absolute

value of the polarization degree will be twice higher in the strained structures where the

degeneracy of the VB states is lifted and only one of the VB states is populated. A sign of the PL

polarization will depend on whether the hh or lh states are involved. For example, the PL will be

+- polarized for the hh transitions, whereas it will be

--polarized if the lh states are involved.

Spin relaxation of the CB electrons will cause a reduction of the PL polarization degree. Since

circular polarization of emission is directly linked to the spin orientation of electrons in the

conduction band created via optical orientation, circular polarization can give the information

about how much electrons are polarized. We would like to point out that no PL polarization is

expected under linear excitation (σx) as equal populations of spin-up and spin down electrons

will be generated.

Spin relaxation

Central issue for developing spintronic devices is how to preserve spin orientation of

carriers. Understanding of spin relaxation mechanisms is, therefore, required. Spin relaxation, i.e.,

disappearance of initial non-equilibrium spin polarization, can be generally understood as a

result of the action of fluctuating in time magnetic fields. In most cases, these are not real

magnetic fields, but rather “effective” magnetic fields originating from the spin–orbit, or,

sometimes, exchange interactions. The magnetic field causes spin precession around the field

direction. However, as the latter randomly changes in time, the initial spin information will be

completely lost after several changes.

Two main parameters describing spin relaxation are spin precession frequency in random

magnetic field, ω, and its correlation time 𝜏𝑐 , i.e., the time during which the field may be roughly

considered as constant. These two parameters are the most commonly used to explain any

mechanism of spin relaxation.

Elliot-Yafet Mechanism [17, 18]

The electrical field, accompanying lattice vibrations or the electric field of charged

impurities is transformed to an effective magnetic field via the spin–orbit interaction. Thus

momentum relaxation is usually accompanied by spin relaxation. For phonons, the correlation

Eq. 2.1

Page 18: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

18

time is on the order of the inverse frequency of a typical thermal phonon. Spin relaxation by

phonons is normally rather weak, especially at low temperatures.

In the case of charge impurities, scattering by an impurity center causes a change of

effective magnetic field and, thus, a change of mean spin direction. As a result, spin relaxation

time can be expressed as the function of scattering time and scattering angle. Thus, spin

relaxation rate is proportional to impurity concentration.

Dyakonov-Perel Mechanism [20]

The Dyakonov-Perel mechanism is due to spin orbit splitting of the conduction band due

to bulk inversion asymmetry (BIA) in non-centro-symetric semiconductors. In this case the

precision frequency is dependent on momentum of electron, ω=Ω(p). An electron with a certain

momentum will experience an effective magnetic field caused by spin-orbit splitting and hence

starts its precession motion around an effective magnetic field axis. If the electron takes long

time before relaxing to a lower momentum state, electron will precess long enough to forget an

initial spin state. So, the spin relaxation time is mostly controlled by momentum relaxation time

at a certain momentum,

1

𝜏s

~Ω 2 𝑝 𝜏p,

where Ω(p) has three components along crystals axis,

Ωx(p)~px(py2 − pz

2), Ωy (p)~py(pz2 − px

2), Ωz(p)~pz(px2 − py

2).

In contrast to the Elliott–Yafet mechanism, now the spin rotates not during, but between the

collisions. Accordingly, the relaxation rate increases when the impurity concentration decreases.

Bir-Aronov-Pikus Mechanism [21]

Bir-Aronov-Pikus mechanism is mainly caused by the exchange interaction between

electrons in the conduction band and holes in the valence band. According to this mechanism,

spin relaxation rate is proportional to a number of holes. In other words, spin relaxation of an

electron in the CB is contributed by exchange interaction with all electrons in the VB.

Spin relaxation of holes in the valance band

In the VB, spin relaxation time is mainly controlled by the spitting between the lh- and hh

states. One can say that the hole “spin” J is rigidly fixed with respect to its momentum p, and

Page 19: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

19

because of this, momentum relaxation leads automatically to spin relaxation. For this reason,

normally it is virtually impossible to maintain an appreciable non-equilibrium polarization of

bulk holes and their spin direction is absolutely random.

Page 20: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

20

Chapter Three: Spin Dependent Recombination (SDR)

General principles of SDR

As was mentioned in chapter one, GaNAs shows fascinating spin dynamics of carriers at room

temperature. Long spin polarization life-time in diluted nitrides can be explained within the

framework of the SDR model initially developed by Weisbush and Lampel in AlGaAs [16]. The

SDR mechanism is due to the well known Pauli principle which states that two electrons cannot

have the same spin orientation in the same orbital state. The key point in SDR is the existence of

a deep paramagnetic center which possesses an unpaired electron before trapping a CB electron.

As a consequence, if the photogenerated electron in the CB and the resident electron on the deep

center have the same spin, the photo-generated electron cannot be captured by the center. The

SDR effect can be explained as the following:

1. In the absence of photoexcitation, an electron at a deep defect level is not spin polarized.

The center can only capture a photogenerated electron from the CB with a spin

antiparallel to the spin of the electron present at the center (figure 3.1 a)).

2. Once the deep paramagnetic center is occupied by two electrons, no more electrons can

be captured by this center until one of electrons (of either spin) recombine with a VB hole

(figure 3.1 b)).

3. Even though the capture process of the CB electron by the center is spin-selective,

recombination of electrons trapped by the center with the VB holes is not. Thus, after a

few circles electrons left on the center become dynamically spin-polarized.

4. When the center is polarized, it acts as a spin-selective filter. The photogenerated CB

electron with a spin direction opposite to that of the center is immediately captured and

recombines with the VB holes. As a result, only the electrons with spins parallel to that

of the center are left in the CB. (Figure 3.1 c)).

5. The same spin orientation of conduction and defect electrons prevents the former from

being captured by the defect, resulting in higher concentrations of free carriers. The only

remaining recombination channel under these conditions is band-to-band recombination-

see figure 3.1 d).

Page 21: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

21

Figure 3.1 a); photo-generated electrons are created by circular polarization excitation; populations of the spin up

and spin down states are not equal due to optical selection rules. Electrons with a spin direction opposite to that of

a paramagnetic center are immediately captured. Due to the Pauli exclusion principle, capture of the electrons with

opposite spin is blocked. b) Once the center forms a singlet state, the capture process is stopped. One of the

captured electrons with either spin recombines with a VB hole. The paramagnetic center is again ready to capture

electrons. c) After some circles the electron trapped by the paramagnetic center is dynamically polarized. Any

electron with the spin direction opposite to that of the trapped electron is extracted from the CB which results in

complete spin polarization of the CB electrons. d) The same spin orientation of conduction and defect electrons

blocks the defect-related recombination channel. Carrier recombination is only possible as a result of band-to-band

transitions.

Optical orientation in the presence of a deep paramagnetic center

Figure 3.2 demonstrates effects of the SDR process on the band-to-band recombination.

If the excitation light is linearly polarized, photogenerated electrons are not polarized. Thus, the

capture process by the center is efficient. Under these conditions the recombination via the center

efficiently competes with the band-to-band recombination and hence the corresponding PL

intensity is low. On the other hand, when the excitation light is circularly polarized, the electrons

are photo-generated with preferential spin orientation. Therefore, the electron trapped by the

centers can be dynamically polarized and, hence, the capturing process is blocked. Therefore, the

band-to-band recombination is more efficient, resulting in the higher intensity of the PL signal.

VB

CB

3.1 d) VB

CB

3.1 c)

Forbidden

VB

CB

3.1 b)

STOP

P

𝜎+

VB

CB

3.1 a)

Page 22: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

22

Figure 3.2; optical excitation and recombination transitions observed under linear (the left part of the Figure) and

circular (the right part of the Figure) excitation, respectively.

SDR ratio

An SDR ratio is used as an indicator of the SDR process since in this case a total PL

intensity under linear excitation always lower than that under circular excitation. The SDR ratio

is defined as in equation 3.1:

𝑆𝐷𝑅 𝑟𝑎𝑡𝑖𝑜 =𝐼𝜎+𝑜𝑟 𝜎−

𝐼𝜎𝑥,

where, 𝐼𝜎+𝑜𝑟 𝜎− and 𝐼𝜎𝑥 are total PL intensities detected under the circular and linear excitations

respectively. When the SDR process dominates, the SDR ratio will be higher than one. This ratio

indicates to what degree the capture of the photogenerated electrons by the center can be blocked

when the centers are dynamically polarized and, hence, the SDR ratio is proportional to the spin

polarization of the CB electrons.

Several processes affect the dynamic behavior of the photogenerated carriers. Firstly, the

depletion rate of free carriers is determined by their capture by the centers. This process is spin-

dependent. Secondly, the recombination between the trapped electrons and the VB holes is also

essential. Since the VB holes rapidly loose their spin orientation, this process is spin independent.

The band to band recombination also contributes to carrier dynamics. All these processes can be

described by the following coupled nonlinear rate equations 3.2 [2]:

𝑑𝑛±

𝑑𝑡= −𝛾𝑒𝑛±𝑁∓ −

𝑛± − 𝑛∓

2𝜏𝑠+ 𝐺± −

𝑛±

𝜏𝑑,

𝑑𝑁±

𝑑𝑡= −𝛾𝑒𝑛∓𝑁± −

𝑁± − 𝑁∓

2𝜏𝑠𝑐+

1

2𝛾𝑕𝑝𝑁↑↓,

𝜎+

VB

CB

𝜎+ 𝜎𝑥

VB

CB

𝜎− 𝜎+

Eq. 3.1

Page 23: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

23

𝑑𝑝

𝑑𝑡= −𝛾𝑕𝑝𝑁↑↓ + 𝐺+ + 𝐺− −

𝑛+ − 𝑛−

𝜏𝑑,

𝑁𝑐 = 𝑁↑↓ + 𝑁+ + 𝑁−, 𝑝 = 𝑛+ + 𝑛− + 𝑁↑↓,

where 𝑛± denotes the number of photogenerated electrons with spin up and down respectively.

𝑁± is the number of the paramagnetic centers with a single spin up/down electron, 𝑁↑↓ is the

number of the centers that already form a singlet state and 𝑁𝑐 is the total number of the defect

centers contributing to the spin filtering process. 𝛾𝑒 (𝛾𝑕 ) is a capture coefficient for electrons

(holes), which is characteristic for the defect. 𝜏𝑠 (𝜏𝑠𝑐 ) is spin relaxation time of the free (trapped)

electrons. The density of free holes is denoted by p. 𝐺± is the photo-generation rate of the spin

up and spin down electrons. τd denotes the free carrier decay time, including all radiative and

spin-independent non-radiative recombination channels except that via the paramagnetic center.

The SDR process is power dependent. Before the defects start to spin filter the free

electrons they need to be dynamically polarized. This is only possible if the number of the

photogenerated electrons is higher than the number of the defect centers.

Two spin pools picture

Let us simplify description of the SDR process by considering two spin pools as

schematically shown in Figures 3.4 a) and b). Suppose that the CB electrons can be subdivided

into two sub groups, spin up and spin down pools. In the SDR process, once the center is

polarized, the pool with the spin orientation opposite to the center will be depleted. The capture

process is very fast initially, however, when all the centers are occupied, the capture process will

stop. Therefore, this decay process of the CB electrons is controlled by how fast the trapped

electrons recombine with the holes.

After one pool is depleted, another decay process will start. This decay process is

controlled by spin relaxation. As shown in figure 3.4 c) if the electron flips its spin, it will be

transferred to another pool and quickly depleted by the center (see figure 3.4 d)). Thus, the PL

decay contain two components related to the hole capture and electron spin relaxation.

Eqs. 3.2

Page 24: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

24

Figure 3.4 a) and b); the idea of two spin pools, the deep paramagnetic center acts as a spin filter depleting

electrons in the spin up pool, decay time of this process is mainly controlled by hole recombination life time. c) and

d). After spin up pool is empty the PL decay time is controlled by spin relaxation which causes spin flips to the

other pool.

Physical realization of an efficient spin dependent-recombination process

Since the proposal of SDR, slightly enhanced electron polarization Pe in e.g. AlGaAs and

GaAs by optical orientation has been demonstrated at low temperatures and was attributed to an

SDR process via deep-level defects. However, it is only until very recently that a giant Pe was

achieved at RT in Ga(In)NAs [22, 23]. From cw- and time-resolved PL, it was shown that very

high degree of circular PL polarization can be achieved in optical orientation experiments in

these alloys, in sharp contrast with the parental GaAs. Moreover, according to the time resolved

PL measurements [22], this circular polarization in GaInNAs remained practically constant

within the measurement window of 2 ns in GaNAs QW whereas it rapidly decreased with a

UP DOWN

Capture by center

Capture by hole

HOLE

Spin flip due to spin relaxation

UP DOWN

HOLE

100% spin polarization 3.4 c)

UP DOWN

Capture by hole

HOLE

SLOW

3.4 b)

UP DOWN

Capture by center

HOLE

FAST

3.4 a)

3.4 d)

Page 25: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

25

characteristic time of 50 ps in the N-free QW (see figure 3.5). This indicated that nitrogen

incorporation caused an apparent increase of the spin relaxation time.

The physical mechnism behind this finding as being due to the SDR process was

suggested by V.K. Kalevich et. al. [23] who found that the strong PL polarization is

accompanied by the strong SDR ratio and that both of them can be suppressed in transvered

magnetic fileds.

Figure 3.5 a); PL and PL polarization of the N-free and N-containing QW sample with N=0.6%. b) Decays of the

circular polarization detected from the same samples as in a) [22].

Figure 3.6 a); calculated energy levels associated with the electronic and nuclear spin states of the Gai2+

defect. The

allowed ESR transitions (mS=±1 and mI=0) occur when the electron spin splitting matches the microwave photon

energy, and are marked by the vertical lines. b) Typical ODMR spectra by monitoring the total intensity of the BB

PL from an RTA-treated GaN0.021As0.979 epilayer, obtained at 3K under x and +

excitation at 850 nm. The

microwave frequency used is 9.2823 GHz. A simulated ODMR spectrum of the identified Gai defect (denoted by Gai-

C) is also shown. From Ref.[2]

3.6 a) 3.6 b)

Page 26: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

26

In order to identify the SDR-active defects and thus to provide the first unambiguous

proof that the strong Pe can indeed be generated by SDR, a combination of optical orientation

with the optically detected magnetic resonance (ODMR) technique was employed [2]. ODMR is

known to be sensitive to SDR, especially if SDR acts as a dominant carrier recombination

channel, and also to be able to identify chemical nature of defects in semiconductors. A Gai2+

self-interstitial was unambiguously identified as the common core of the defects responsible for

the monitored SDR, based on a hyperfine structure – see Figure 3.6 This study has shown a

promising way to construct a spin filter by introducing a suitable defect center to a

semiconductor material.

Page 27: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

27

Chapter Four: Experimental Approach

Optical orientation PL spectroscopy

PL spectroscopy is a contactless and non-destructive method of probing the electronic

structure of a semiconductor. The principle of the PL measurements is simple: when a

semiconductor sample is optically excited with a photon having energy above the band gap of

the semiconductor, electrons and holes are created, usually in the near surface region by

absorption of the excitation light. These photogenerated electrons and holes diffuse into the bulk

and at the same time, they relax and recombine via various channels. Some of the most important

applications of the PL spectroscopy are listed below:

Bandgap determination: Radiative transitions in semiconductors can occur between

states in the conduction and valence bands, with the energy difference equal to the

bandgap energy. This can be used to determine the bandgap energy of the semiconductor

provided that the origin of the PL transitions is proven to be the band-to-band

recombination.

Impurity levels and defect detection: Radiative transitions in semiconductors often

involve localized defect levels. The PL energy associated with these levels can be used to

identify specific defects, and the PL intensity, if calibrated, can be used to determine their

concentration.

Recombination mechanisms: The return to equilibrium, known as recombination, can

involve a radiative recombination process. Properties of the corresponding PL such as its

line shape, dependences of the PL intensity on photo-excitation power and temperature

can be used to understand the origin of the radiative recombination.

Material quality: In general, competing NR processes are associated with localized

defect levels, whose presence is harmful to material quality and subsequent device

performance. As the NR processes compete with PL, material quality can be evaluated by

quantifying an amount of radiative recombination.

A typical PL set-up can be divided into three parts; an excitation side, a cryostat, and a detection

side.

Excitation side: An excitation source is used to create photogenerated electron-hole pairs. In our

experiments, a tunable Ti-sapphire laser was used for these purposes. Resonance cavity

conditions in a Ti-sapphire rod can be adjusted to tune the laser wavelength within the range of

750-1100 nm. Long Wavelength Past (LWP) and Short Wavelength Past (SWP) filters were used

to avoid any leakage of stray laser light.

Page 28: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

28

A focusing lens was placed close to a cryostat window. Since the SDR process is

sensitive to the excitation power, the laser beam was focused. For this purpose, a fine adjustable

lens holder was used.

Cryostat: PL measurements are often performed at low measurement temperatures, i.e around T

= 3 - 6 K. This can be achieved by using liquid He which flows into a cryostat where a sample is

placed. The cryostat usually consists of four chambers. A vacuum chamber with vacuum in the

range of 10−6 mbar is used to thermally isolate other chambers from the environment. The 2nd

chamber contains liquid nitrogen to pre-cool the sample chamber down to the temperature of

around 160 K. The 3rd

chamber will be filled with liquid He. The helium chamber and the sample

chamber are linked via a needle valve. The He flow between these chambers can be controlled

by using a mechanical pump. The temperature can be adjusted in the range of 2-9 K by changing

the flow rate. To achieve temperatures from 10 to 300 K, a heater is used.

Detection side: The PL signal from a sample can be collected and focused by two lenses on an

entrance slit of a monochromator. A photodetector will then register the PL emission. Two types

of detector were used in this work, i.e. a Si charge-coupled device (CCD) and a Ge detector. The

former is sensitive in the spectral range of 300 – 1050nm, whereas the later can be used to detect

emissions with longer wavelengths up to 1600 nm. By scanning the monochromator through the

desired energy range, and registering the intensity, a PL spectrum is obtained.

Lock-in technique

The PL signals were detected using the lock-in technique. By modulating the intensity of

the excitation light beam at a certain frequency and using a lock-in amplifier, stray light, that is

not connected to the PL emission, will be discriminated – see Figure 4.1.

Figure 4.1; lock-in amplifier technique; only a signal in-phase with reference is amplified and noise can be

subtracted.

Page 29: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

29

The PL set up can be easily modified for optical orientation measurements by placing

appropriate polarizers in detection and excitation optical paths. At the excitation side, the

excitation beam is circularly polarized by installing a linear polarizer followed by a quarter wave

plate. If optical axis of the quarter wave plate is rotated ±45 degree from the optical axis of

incoming linearly polarized light, right-handed (σ+) and left-hand (σ -) polarized light (see figure

4.2) will be produced. On the detection side, a quarter wave plate combined with a linear

polarizer are again used to monitor a polarization state of the PL emission. The experimental

set-up used for optical orientation measurements is shown schematically in figure 4.3.

Figure 4.3; photoluminescence set up for optical orientation PL measurements, the set up is a typical PL set up

with retarders installed to produce/ detect circularly polarized light.

Ar+ laser Ti: sapphire

Linear polarizer

𝜆/4 retarder

Focusing lens

Lock-in amplifier

Chopper

sample

Cryostat Collection lens Focusing lens

Linear

retarder

Monochrometer

Detector

Computer

Figure 4.2; the principle of a retarder. The

principle of retarder; the figure represents

quarter wave plate retarder, in case that linearly

polarized input is deviated 45 degree from optical

axis, the output will be circularly polarization

according from the chance in phase delay speed

when light passes though the retarder.

Page 30: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

30

Magnetic resonance technique

Electron Paramagnetic Resonance (EPR)

EPR is a spectroscopic method1 which can be used to study paramagnetic systems, i.e. systems

containing one or several unpaired electron. An unpaired electron has an intrinsic spin angular

momentum S with an associated magnetic moment 𝒎 = −𝜇𝐵𝒈𝒆𝑺 where 𝑔𝑒 is the electron g-

factor and 𝜇𝐵 is the Bohr magneton. If the unpaired electron is placed in a static magnetic field B,

the so-called Zeeman interaction energy between the applied field and the magnetic moment is

given by the classical expression E = -m·B. This expression can be represented by the spin

Hamiltonian

𝑯 = 𝜇𝐵𝒈𝒆 ∙ 𝑺 ∙ 𝑩.

There are two allowed directions of the electron spin S=1/2, parallel or antiparallel to the

direction of the static magnetic field B, which is applied along the z-axis. These can be

represented by the two spin states |1

2,

1

2 and, |

1

2, − 1

2 respectively, having the corresponding

spin quantum number 𝑚𝑠 = ±1/2. The degeneracy of the energy level of the electron will thus be

removed in the presence of the external field as shown in Figure 4.4, in which the level is split

into two sublevels. In order to induce a transition between two sublevels, an electromagnetic

field with energy quanta hν with the time-dependent component perpendicular to the static

magnetic field is applied. In thermal equilibrium the population difference between the two spin

states is given by the Boltzmann distribution

𝑁−

𝑁+= exp(−𝑔𝑒𝜇𝐵𝐵𝑧/𝑘𝐵𝑇),

𝑁− and 𝑁+ are the populations of the different spin states. At normal temperature (T< 300 K), a

slight difference in the relative population between the two states is anticipated, and hence it is

possible to induce a transition. If an energy quantum hν is absorbed the following condition must

be satisfied according to Planck’s law

𝑕𝜈 = 𝜇𝐵𝒈𝒆 ∙ 𝑺 ∙ 𝑩.

This relation defines the basic resonance condition in the EPR experiment. The energy separation

between the two sublevels depends on the magnitude of the applied magnetic field. Note that the

1 It is also reffered as Electron Spin Resonance (ESR).

Eq. 4.1

Eq. 4.2

Eq. 4.3

Page 31: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

31

value of the g-factor in a semiconductor deviates from the free electron value ge = 2.0023. This is

due to the effect of the orbital angular momentum L of the unpaired electron. The g-value is

usually anisotropic, i.e. the magnitude depends on the direction of the static magnetic field

relative to the orientation of the paramagnetic centre.

Figure 4.4; microwave induced transition and corresponding EPR signal of two cases: a) S=1/2, I=0 and b) S=1/2,

I=1/2.

In practice, an EPR setup basically consists of several essential parts such as a cavity

where the sample is placed, a magnet to produce the static magnetic field and an electromagnetic

source, usually with a fixed frequency in the range of 9-95 GHz. The resonance occurs when the

energy separation between two states caused by an applied magnetic field is identical to the

microwave energy – Equation 4.3. In order to increase the sensitivity of the spectrometer, a small

AC component is added to a DC magnetic field. This results in an AC modulated EPR signal,

which can be detected using a lock-in amplifier. Consequently, the EPR spectrum is recorded as

the first derivative of microwave intensity dI/dB reflected from the cavity versus the magnetic

field B (see Figure 4.4.)

The EPR technique has been successfully applied to study the electronic structure and

identification of defects in semiconductors. In a more general form, Equation 4.1 can be

rewritten as

𝑯 = 𝜇𝐵𝒈𝒆 ∙ 𝑺 ∙ 𝑩 + 𝑺 ∙ 𝑫 ∙ 𝑺 + 𝑺 ∙ 𝑨𝒊

𝒊

∙ 𝑰𝒊.

Here 𝑺 and 𝑰𝒊 represent an effective electronic spin and a nuclear spin of a defect or

ligand atom i. the anisotropy of the g-tensor and D-tensor reflects the symmetry of the crystal

E E

+1/2

-1/2

-1/2

+1/2

b)

dB

dI

B

B

mS=+1/2

mS=-1/2

B

dB

dI

S=1/2 S=1/2

B

mS = -1/2

mI I=1/2

a)

mS=+1/2

Eq. 4.4

Page 32: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

32

lattice and the defect. The first term describes the usual linear term of electron Zeeman

interaction. The second term introduces a fine structure, i.e. zero-field splitting, important only

for S > 1/2. The most important information in EPR experiments is usually obtained from the

hyperfine coupling, which is due to the interaction between the magnetic moments of the

effective electronic spin S and the nuclear spin Ii, which is described by the third term in

Equation 4.4. The nuclear Zeeman term and the other higher order terms have not been included

in Equation 4.4 due to their negligible effects in most cases of EPR and ODMR investigations.

Let us consider a simple case (S=1/2) with an isotropic g-factor and an isotropic central

hf interaction which is small compared to the electron Zeeman interaction. Equation 4.4 can be

solved by a perturbation theory in the first order and for energies one obtains

𝐸 = 𝑔𝜇𝐵𝐵𝑚𝑆 + 𝐴𝑚𝐼𝑚𝑆 ,

with eigenfunctions Ψ = | 𝑚𝐼 , 𝑚𝑆 . For S=1/2, I=1/2 there are now four energy levels instead of

two without the hf interaction because of the mS = ±1/2 and mI = ±1/2 quantum numbers.

Application of a microwave field induces the EPR transitions with the selection rule

∆𝑚𝑠 = ±1, ∆𝑚𝐼 = 0.

Instead of one transition observed in the case of I=0, there are now two lines with the separation

between them ∆B=A/(gμB).

In general, there are 2I+1 lines due to hf splitting. By analyzing the hf pattern obtained

from EPR spectra we are able to identify the chemical and electronic properties of the defect and

its surroundings. One excellent example of this can be found in ref. [15] where two Ga

interstitials were ambiguously identified based on the analysis of the hf interaction. Gallium

consists of two isotopes, 69

Ga with 60.4% abundance and 71

Ga with 39.6% abundance. Both

isotopes have a nuclear spin I=3/2. The hf interaction of each isotope with an unpaired electron

gives rise to four transitions with the contribution to the relative intensity following the ratio of

natural abundances. Due to the difference in their nuclear magnetic moment, the two Ga isotopes

give rise to slightly different hf splittings leading to a characteristic hf structure shown in Figure

4.5. This is the signature of the hf interaction involving a Ga atom.

Though EPR shows a great potential in defect indentification, it still has some limitations.

First of all, a paramagnetic ground state is required. Some defects have zero-spin ground state

and thus cannot be detected in EPR. Secondly, no information on carrier recombination related to

defects can be obtained by EPR. And thirdly, the sensivity is low due to microwave detection.

Fortunately, the first limitation can be overcome if another charge state of the same defect can be

reached by changing the Fermi level position, e.g by doping with shallow impurities or by

Eq. 4.5

Eq. 4.6

Page 33: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

33

illuminating samples. The last two limitations could only be resolved if another methods or

extended techniques are used. A combination of EPR with optical detection methods such as PL

is a solution to the problems.

Optically Detected Magnetic Resonance

Optically detected magnetic resonance is a combination of EPR and PL. The technique is

based on the fact that the recombination processes are spin-dependent. When the microwave

field induces transitions between two Zeeman sublevels that have different recombination rates

or polarizations, the total PL intensity or its polarization can be changed. ODMR spectrum is

obtained by a measurement of this change versus magnetic field (Figure 4.6). Figure 4.7 shows a

schematic illustration of an ODMR setup.

ODMR measurements not only preserve all the potentials from conventional EPR and PL

but also add more advantages. It is more sensitive due to higher sensitive optical detection over

the microwave detection. This advantage makes ODMR suitable for studies of thin films, layered

and quantum structures. The radiative recombination spectrum from PL measurements of a deep

level defect often shows up as a broad featureless band, from that, very little information can be

obtained. By measuring the spectral dependence of the ODMR signal, the ODMR spectrum can

be assigned to the relevant PL spectrum of a specific defect, which is suitable for studies of

carrier recombination processes and for assigning them to corresponding defects.

Typical ODMR set up is shown in Figure 4.7. The sample is placed in a microwave

cavity inside a cryostat to obtain liquid He temperature. Liquid He is continually supplied by a

He transfer tube which is connected to a liquid He reservoir. A static magnetic field is provided

by a magnetic coil. A microwave field with a frequency of about 9.5 MHz (X-band) is generated

3200 3400 3600

(a)

(b)

(c)

95GHz

OD

MR

Inte

nsi

ty (

a.u.)

Magnetic field (mT)

Figure 4.5; (a) simulation at 95GHz of

the hf splitting arising from the

interaction between an unpaired

electron and the nuclear spin of a Ga

atom. The contribution from (b) 69

Ga

and (c) 71

Ga.

Page 34: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

34

in the cavity by a microwave generator through a waveguide. The microwave frequency is

always kept constant and the static magnetic field can be swept from 100 to 10000 Guass by

applying a current to the magnetic coil. Optical detection is used. For these purposes, the PL

emission from the sample is excited by a laser (Ti-Sapphire for GaNAs) and is detected by a

detector without a monochromator. The PL signal is detected by selecting proper LWP and SWP

filters.

Figure 4.7; schematic illustration of an ODMR set-up.

Ar+ laser Ti: sapphire

Linear polarizer

𝜆/4 retarder

Focusing lens

Lock-in amplifier

Chopper

Collection lens Focusing lens

Detector

Computer

Microwave

generator

Chopper

Static magnetic field

E

B

B

S=1/2

𝑛1

1

𝑛2

2

k2

k1

∆I

Figure 4.6; principle of an ODMR experiment.

Microwave field induces a transition between two

sublevels. The ODMR signal is obtained as a

change of total light ∆I~∆k∆n.

n1, n2 populations of the spin at sublevels.

∆k= k1- k2 the difference in recombination rates of

two sublevels.

∆n number of carriers transferred between two

sublevels due to microwave field.

Page 35: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

35

Chapter Five: Experimental Results

Defect Engineering for Spin Filtering Effect in GaNAs

According to previous findings, GaNAs is a very promising material for spin filtering

which can be accomplished at room temperature and without application of an external magnetic

field. However, the fundamental knowledge on how to control and optimize this ability is still

lacking. The purpose of this work is to understand effects of growth parameters and structural

design on the formation of deep centers responsible for SDR aiming at optimization of spin

filtering. First of all, the effect of quantum confinement on the spin filtering ability is examined.

This is performed under conditions of electron injection from GaAs barrier layers, i.e. under

conditions relevant to device applications. Secondly, optimization of the fabrication conditions

(i.e. growth temperature and post-growth annealing) for efficient formation of spin-filtering

defects is performed. Effects of doping on the formation of these defects are also analyzed. And

finally, defect formation during different epitaxial processes, such as molecular beam epitaxy

growth (MBE) and metal-organic chemical vapor deposition (MOCVD), is also studied.

5.1 Defect engineered spin filter from a low dimensional semiconductor structure; spin

filtering effect in QW structures

In this set of measurement, PL and ODMR measurements under optical orientation were

performed for a set of GaNAs multiple quantum well (MQW) structures. Parameters of the

samples are summarized in table 5.1.1. The measurements were performed at room temperature

(300 K) for optical PL orientation and at 6 K for ODMR. Excitation laser beam was aligned

parallel to a growth direction.

Sample

QW

width

GaAs

barrier

width

GaAs

buffer

layer

GaAs

capping

layer

Growth

method

Growth

Temperature

Substrate

Nitrogen

composition

(%)

GaAs

band-

(300 K)

GaNAs

peak

(300K)

2521

30 Å

7-

period

202 Å

2500 Å

500 Å

MBE

420 C

Semi-

insulating

GaAs

1.6

875.5

nm

956.5

Nm

2522

50 Å

7-

period

202 Å

2500 Å

500 Å

MBE

420 C

Semi-

insulating

GaAs

1.6

875.5

nm

987.0

Nm

2523

70 Å

7-

period

202 Å

2500 Å

500 Å

MBE

420 C

Semi-

insulating

GaAs

1.6

875.5

nm

997.0

Nm

Page 36: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

36

Table 5.1.1; parameters of the structures, all samples contain 7-periods GaN0.016As0.984/GaAs QWs grown on a

semi-insulating GaAs substrate with a GaAs capping layer.

The excitation wavelength was 827 nm. Under these conditions most of the carriers

participating in the band-to-band recombination in the GaN0.016As0.984 QWs are injected from

GaAs, since a total thickness of the GaAs barriers is much larger than that of the GaNAs QWs.

For GaAs, such excitation can be used for optical orientation as the spin-orbit--split VB states do

not participate in the absorption process and a preferential spin orientation of the CB electrons is

created. Circular polarization and the SDR ratio are detected via the GaNAs- related band-to-

band PL emission, to determine the ability of this material to spin filter the injected electrons.

Figure 5.1.1; PL spectra of the GaNAs/GaAs QW samples. The low energy PL band originates from the band-to-

band emission in the GaNAs QWs.

PL spectra of the investigated samples are shown in figure 5.1.1. The strong band-to-band

emission was observed at room temperature for all samples, allowing the SDR measurements.

The results of these measurements are summarized in figure 5.1.2, taking as an example the 2521

sample. The SDR ratio of 1.23 at the PL peak position and a circular polarization degree of 12%

were observed for the excitation power W of 200 mW.

2524

90 Å

7-

period

202 Å

2500 Å

500 Å

MBE

420 C

Conducting

GaAs

1.6

875.5

nm

1003.5

nm

800 850 900 950 1000 1050 1100

2521 N = 1.6% 30 A

2522 N = 1.6% 50 A

2523 N = 1.6% 70 A

2524 N = 1.6% 90 A

PL

Int

ensi

ty (

Arb

itar

y un

it)

wavelength (nm)

Full spectrum 2521, 2522 and 2523 multi-QW(300 K)

exc. wavelength 827 nm

Exc. power = 200 mW

Page 37: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

37

Figure 5.1.2; results of optical orientation measurements performed for the 2521 sample.

Fig. 5.1.3; power dependences of the SDR ratio (a) and the circular polarization degree (c-d) measured for the

investigated QW samples.

0 50 100 150 2000.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6a)

2521 L = 30 A

2522 L = 50 A

2523 L = 70 A

2523 L = 90 A

cir

cu

lar

po

lari

za

tio

n

cir

cu

lar

po

lari

za

tio

n

cir

cu

lar

po

lari

za

tio

n

excitation power (mW)excitation power (mW)

excitation power (mW)

SD

R r

ati

o

excitation power (mW)-50 0 50 100 150 200 250

-0.10

-0.05

0.00

0.05

0.10b)Exc:

0 50 100 150 2000

5

10

15

20

c)Exc:+

0 50 100 150 200 2500

-5

-10

-15

-20d)Exc:

900 960 1020 900 960 1020

900 960 1020 900 960 1020

1.0

1.2

1.4

1.6

-5

0

5

10

15

20

-20

-15

-10

-5

0

5

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

PL I

nten

sity

(A

rb.U

nits

)Exc:

x

2521

T: 300 K

Cir

cula

r po

lari

zatio

n C

ircu

lar

pola

riza

tion

Exc:

Det:

+

Exc:

Laser power: 200 mW

Excitation wavelength : 827 nm

Det:

+

C

ircu

lar

pola

riza

tion

Exc:+

Wavelength, (nm)S

DR

Rat

io (/

Det:

+

L = 30 A

Page 38: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

38

Both SDR ratio and circular polarization degree decrease with decreasing excitation

power, as shown in figure 5.1.3. The same trend was observed for all investigated structures: the

SDR ratio and the PL polarization degree increase with W and saturate at high excitation powers.

This can be explained by dynamic polarization of paramagnetic defect centers. When W is low, a

number of photogenerated electrons is lower than a number of deep paramagnetic centers.

Therefore, the centers are not polarized and photogenerated electrons are rapidly depleted by the

centers. After increasing the excitation power the number of electrons becomes high enough to

polarize the centers and the SDR process dominates. Further slight increase of W will not affect

the center polarization and the SDR ratio and spin polarization saturate.

Also obvious from Figure 5.1.3, the saturation value of the SDR ratio increases with

increasing width of the QW. Possible explanations for this effect are as follows.

1. The effect of band-to-band recombination; quantum confinement- induced enhancement

of the band-to-band recombination rate in narrow QWs.

In narrow QW structures, strong confinement-induced overlap of electron and hole wave

functions promotes the efficient band-to-band recombination. This would suppress

importance of the defect-related recombination and the SDR process and would degrade

the spin filtering.

2. The effect of electron spin relaxation; acceleration of electron spin relaxation in narrow

QWs.

Spin relaxation usually accelerates in narrow QWs, promoted via the Dyakonov-Perel

mechanism [20]. This would diminish the ability of the injected electrons to polarize the

defect centers which would, in turn, lead to a reduction of the SDR ratio.

To identify chemical nature of the deep paramagnetic defects responsible for the SDR

process in the investigate samples and to determine the origin of the observed degradation of the

spin filtering efficiency in the narrow QWs, ODMR measurements were performed. A typical

ODMR spectrum is shown in Figure 5.1.4 a). Similar spectra were also detected from other

structures. The ODMR spectrum shows the following two distinct features originated from

different defects. The first one is a single strong line situated in the middle of the ODMR

spectrum, with a g-value close to 2. Due to a lack of hyperfine (HF) structure, unfortunately, the

chemical nature of the corresponding defect cannot be identified. Below we shall simply refer to

it as the “unknown 1” defect. The second feature of the ODMR spectra consists of a complicated

pattern of lines spreading over a wide field range. Such multiple ODMR lines arise from a high

Page 39: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

39

electron spin state exhibiting a zero-field splitting caused by a defect crystal field or from HF

interaction involving a high nuclear spin, or from several overlapping ODMR signals due to

different defects. To resolve this issue, the obtained ODMR spectrum was compared with the

results of Ref.[2]. It was found that the ODMR spectrum in fact consists of three groups of lines

from three different defects (denoted as Gai-A, Gai-B and Gai-C).

Figure 5.1.4 a); ODMR spectrum of sample 2523, simulation fitting indicated the mixing of three kinds Gai defect

denoted A, B and C. ODMR spectrum was measured under both linear and circular excitation but nothing

significantly change was observed. b) Simulation curve of all defects participating to ODMR spectra. c) Simulation

cruves o f each Ga-interstitial defect with two natural isotopes abundance.

Indeed, the spectrum can be simulated using a spin-Hamiltonian

𝑯 = 𝜇𝐵𝒈𝒆 ∙ 𝑺 ∙ 𝑩 + 𝐴𝑺 ∙ 𝑰

Here, 𝜇𝐵 is the Bohr magneton, g the electronic g-factor, and A the hyperfine parameter.

Hyperfine parameter is set to be a scalar due to the fact that the ODMR spectrum is isotropic

with a rotation of magnetic field B with respect to the crystallographic axes. Spin Hamiltonian

parameters of the Gai- related defects were taken from ref. [15] and ref. [2] and are summarized

in Table 5.1.3. It is apparent that the agreement between the simulations and the experimental

results is excellent, which justifies the assignment. The experimental results again confirm that

-100 0 100 200 300 400 500 600 700

x

Sim

Magnetic field (mT)

2523 L = 70 A

-100 0 100 200 300 400 500 600 700

unknown "I"

Gai-C

Gai-B

Gai-A

OD

MR

(A

rb

. U

nit

s)

total

Gai-A 71

Gai-A 69

Gai-A

total

Gai-B 71

Gai-B 69

Gai-B

total

Gai-C 71

Gai-C 69

Gai-C

a)

b)

c)

Page 40: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

40

Gai acts as the core of the spin-dependent recombination center. This conclusion is based on the

following experimental facts. Firstly, the observed multiple ODMR lines arise from a hyperfine

structure derived from a strong interaction between an unpaired localized electron spin (S=1/2)

and a nuclear spin of an atom that has two isotopes with a nuclear spin I=3/2 and a 60/40 ratio of

natural abundance. This gives rise to four allowed ODMR transitions (mS=±1 and mI=0) for

each Ga isotope, see Fig.5.1.4 c). Ga is the only atom with such unique properties, i.e. Ga has

two naturally abundant isotopes, 69

Ga (60.4% abundant) and 71

Ga (39.6% abundant), and a

nuclear spin I=3/2 for both isotopes. Thus, the identification of a Ga atom in the defect core is

beyond doubt. Secondly, the ODMR spectra were shown to be isotropic with a rotation of

magnetic field with respect to the crystallographic axes. This finding revealed that the electron

wave-function at the defects should be s-like. This is consistent with the observed strong

hyperfine interaction, as the s-like electron wavefunction results in a strong Fermi contact term.

The Ga atom involved in the defect should then be a Gai2+

self-interstitial in which the unpaired

electron has an A1 electronic state, as a GaAs antisite was predicted to possess a non-A1 state that

should lead to a strongly anisotropic ODMR spectrum.

Type Isotope g- factor Hyperfine constant (A)

(𝟏𝟎−𝟒 𝒄𝒎−𝟏)

Gai-A

69 2.005 770

71 2.005 1000

Gai-B

69 1.960 1250

71 1.960 1590

Gai-C

69 2.000 620

71 2.000 806

Unknown “I” - 2.003 -

Table 5.1.3; spin Hamiltonian parameters of Gai A, B and C. All types of Gai interstitial defects contains two

natural Ga isotopes, i.e. 𝐺𝑎69i (60.4% abundance) and 𝐺𝑎71

i (39.6% abundance).

The intensity of the ODMR spectra was found to strongly depend on the quantum well

width as illustrated in figure 5.1.5. The observed dependence is consistent with both mechanisms

(i.e. the effect of band-to-band recombination and the effect of electron spin relaxation),

suggested to be responsible for the decreasing filtering efficiency in the narrow QW. Indeed:

1. The enhancement of the band-to-band recombination will suppress the role of the defect-

related recombination and, therefore, the ODMR intensity.

2. A reduction of the spin relaxation time for the CB electrons will lead to a weak

dynamical polarization of the paramagnetic center. This will decrease a population

Page 41: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

41

difference between the sublevels at the defect center resulting in the weaker ODMR

intensity.

In summary, the GaNAs/GaAs multiple quantum well structures can be employed for

spin filtering of the injected electrons at room temperature. However, the quantum confinement

is found to degrade the spin filtering ability of GaNAs.

5.2 Effect of growth temperature and post-growth treatment on the SDR process

Since both growth temperature and post-growth annealing will likely influence the

formation of the NR centers, it is important to understand how they will affect the spin-filtering

process. Parameters of the samples selected for these studies are listed in table 5.2.1 a) and b).

Table 5.2.1 a); parameters of the samples used to investigate effects of RTA on the spin-filtering process.

.

Sample

Epilayer

Growth

method

Growth

Temperatu

re

Post

growth

treatment

Substrate

Nitrogen

compositi

on (%)

GaAs

band-

gap

(300 K)

GaNAs

band-gap

estimate

(300 K)

GaNAs peak

(300K)

2468

1000 Ǻ

Gas

source

MBE

420 C

-

Semi-

insulating

GaAs

1.3

875.5 nm

1026.5 nm

1018.5 nm

2468

RTA

1000 Ǻ

Gas

source

MBE

420 C RTA

Semi-

insulating

GaAs

1.3 875.5 nm

1026.5 nm

1018.5 nm

Figure 5.1.5; ODMR intensity as a

function of the QW width. The ODMR

signal increases when the QW width is

increased.

20 30 40 50 60 70 80-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

OD

MR

(a

rb.u

nit)

Well width (Å)

Page 42: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

42

Table 5.2.1 b); parameters of the samples used to investigate effects of growth temperature on the spin-filtering

process.

Post-growth RTA

Results of optical orientation measurements performed for the samples 2468 and

2468RTA are shown in figure 5.2.1 a) and b), respectively. Both samples demonstrate the spin

filtering effect at room temperature.

Figure 5.2.1 a) and b); results of optical orientation and SDR measurements performed for the 2468 and 2468RTA

samples under the excitation power of 200 mW.

In order to quantify changes in defect concentrations after RTA, excitation power dependences

of the PL polarization degree were measured and simulated using the set of rate equations:

Sample

QW

width

GaAs

barrier

width

GaAs

buffer

layer

GaAs

capping

layer

Growth

method

Growth

Temperature

Substrate

Nitrogen

composition

(%)

GaAs

peak

(300 K)

GaNAs

peak

(300K)

2458

30 Ǻ

7-

period

202 Ǻ

2500 Ǻ

500 Ǻ

MBE

420 C

Semi-

insulating

GaAs

1.2

875.5

nm

1005.1

Nm

2513

50 Ǻ

7-

period

202 Ǻ

2500 Ǻ

500 Ǻ

MBE

580 C

Semi-

insulating

GaAs

1.1

875.5

nm

1000.8

Nm

a) b) Before RTA After RTA

Page 43: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

43

𝑑𝑛±

𝑑𝑡= −𝛾𝑒𝑛±𝑁∓ −

𝑛± − 𝑛∓

2𝜏𝑠+ 𝐺± −

𝑛±

𝜏𝑑,

𝑑𝑁±

𝑑𝑡= −𝛾𝑒𝑛∓𝑁± −

𝑁± − 𝑁∓

2𝜏𝑠𝑐+

1

2𝛾𝑕𝑝𝑁↑↓,

𝑑𝑝

𝑑𝑡= −𝛾𝑕𝑝𝑁↑↓ + 𝐺+ + 𝐺− −

𝑛+ − 𝑛−

𝜏𝑑,

𝑁𝑐 = 𝑁↑↓ + 𝑁+ + 𝑁−, 𝑝 = 𝑛+ + 𝑛− + 𝑁↑↓,

Under the steady-state conditions:

𝑑𝑛±

𝑑𝑡=

𝑑𝑁±

𝑑𝑡=

𝑑𝑝

𝑑𝑡= 0.

For numerical fit, we have used the time constants that were reported in the literature [2], i.e. τr =

10 ns16

and τs=150 ps. τsc is insensitive in the analysis, as long as it is >1.5 ns. These parameters

were set identical for both 2468 and 2468RTA samples. This only leaves γe/γh and γeN as fitting

parameters, where N is the total defect concentration. (As the absolute values of γe and defect

concentration N cannot be determined independently in our experiments, we used a combined

fitting parameter γeN that represents a capture rate of free electrons by the defect and can also be

employed to compare relative defect concentrations in different samples.) The obtained fitting

curves are displayed by the dashed lines in Figure 5.2.2, with γe/γh =4 and γeN values given for

each sample, showing a reasonably good agreement with the experimental results.

0 50 100 150 200

4

6

8

10

12

cir

cu

lar

(sp

in)

po

lari

za

tio

n (

%)

excitation power (mW)

Before RTA: 𝛾𝑒𝑁 = 0.088 ps-1

After RTA: 𝛾𝑒𝑁 = 0.042 ps-1

2468 and 2468 RTA

Figure 5.2.2; circular (spin) PL

polarization as a function of an excitation

power. The dots denote the experimental

data. The dashed lines are the simulated

curves. After RTA, the number of defects

contributing to the SDR is reduced.

Page 44: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

44

As shown in figure 5.2.2, after the post-growth RTA the relative defect concentration is

reduced by half. Physical nature of the SDR process can be clearly seen from this analysis. In

the 2468 sample, the number of defect centers exceeds the number of the photogenerated

electrons. Therefore, the saturation of the PL polarization can not be reached even at the highest

photoexcitation power of 200 mW as it is insufficient to polarize all defects. However, after the

RTA treatment the defect concentration is reduced and the defects can be polarized under a

lower density of the photogenerated electrons (i.e. when W=40 mW). With further increase of

W, on the other hand, the capture process becomes relatively less important, as it is limited by

the defect concentration. This degrades the spin filtering effect.

Similar conclusions are also reached from the ODMR measurements which show that the

ODMR intensity is reduced after RTA – see figure 5.2.3.

Growth temperature

Growth temperature typically influences the defect formation in a semiconductor material. To

understand its effects on the SDR process all measurements were repeated for the samples with

similar structure but grown at different temperatures, i.e. 𝑇𝑔 = 420o C for the #2458 and 𝑇𝑔 =

5800 C for the #2513. Spectral dependences of the SDR ratio and the circular PL polarization are

presented in figure 5.2.4 a) and b). Both samples unambiguously demonstrate the SDR process.

The corresponding ODMR spectra are shown in figure 5.2.5. The ODMR intensity is apparently

higher for the structure grown at lower temperature. The same conclusion was reached after

fitting the excitation power dependences of the PL polarization using the coupled rate equations -

figure 5.2.6.

Figure 5.2.3; ODMR spectra

measured from the 2468 sample

before and after RTA. The

simulation curve was obtained

assuming that the ODMR spectrum

in the as-grown sample contains

contribution from Gai-A, Gai-B and

Gai-C defects, as well as from the

“unknown 1” signal. The ODMR

intensity is dramatically reduced

after RTA indicating a reduction of

the defect concentration. -100 0 100 200 300 400 500 600 700

OD

MR

(A

rb.

Un

its)

x

Magnetic field (mT)

Simulation Gai-A+B+C+ unknown "I"

Before RTA

After RTA

Page 45: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

45

Figure 5.2.4 a) and b); results of optical orientation and SDR measurements performed for the 2458 and 2513

samples under the excitation power of 200 mW excitation.

Figure 5.2.5; ODMR spectra

recorder from the samples grown at

𝑇𝑔 as indicated in the Figure.

a) b) 𝑻𝒈 = 420 C 𝑻𝒈 =580 C

0 100 200 300 400 500 600 700

OD

MR

(A

rb.

Un

it)

Magnetic field (mT)

Tg = 580 C

x

Tg = 420 C

Page 46: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

46

0 50 100 150 2000

2

4

6

8

10

12C

irc

ula

r (s

pin

) p

ola

riza

tio

n (

%)

excitation power (mW)

The observed reduction of the defect concentration during the high temperature growth is

probably not surprising as at higher Tg a Ga atom arrived to a substrate will have kinetic energy

high enough to move to a suitable substitutional position to form the perfect alloy.

The results presented in this section clearly demonstrate that the concentration of Gai-

related centers responsible for SDR can be controlled by varying the growth temperature and via

the post growth annealing.

5.3 Effects of doping on the formation of the Gai-interstitial paramagnetic centers.

It is well known that the defect formation is largely affected by the Fermi level position

during the growth determined by doping. To clarify importance of this effect for the formation of

the Ga-interstitials, samples with different doping were studied.

5.3.1 P-type doping

GaNAs:C epilayer with nitrogen composition of 0.54% was studied. According to the

Hall measurements, the hole concentration in the sample was 2.3e17

cm-3

. In order to identify the

band-to-band emission from the alloy, temperature dependent PL measurements were employed

-see Figure 5.3.1.1. It was found this PL dominates at all measurement temperatures. Indeed, the

PL maximum position exhibits the characteristic S-shape temperature behavior as discussed in

the first chapter. From the ODMR measurements, the employed doping favors the formation of

the Ga𝑖- C defect as demonstrated in figure 5.3.1.2.

𝑇𝑔 = 420 𝐶 : 𝛾𝑒𝑁 = 0.087 ps-1

𝑇𝑔 = 580 𝐶 : 𝛾𝑒𝑁 = 0.065 ps-1

Figure 5.2.6; circular (spin) PL

polarization as a function of excitation

power. The dots denote the

experimental data. The dashed lines are

the simulated curves. After RTA, the

number of defects contributing to the

SDR is reduced.

Page 47: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

47

5.3.2 N-type doping

Figure 5.3.2.1 a) and b) shows PL spectra measured from two investigated n-type GaNAs

epilayers with similar N compositions of 0.21% (EB129) and 0.23% (EB128). Electron

concentrations in the samples were −3.3 × 1014 cm-3(EB129) and−4.8 × 1015 cm-3 (EB128),

as determined from the Hall effect measurements. The GaNAs PL emission clearly dominates in

both structures. The corresponding ODMR spectra measured when monitoring these emissions

are shown in figure 5.3.2.2 a) and b). The intensity of the ODMR signals increases for the

EA719 N = 0.54% n = 2.3e17 cm-3

-100 0 100 200 300 400 500 600 700

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

x

OD

MR

(n

orm

ali

zed

)

Magnetic field (mT)

Sim Gai-C

Figure 5.3.1.2; ODMR spectrum of

GaNAs:C epilayer detected via the near-

band-edge emission. The spectrum is

related to the Ga𝑖-C defect center.

700 750 800 850 900 950 1000 1050 1100 1150

6 K

60 K

120 K

180 K

240 K

300 K

PL

In

ten

sity

(N

orm

ali

zed

)

wavelength (nm)

EA719 N = 0.54% n = 2.3e17 cm-3

Figure 5.3.1.1; temperature dependence

measured from the GaNAs:C epilayer.

Page 48: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

48

sample with the higher carrier density which indicates that the formation of the involved centers

is promoted by the n-type doping. From the performed angular dependent measurements it can

be concluded that at least two components contribute to the ODMR spectra, as relative intensities

of different lines within the spectra vary with B. This is especially pronounced for the EB129

sample – see Figure 5.3.2.3 a).

700 750 800 850 900 950 1000 1050 1100 1150

6 K

60 K

120 K

180 K

240 K

300 K

PL

In

ten

sity

(N

orm

ali

zed

)

wavelength (nm)

EB128 N = 0.23% n = -1.8e15 cm-3

700 750 800 850 900 950 1000 1050 1100 1150

6 K

60 K

120 K

180 K

240 K

300 K

PL

In

ten

sity

(N

orm

ali

zed

)

wavelength (nm)

EB129 N = 0.21% n = -3.3e13 cm-3

Figure 5.3.2.1 a); temperature

dependent PL spectra measured from

the EB129 sample (n = −3.3 ×

1014 cm-3).

Figure 5.3.2.1 b); temperature

dependent PL spectra measured from

the EB128 (n = −1.8 × 1015 cm-3 ).

This sample shows relatively higher

intensity of the GaNAs emission as

compared with EB129.

Page 49: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

49

Figure 5.3.2.2 a) and b); ODMR spectra detected via the near band edge emission from the samples as specified in

the figure.

Figure 5.3.2.3 a) and b.; angular dependences of the ODMR spectra. Note that a relative intensity of the 480 mT

line changes with the angle.

The existence of two ODMR components was further confirmed by varying experimental

conditions, such a microwave power and measurement temperature. The results of these

measurements are summarized in figure 5.3.2.4.

a) b) EB128 N = 0.23, n =-1.8e15 cm-3 EB129 N = 0.21, n =-3.3e13 cm-3

-100 0 100 200 300 400 500 600 700 800 900

WINDOW:

LWP 1250

OD

MR

(A

rb.

Un

it)

Magnetic field (mT)

Sim

x

b)

EB129 EB128

-100 0 100 200 300 400 500 600 700 800

WINDOW:

LWP+SWP 1000OD

MR

(A

rb.

un

it)

Magnetic field (mT)

x

Sim

a)

0 100200300400500600700800

0 degree

40 degree

60 degree

80 degree

Magnetic field (mT)

OD

MR

(nor

mal

ized

)

0 100 200 300 400 500 600 700

0 degree

20 degree

40 degree

60 degree

80 degree

Magnetic field (mT)

OD

MR

(nor

mal

ized

)

Page 50: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

50

Figure 5.3.2.4 a); microwave power dependence of the ODMR spectra measured from the EB129 sample, the

relative intensities of the peak at 48o mT (g = 1.357) and the others lines depend on the microwave power. b) the

same trend was observed when the temperature was changed. These results show that at least two components

contribute to the ODMR signal.

As the ODMR spectra are isotropic and contain more than four lines it is probable that at

least one component is related to the Ga𝑖-interstitial defect. Thus simulations using the spin-

Hamiltonian were performed. Best fit of the experimental data was obtained when using the

following parameters: g = 1.960, A ( 𝐺𝑎69i) = 1000 and A ( 𝐺𝑎71

i)= 1270. The simulation curve

using these parameters is shown in the upper part of Figure 5.3.3.2 and can reasonably account

for the majority of the detected ODMR lines. It is interesting to note that the obtained parameters

differ significantly from those of the previously studied Ga interstitial defects. This likely

indicates a different local configuration of the Ga interstitials in n-type GaNAs, e.g. due to

perturbations by Si.

5.4 Effects of growth techniques on the defect formation

The very important question is how the Gai defects are formed. The defects have never

been found in GaAs, which implies that their formation is related to introduction of nitrogen

atoms. Recently it has been reported that the formation of Gai is induced by N bombardment

during the MBE growth process [24]. In principle, this can explain the defect formation in all

previously discussed structures as they were all grown by MBE. Alternatively, the defect

formation can also be induced by the presence of nitrogen as it may minimize a total energy of

the system. To check whether or not this is indeed the reason for the defect formation we have

studied ODMR properties of GaNAs epliyaer grown by MOCVD. Here, the defect formation

should be mainly determined by thermodynamics during the growth process, as N bombardment

is no longer present. Parameters of the investigated samples which were all grown on semi-

insulating GaAs substrates are listed in table 5.4.1.

0 100 200 300 400 500 600 700

Microwave power

200 mW

100 mW

50 mW

OD

MR

(n

orm

aliz

ed)

Magnetic field (mT)

a) b)

0 100 200 300 400 500 600 700

N = 0.21%

n-doped (Si) -3.3e14 cm-3

WINDOW:

LWP+SWP 1000

Temperature

5 K

13 K

OD

MR

(n

orm

aliz

ed)

Magnetic field (mT)

EB128 N = 0.23, n =-1.8e15 cm-3 EB129 N = 0.21, n =-3.3e13 cm-3

Page 51: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

51

Table 5.4.1; parameters of the investigated MOCVD-grown GaNAs epilayers. GaNAs bandgap energies were

estimated from the BAC model.

PL spectra measured at 6K from the investigated samples are shown in figure 5.4.1. As is

seen from the figure, the intense band-to-band emission is observed from the MD232 (N =

0.36%) and MD 207 (N = 0.94%) samples, whereas it is rather week for all other structures.

Figure 5.4.1; PL spectra detected from the MOCVD samples.

Sample

Type

Nitrogen

composition (%)

Doping

Carrier

concentration

(cm−𝟑)

Estimated 𝑬𝒈

(6 K)

GaNAs

𝑬𝒈 estimate

(300 K)

MD234

epilayer <0.1% - 5× 1016

<839.63 nm <889.55 nm

MD204

epilayer 0.29% - 6.8× 1016

870.18 nm 917.44 nm

MD232

epilayer 0.36% - 7.4× 1016

879.60 nm 926.58 nm

MD230

epilayer 0.67% - 1.0× 1017

839.63 nm 889.55 nm

MD207

epilayer 0.94% - 2.0× 1016

949.95 nm 998.40 nm

800 900 1000 1100

MD 234 (N < 0.10%)

MD 204 (N = 0.29%)

MD 232 (N = 0.36%)

MD230 (N = 0.67%)

MD207 (N = 0.97%)

PL I

nten

sity

(A

rbita

ry u

nit)

Wavelength (nm)

Full spectrum (MOCVD) at T = 6 K

945 nm

882.18 nm915.8 nm

870 nm840nm

Page 52: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

52

Defect properties of the samples were studied by using the ODMR technique.

Representative ODMR spectra recorded via the near-band-edge PL are shown in Fig. 5.4.2. In

all samples the dominant ODMR signal (denoted as Gai-C*) originates from the Ga interstitials

with parameters which are very close to that for the Gai-C center detected in the MBE-grown

GaNAs. The simulated ODMR spectrum using the spin-Hamiltonian is shown in the lower part

of the figure and reasonably agrees with the experimental one, which justify the choice of the

used parameters. As expected, the signal is negative which means that the involved defects

participate in the competing NR recombination. In addition, a positive ODMR signal is found in

the sample with N=0.67%. This signal becomes more intense when detecting via the defect-

related emission at longer wavelength. As the involved recombination center does not compete

with the band-to-band transitions, it is unlikely important for SDR and therefore, will not be

discussed in this work.

-0.0004

0.0000

0.0004

N < 0.1 %

-0.006

-0.004

-0.002

0.000N = 0.29 %

-0.0015

-0.0010

-0.0005

0.0000 N = 0.36 %

0.0000

0.0005N = 0.67 %

0 100 200 300 400 500 600 700

-1.8

-1.2

-0.6

0.0

0.6 Simulation

Gai-C*

Magnetic field (mT)

Near band edge window

Figure 5.4.2; ODMR spectra of MOCVD – grown GaNAs. The spectra were detected at the near band edge spectral

window.

In summary, formation of Ga interstitials was for the first time observed in GaNAs grown

by MOCVD. These results prove that these defects are common grown-in defects in GaNAs

formed in these alloys upon N incorporation independent of the growth procedure. The defects

act as an important recombination center and, therefore, will likely affect performance of all

electronic devices based on dilute nitrides.

Page 53: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

53

Summary

Spin filtering properties of novel GaNAs alloys were extensively studied in this thesis by

using optical orientation and spin resonance techniques. It has been proven that a GaNAs layer

can be utilized as a spin filter for the injected carriers from other materials. It was shown that the

main physical mechanism behind spin filtering is spin-dependent recombination via Ga

interstitial-related defects revealed from the ODMR measurements. These defects were found to

be the dominant grown-in defects in GaNAs, commonly formed during both MBE and MOCVD

growths. Several parameters were found to affect the efficiency of SDR and, therefore, of spin-

filtering, such as growth temperature, post-growth annealing, doping and quantum confinement

in the corresponding low-dimensional structures. Our results clarify approaches to be utilized to

achieve the efficient spin filter and also demonstrate the capability to integrate the GaNAs spin

filter with others functional semiconductor devices. We hope that a relievable, functional spin

filter with reasonable prize will be available to global market in the nearest future.

“I see spin in your future”

Yuttapoom Puttisong

Page 54: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

54

Bibliography

[1] I. A. Buyanova and W.M. Chen, Physics and Applications of Dilute Nitrides (Taylor & Francis Books, 2004).

[2] X. J. Wang, I.A. Buyanova, F.Zhao, D. Lagarde, A.Balocchi,X. Marie, C.W. Tu, J. C. Harmand and W.M. Chen,

nature material, DOI:10.10.38/NMAT2385.

[3] Markus Weyers, Michio Sato, Hiroaki Ando, Jpn. J.Appl. Phys. 31, L853 (1992).

[4] M. Sato, Mater. Res. Soc. Symp. Proc. 395, 285 (1996).

[5] Masahiko Kondow, Kazuhisa Uomi, Kazuhiko Hosomi, Teruo Mozume, Jpn. J. Appl. Phys. 33, L1056 (1994).

[6] WG Bi, CW Tu, Appl. Phys. Lett. 70, 1608-1610 (1997).

[7] J. D. Perkins, A. Mascarenhas, Y. Zhang, J. F. Geisz, D. J. Friedman, J. M. Olson, S. R. Kurtz, Phys. Rev.

Lett. 82, 3312 (1999).

[8] W. Shan, W. Walukiewicz, J. W. Ager, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, S. R. Kurtz,

Phys. Rev. Lett. 82, 1221 (1999).

[9] W. Walukiewicz, W. Shan, J. W. Ager, D. R. Chamberlin, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson,

S. R.Kurtz, “Nitrogen-induced modification of the electronic structure of group III-N-V alloys”, Proc. 195th

Meeting of the Electrochem Soc., Seattle, WA, May2-6, 1999; in”Photovoltaics for the 21st Century”, vol.99-11, p.

190 (1999).

[10] E. D. Jones, N. A. Modine, A. A. Allerman, S. R.Kurtz, A. F. Wright, S. T. Torez, X. Wei, Phys. Rev. B

60,4430 (1999).

[11] T. Mattila, S. -H. Wei, A. Zunger, Phys. Rev. B 60,R11245 (1999).

[12] E. D. Jones, N. A. Modine, A. A. Allerman, I. J. Fritz, S. R. Kurtz, A. F. Wright, S. T. Torez, X. Wei, Proc.

SPIE 3621, 52 (1999).

[13] I. A. Buyanova, W. M. Chen and B. Monomar, MRS Internet J. Nitride Semicond. Res. 6, 2 (2001).

[14] J. H. Davies, The Physics of Low-dimensional Semiconductors: An Introduction, (Cambridge Universtty press,

1998)

[15] N. Q. Thinh, I. A. Buyanova, P. N. Hai, and W. M. Chen, H. P. Xin and C. W. Tu, Phys. Rev. B 63, 033203

(2001)

[16] C. Weisbuch and G. Lampel, Solid State Commun, 14, 141 (1974).

[17] F. Meier, B. P. Zakharchenya (eds.), Optical Orientation (North-Holland, Amsterdam, 1984).

[18] R.J. Elliott, Phys. Rev. 96, 266 (1954).

[19] Y. Yafet, in Solid State Physics, vol. 14, ed. by F. Seits, D. Turnbull (Academic, NewYork, 1963), p. 1.

[20] M.I. Dyakonov, V.I. Perel, Fiz. Tverd. Tela 13, 3581 (1971); Sov. Phys. Solid State 13,3023 (1972).

Page 55: Final Thesis - DiVA portalliu.diva-portal.org/smash/get/diva2:224551/FULLTEXT01.pdf · 2009. 6. 18. · Title: Final Thesis Author: Yuttapoom Created Date: 6/18/2009 8:26:37 AM

55

[21] G.I. Bir, A.G. Aronov, G.E. Pikus, Z. Eksp. Teor. Fiz. 69, 1382 (1975); Sov. Phys. JETP42, 705 (1976).

[22] L.Lombez, P.-F. Braun, H Carere, B. Urbaszek, P. Renucci, T. Amand , X. marie, J.C.Harmand and V. K.

Kalevich, , Appl. Phys. Lett. 87, 252115 (2005).

[23] V. K. Kalevich, E. I. Ivchenko, M. M. Afanasiev, A. Yu. Shiryaev, A. Yu. Egorov, V.M. Ustinov, B. Pal and Y.

Masumoto, JETP Letters 82(7), 455-458 (2005).

[24] W. M. Chen, I. A. Buyanova and H. Yonezu, Physica B 376-377, 545-551(2006).