time resolved spectroscopy in inas and insb based narrow ... · first and foremost, i would like to...

Time Resolved Spectroscopy in InAs and InSb based Narrow-Gap

Semiconductors

Mithun Bhowmick

Dissertation submitted to the Faculty of the

Virginia Polytechnic Institute and State University

In partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Physics

Giti Khodaparast, Chair

Hans Robinson

Chenggang Tao

Rahul Kulkarni

July 11, 2012

Blacksburg, Virginia

Keywords: Time Resolved Spectroscopy, Ferromagnetic Semiconductors, Narrow-Gap

Semiconductors, Carrier and Spin Relaxation, InMnAs, InMnSb, InSb Quantum Wells

Copyright 2012, Mithun Bhowmick

Time Resolved Spectroscopy in InAs and InSb based Narrow-Gap

Semiconductors

Mithun Bhowmick

(ABSTRACT)

As the switching rates in electronic and optoelectronic devices are pushed to even higher fre-

quencies, it is crucial to probe carrier dynamics in semiconductors on femtosecond timescales.

Time resolved spectroscopy is an excellent tool to probe the relaxation dynamics of pho-

toexcited carriers; where after the initial photoexcitation, the nonequilibrium population

of electrons and holes relax by a series of scattering processes including carrier-carrier and

carrier-phonon scattering. Probing carrier and spin relaxation dynamics in InAs and InSb

based narrow-gap semiconductors is crucial to understand the different scattering mecha-

nisms related to the systems. Similar studies in InSb quantum wells are also intriguing,

especially for their scientifically unique features (such as small effective mass, large g-factor

etc). Our time resolved techniques demonstrated tunability of carrier and spin dynamics

which might be important for charge and spin based devices. The samples studied in this

work were provided by the groups of Prof. Wessels (Northwestern University) and Prof.

Santos (University of Oklahoma). Theoretical calculations were performed by the group of

Prof. Stanton (University of Florida). The THz measurements were performed at Wright

State University in collaboration with Prof. Jason Deibel. This work has been supported

by the National Science Foundation through grants Career Award DMR-0846834, AFOSR

Young Investigator Program 06NE231. A portion of this work was performed at the Na-

tional High Magnetic Field Laboratory (in collaboration with Dr. Stephen McGill), which is

supported by National Science Foundation Cooperative Agreement No. DMR-0654118, the

State of Florida, and the U.S. Department of Energy.

iii

Acknowledgments

This dissertation would not have been possible without the guidance and the help of several

individuals who in one way or another contributed and extended their valuable assistance in

the preparation and completion of this study.

First and foremost, I would like to express utmost gratitude to my advisor Prof. Giti Kho-

daparast for her untiring and unfailing support and guidance not only for my research, but

also for training me to be a proper member of the scientific community. I would also like

to thank other members of my committee, Prof. Hans Robinson, Prof. Chenggang Tao,

and Prof. Rahul Kulkarni, for their time, effort, and invaluable evaluations. I am thankful

to work in a wonderful group; my heartfelt thanks goes to Kanokwan Nontapot, Matthew

Frazier, and Travis Merritt for the support and unconditional friendship I received from

them. Many thanks to Christa Thomas, for her patience and guidance to get me through

all the necessary steps of graduation, and for providing crucial insights during my graduate

studies. I am very thankful to Scott Allen, John Miller, Ron Stables and all the members

of machine shop for their assistance, tools, and sincere effort. I am grateful to Travis Heath

and Roger Link for their help with the software problems I faced. Many thanks to Laszlo

iv

Papp for sharing invaluable knowledge about electronic shop and helping me out in numerous

ways during the troubled times with our cooling system, and to Betty Wilkins for making

the travel arrangements fast and painless. My sincere gratitude to all the members of the

Physics department faculty, staff, and fellow graduate students for providing a wonderful

environment in which I studied and researched.

It would never be possible to pursue so many years of education without the unconditional

support, love, and patience from my family. I owe a great deal to my parents, Mr. Dinesh

Bhowmick and Renukana Bhowmick, for all the struggle we shared in the past, and for all

the times we survived at the end to meet success. My sincere thanks goes to my best friend

and fiance Shuchismita, who kept me motivated till the last day of my work and had never

let me down.

Finally, I am immensely thankful for the financial support provided by National Science

Foundation and Air Force Office of Scientific Research. All photographs used in this disser-

tation were taken by author, 2012.

v

Contents

1 Introduction 1

1.1 Scope and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Ferromagnetic III-V Semiconductors . . . . . . . . . . . . . . . . . . . . . . 2

1.3 InSb Quantum Well Structures . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Bibliography 16

2 Narrow Gap based Materials 20

2.1 MOVPE grown InMnAs and InMnSb thin films . . . . . . . . . . . . . . . . 21

2.1.1 Growth and Basic Properties . . . . . . . . . . . . . . . . . . . . . . 21

2.1.2 Earlier Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 MBE grown InSb heterostructures . . . . . . . . . . . . . . . . . . . . . . . . 25

vi

2.2.1 Growth and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.2 Earlier Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Bibliography 30

3 Experimental Methods 32

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Time Resolved Differential Transmission technique . . . . . . . . . . . . . . . 33

3.3 Time Resolved Magneto Optical Kerr Effect technique . . . . . . . . . . . . 35

3.4 Carrier and Spin Relaxation Measurement Schemes . . . . . . . . . . . . . . 35

3.5 Experimental Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5.1 Laser sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5.2 Optical Components: . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5.3 Components employed for data acquisition . . . . . . . . . . . . . . . 41

3.6 Detailed Description of the Experimental Set ups . . . . . . . . . . . . . . . 43

3.6.1 Degenerate Differential Transmission Measurements . . . . . . . . . . 43

3.6.2 Non Degenerate Differential Transmission Measurements . . . . . . . 45

3.6.3 Non Degenerate Differential Reflectivity Measurements . . . . . . . . 46

vii

3.6.4 Magneto Optical Kerr Effect (MOKE) Measurements . . . . . . . . . 47

Bibliography 50

4 InMnAs and InMnSb 51

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2 Degenerate Differential Transmission . . . . . . . . . . . . . . . . . . . . . . 55

4.2.1 Degenerate Measurements in InMnAs . . . . . . . . . . . . . . . . . . 55

4.2.2 Degenerate Measurements in InMnSb . . . . . . . . . . . . . . . . . . 56

4.3 Non-degenerate Differential Transmission Measurements . . . . . . . . . . . 59

4.3.1 Non-degenerate Differential Transmission in InMnAs . . . . . . . . . 59

4.3.2 Non-degenerate Measurements in InMnSb . . . . . . . . . . . . . . . 65

4.4 Spin Relaxation Measurements in InMnAs . . . . . . . . . . . . . . . . . . . 65

4.4.1 Polarization Resolved Differential Transmission Measurements (PRDT) 65

4.4.2 MOKE Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.5 Calculation of Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . 69

4.6 Contributions to the differential transmission spectra . . . . . . . . . . . . . 71

4.7 Terahertz Time-Domain Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 76

viii

4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Bibliography 81

5 InSb based Quantum Wells 85

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.2 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.3 Experimental Results: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3.1 Degenerate pump/probe scheme . . . . . . . . . . . . . . . . . . . . . 89

5.3.2 Non-degenerate pump/probe scheme . . . . . . . . . . . . . . . . . . 92

5.3.3 Fluence Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.3.4 Polarization Resolved Differential Transmission(PRDT) . . . . . . . . 99

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Bibliography 104

ix

List of Figures

1.1 Combining electronic charge and spin can lead to novel devices. Adapted from

http://www.nims.go.jp/apfim/spintronics.html . . . . . . . . . . . . . . . . . 3

1.2 Coupling of Mn spins below curie temperature in ferromagnetic Ga(Mn)As.

Adapted from web.physics.ucsb.edu/gwinngroup/Gwinn Group Research in-

terests.html (”Magnetism in Semiconductors”). . . . . . . . . . . . . . . . . 5

1.3 Curie temperatures of several p-type III-V materials. Adapted from R. Se-

shadri Current Opinion in Solid State and Materials Science Vol. 9, Issues 12,

Pages 17 (2005). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Room temperature ferromagnetism in MOVPE grown InMnAs films where

Curie temperature was found to be independent of Mn content. Adapted

from A. J. Blattner and B. W. Wessels, Appl. Surf. Sci. 221 155 (2004). . . 7

1.5 InSb/AlInSb Quantum Well heterostructures. Adapted from www.quantum-

algorithms.html. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

x

1.6 Spin polarized field effect transistor (SFET), as proposed by Dutta and Das

in 1990. Adapted from www.nims.go.jp/apfim/SpinFET.html. . . . . . . . . 12

2.1 X-ray diffraction and STEM images for MOVPE grown InMnAs thin film.

Adapted from A.J. Blattner, B.W. Wessels, Applied Surface Science 221

155159 (2004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Band gap vs. Lattice constants for III-V compounds. Clearly, InSb has

the narrowest band gap among all the III-V semiconductors. Adapted from

www.ecse.rpi.edu/schubert/LightEmittingDiodes.org/chap12/chap12.htm. . . 24

2.3 MOVPE grown InMnAs samples. . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Example of a typical MBE grown symmetrically doped InSb QW. . . . . . . 27

3.1 Degenerate and Non degenerate differential transmission schemes. . . . . . . 34

3.2 Different components of the Laser sources used. . . . . . . . . . . . . . . . . 38

3.3 Role of a half-wave plate. When a linearly polarized light that is composed of

two components, parallel (green) and perpendicular (blue) to the optical axis

of the wave plate, enters a wave plate, the parallel wave propagates slower

than the perpendicular one. At the other end of the plate, the parallel wave is

exactly half of a wavelength delayed relative to the perpendicular wave. This

fact results in output light that is orthogonal to the input state. Adapted

from: http://en.wikipedia.org/wiki/Wave plate. . . . . . . . . . . . . . . . . 40

xi

3.4 Schematic diagram of Degenerate Differential Transmission setup for carrier

relaxation measurements. The same setup was used for spin relaxation mea-

surements, in presence of quarter wave plates. . . . . . . . . . . . . . . . . . 44

3.5 Schematic diagram of Non Degenerate Differential Transmission setup for car-

rier relaxation measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.6 Schematic diagram of Non Degenerate Differential Reflectivity setup for car-

rier relaxation measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.7 Schematic diagram of one color MOKE setup for spin relaxation measurements. 48

4.1 a) DT in MOVPE grown ferromagnetic InMnAs at 290 K and 77 K with

pump/probe fixed at 3.467µ m. b) A different pattern in the relaxation was

observed for the pump/probe at 3.1 µm. Adapted from M. Bhowmick et al,

Physical Review B, 85, 125313 (2012). . . . . . . . . . . . . . . . . . . . . . 57

4.2 Wavelength dependence of degenerate DT in InMnSb at 290 K. The pump/probe

wavelengths were fixed to MIR. The change in DT was found to be much

smaller in case of 4.3 µm, (∼ 1%) than that of the other wavelengths. . . . . 58

4.3 Comparison of degenerate DT in InMnSb at 290 K and 77 K when pump/probe

was tuned to 3.8 µm. At 77 K, the percentage change in DT is larger than

that at 290 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

xii

4.4 Two-color differential transmission measurements in InMnAs ferromagnetic

film at 290 K and different pump fluences. The pump/probe pulses were 800

nm and 3.467 µm, respectively. The peak of the DT, −∆T/T0 = (T0−T )/T0,

increases from 30% to ∼ 60%, is suggesting larger photoinduced absorption

at higher laser fluences. Adapted from M. Bhowmick et al, Physical Review

B, 85, 125313 (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.5 Two-color differential transmission measurements in InMnAs ferromagnetic

film at 290 K for different probe wavelengths in MIR. The relaxation dynamic

is dominated by photoinduced absorption. The exponential fits are shifted for

clarity. The inset demonstrates an example of the measurements at 77 K for

pump/probe at 800 nm/3.467 µm, respectively. Adapted from M. Bhowmick

et al, Physical Review B, 85, 125313 (2012). . . . . . . . . . . . . . . . . . . 62

4.6 Two-color DT measurements of InMnAs ferromagnetic film, at several tem-

peratures. The pump/probe pulses were 800 nm and 2 µm. The photoinduced

bleaching is dominating the temporal evolution of the DT. Adapted from M.

Bhowmick et al, Physical Review B, 85, 125313 (2012). . . . . . . . . . . . . 63

4.7 Two-color DT measurements of the InMnAs ferromagnetic film in two different

configurations and relaxation dynamics. a) When the film is pumped from

the ferromagnetic side. b) When the film is pumped from the GaAs side.

Adapted from M. Bhowmick et al, Physical Review B, 85, 125313 (2012). . . 64

xiii

4.8 Two-color DT signals from InMnAs at different applied fields at 5 K. Adapted

from M. Bhowmick et al, Physical Review B, 85, 125313 (2012). . . . . . . . 64

4.9 Two-color DT signals from InMnSb at different wavelengths. The exponential

fits are shifted for clarity. For all wavelengths, photo-excited carriers did not

fully relax in a time scale of 25 ps. . . . . . . . . . . . . . . . . . . . . . . . 66

4.10 Two-color DT from InMnSb at 77K demonstrated no significant difference in

the relaxation pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.11 Two-color DT from InMnSb at 77K and 290K for two wavelengths. Clearly,

77K traces show a combination of fast and slow relaxation components after

initial sharp change due to free carrier Drude absorption. . . . . . . . . . . . 67

4.12 (a) Polarization-resolved differential transmission measurements at 3.467 µm.

(b) The subtraction represents the degree of spin polarization, and demon-

strates an exponential decay of about 1 ps through the fitting curve. Adapted

from M. Bhowmick et al, Physics Procedia, (3) 1167-1170 (2010). . . . . . . 68

4.13 MOKE measurements on InMnAs with pump/probe fixed at 800 nm. The

measurement demonstrated a spin relaxation ∼ 2 ps. Adapted from Giti A.

Khodaparast et al, Proc. of SPIE: Vol. 7608 76080O-1 (2010). . . . . . . . . 69

xiv

4.14 Electronic structure of In0.96Mn0.04As at T= 290 K for B =0. The energy

bands are spin-split due to the ferromagnetism. The allowed optical tran-

sitions for a pump wavelength of 800 nm (1.55 eV) are shown by the (red)

arrows. The dotted line at 1.08 eV shows the threshold for Γ valley electrons

to scatter to the satellite L valley. Adapted from M. Bhowmick et al, Physical

Review B, 85, 125313 (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.15 Electronic structure of In0.96Mn0.04As at T= 290 K for B =0. The energy

bands are spin-split due to the ferromagnetism. The allowed optical tran-

sitions are shown for a probe wavelength of 3.5 µm (black arrows) and 2.0

µm (red arrows). Adapted from M. Bhowmick et al, Physical Review B, 85,

125313 (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.16 Terahertz time-domain spectroscopy (TDS) allows for non-contact evaluation

of the frequency-dependent electronic/optical properties of novel materials.

Obtained from Prof. Jason Deibel of Wright State University through personal

communication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.17 Terahertz time-domain spectroscopy (TDS) in MOVPE grown InMnAs and

InMnSb films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.18 Temperature dependence of THz peak-to-peak signals in MOVPE grown In-

MnAs and InMnSb films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

xv

5.1 Carrier relaxation in a degenerate MIR pump/probe scheme close to interband

transitions at room temperature. The initial relaxation time lasts for ∼ 1 ps

followed by a slower component. . . . . . . . . . . . . . . . . . . . . . . . . . 91


transitions at 77 K. The dynamic is similar to the measurements at room

temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


transitions at 290 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.4 Carrier relaxation in a Non degenerate pump/probe scheme tuned to NIR/MIR

respectively, at 290 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.5 Temperature dependence in S592 employing Non degenerate scheme. No sig-

nificant difference was observed between 77 K and 290 K traces. . . . . . . . 96

5.6 Carrier relaxation in a Non degenerate pump/probe scheme, with 800 nm

pump and MIR probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.7 Carrier relaxation in a Non degenerate pump/probe scheme , with 800 nm

pump and MIR porbe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.8 Fluence dependence of carrier relaxation in a non degenerate pump/probe

scheme in the 100 nm PQW with 4% alloy (S607). . . . . . . . . . . . . . . . 99

xvi

5.9 The optical polarization for a symmetric QW at 290 K (S939), employing the

spin polarized differential transmission technique. The optical polarization is

decaying exponentially with a decay constant related to the spin lifetime. . . 100

5.10 The optical polarization at 290 K for an undoped MQW (S591) employing

the spin polarized differential transmission technique. . . . . . . . . . . . . . 101

5.11 The optical polarization at 290 K for a parabolic sample (S607) employing

the spin polarized differential transmission technique. . . . . . . . . . . . . . 102

xvii

List of Tables

2.1 A few electronic and magnetic properties of MOVPE grown InMnAs and In-

MnSb thin fims. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Characteristics of the samples studied in this work. The densities and mobili-

ties are from the measurements at 4.2 K. In the doped samples, only the first

subband is occupied and the Fermi levels, EF , are with respect to the bottom

of conduction band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.1 Characteristics of the samples studied in this work. The densities and mobili-

ties are from the measurements at 4.2 K. In the doped samples, only the first

subband is occupied and the Fermi levels, EF , are with respect to the bottom

of conduction band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2 Possible interband transitions in a 30 nm square quantum well with with 9%

alloy concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

xviii

5.3 Possible interband transitions in a 11.5 nm square quantum well with with

15% alloy concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.4 Possible interband transitions in a 32.5 nm square quantum well with with 9%

alloy concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

xix

Chapter 1

Introduction

1.1 Scope and Overview

The objectives of this thesis are:

1. To probe carrier and spin relaxation dynamics in MOVPE grown ferromagnetic InMnAs

and InMnSb.

2. To study the effects of several parameters (such as temperature, pump fluence, wave-

length, and externally applied magnetic field) on the relaxation dynamics.

3. To investigate and control of interband dynamics in InSb quantum well heterostructures.

4. To model the observed dynamics.

To provide the background on the material systems studied in this work, the growth tech-

niques, structures, and other related properties of III-V ferromagnetic films and InSb based

1

Mithun Bhowmick Chapter 1. Introduction 2

heterostructures will be discussed in chapter 2, along with an overview of earlier works on

the same materials. The experimental methods will be described in Chapter 3, highlighting

on the differential transmission technique and related spectroscopic details. Chapter 4 will

present the experimental results for InMnAs and InMnSb thin films. Similarly, a detailed

study of carrier and spin relaxation measurements in InSb quantum wells will be reported

in Chapter 5.

1.2 Ferromagnetic III-V Semiconductors

The enormous growth of microelectronic devices in the past 50 years has prompted material

scientists for a quest of new materials, with possibility to pack more logic in a single chip. As

shown in Fig. 1.1, a need to combine complementary properties of electronic charge and spin

has given birth of a new field of research called ”spintronics”. Synthesizing materials with

both semiconductivity and strong magnetic properties were sought after goals, particularly

after the discovery of interaction between semiconducting bulk properties and ferromag-

netism. During the years of 60’s and 70’s, material properties were studied extensively in

search of this unique interplay [1, 2]. However, very soon the enthusiasm faded because of

the engineering difficulties associated with growing the materials, and a low success rate

of having an elevated ferromagnetic transition temperature. This transition temperature,

more popularly called as Curie temperature (Tc), ought to be close to room temperature

for most practical applications. By the end of 80’s, the interest in these group of materials


became almost invisible, and thus practically ended the age of first generation ferromagnetic

semiconductors.

Figure 1.1: Combining electronic charge and spin can lead to novel devices. Adapted from

http://www.nims.go.jp/apfim/spintronics.html

The second generation of semiconducting materials with ferromagnetic properties came to

limelight shortly after this, with the idea of incorporating magnetic elements in non magnetic

material hosts through alloying. The resulting materials were often called Diluted Magnetic

Semicondcutors (DMS’s) which would contain very small amount (< 20 %) of transition

metal as magnetic element in a II-VI host compound (typically ZnSe or CdTe). II-VI mag-

netic semiconductors were studied extensively [3, 4], only to discover that they were either

paramagnetic, or anti-ferromagnetic [1]. The origin of magnetism in II-VI based semicon-


ductors was attributed to the exchange interaction between the conduction carriers and the

localized magnetic moments [7].

An alternative to II-VI semiconductors was thought to be III-V compounds. III-V semi-

conductors were better choice as replacements since they were already known for their ap-

plications in electronics in the form of lasers and transistors. The first III-V ferromagnetic

InMnAs films were prepared by Munekata and co workers through Molecular Beam Epi-

taxy (MBE) in 1989 [1]. Two years later, ferromagnetism was reported in p-type InMnAs

thin films and generated immense interest in that material system. The enthusiasm was

nicely complemented and enhanced during the years of 90’s, which proved to be a great

decade in the history of development of DMS. A Curie temperature of 35 K was reported

in InMnAs/(Al,Ga)Sb heterostructures which serves as a prototype for spin injection in

semiconductors [6]. In the next few years, ferromagnetic GaMnAs and InMnAs were grown

[8, 9, 10]. Since it was predicted by the calculations that the Curie temperature for GaMnAs

would be larger than that of InMnAs, most of the studies regarding these materials centered

around GaMnAs, leading to a breakthrough of having a material with 110K Tc in 1996 [8].

By the end of 2005, a series of relevant materials like GaMnN, AlCrN, and ZnCoO were

discovered with ferromagnetism [11].

As mentioned earlier, InMnAs was initially ignored because of theoretically predicted low

Curie temperatures. However, a Curie temperature of 90 K was reported for MBE grown

InMnAs in 2006 [14]. The calculated values of the Curie temperature in III-Mn-V compounds

were traditionally obtained from Ruderman, Kittel, Kasuya, and Yosida (RKKY) theory of


Figure 1.2: Coupling of Mn spins below curie temperature in ferromagnetic Ga(Mn)As.

Adapted from web.physics.ucsb.edu/gwinngroup/Gwinn Group Research interests.html

(”Magnetism in Semiconductors”).

DMS. As time progressed, more and more evidences were accumulated of the limitations

of this theoretical model, and it was realized that the approximations used in RKKY is

too restrictive for the accurate quantitative prediction of Curie temperature [15, 16]. On

the other hand, adopting a scaling argument could predict very high Tc values for InMnAs

and GaN. Using the scaling approach, a massive 280 K Tc was obtained by calculation for

InMnAs, and the focus shifted back to InMnAs again [2].

Finally, in 2001, Metalorganic Vapor Phase Epitaxy (MOVPE) grown InMnAs was reported

to have a Tc of 330 K [19, 3]. Subsequent studies ensured phase purity and the high Curie

temperature was attributed to atomic-scale magnetic clusters.

The origin of ferromagnetism in DMS has been a topic of debate for a long time. The

exact form and nature of exchange mechanism responsible for mediating ferromagnetism is

not yet well understood. In general, magnetism in non-metallic substances is associated


Figure 1.3: Curie temperatures of several p-type III-V materials. Adapted from R. Seshadri

Current Opinion in Solid State and Materials Science Vol. 9, Issues 12, Pages 17 (2005).

with short range exchange interaction. In DMS, the distance is relatively longer (1-3 nm)

because of the small amount of magnetic ions present. An early model tried to explain

ferromagnetism in DMS by considering the whole system as a combination of delocalized

band electrons and 3d electrons from the magnetic ions with localized moments [21]. The

electrical and optical properties of the ions were attributed to the delocalized electrons,

whereas the magnetic properties were due to the localized magnetic moments. It was also


assumed that strong spin-dependent sp-d exchange interactions were present between the two

sub systems. The stabilization of anti-ferromagnetism in II-VI compounds was explained by

this sp-d superexchange mechanism [22]. The same model, however, can not be applied to

the III-V compounds, for the superexchange model only leads to anti-ferromagnetic behavior

[22].

Figure 1.4: Room temperature ferromagnetism in MOVPE grown InMnAs films where Curie

temperature was found to be independent of Mn content. Adapted from A. J. Blattner and

B. W. Wessels, Appl. Surf. Sci. 221 155 (2004).

To explain ferromagnetism in III-V compounds, several models have been proposed; however,

there is currently no single theory that can provide an accurate prediction for Tc in different

III-V ferromagnetic semiconductors for different carrier density regimes. The mean field


theory predicts that Tc should scale with Mn concentration (x) and hole concentration (p) as

x p1/3. Reasonable agreement between theory and experiments has been noted for GaMnAs.

In contrast, the observation of a Tc of 10 K for InMnAs films with carrier concentration of

1018 cm−3 is inconsistent with calculations. Based on the calculations, InMnAs with a hole

concentration of 1018 cm−3 should have a Tc of 8 K instead of the experimentally observed

90 K. The case for InMnAs grown by MOVPE is even more complex, especially if disorders

are considered [4]. The theory of hole mediated ferromagnetism does not fit well with the

observations in the MOVPE grown systems. According to hole mediated theory, the Curie

temperature should scale with Mn concentration, which is not the case in InMnAs thin films

prepared by MOVPE technique. MOVPE grown films with a carrier concentration of 1018

cm−3 have Tc of 330 K and the Tc is nearly independent of carrier concentration.

With all these open questions and unresolved anomalies, it has become very important to

probe the hole-mediated ferromagnetism in III-Mn-V materials, and study the carrier and

spin dependent phenomena uniquely present in these magnetic structures. Since magnetic

III-V compounds could be incorporated in non-magnetic III-V’s, the detailed understanding

of the structures would lead us to great deal of tunability. As mentioned earlier, the mean

field theory is an effective way to model ferromagnetism in certain cases, but has several lim-

itations as well. It is of uttermost importance to test experimentally the limits to which the

theory could be applied by altering the experimental conditions (such as magnetic impurity

concentrations, thickness, temperature, external magnetic field etc).

Most of the understanding of carrier relaxation in MBE grown (III,Mn)V ferromagnetic


structures has been based on two-color differential reflectivity spectroscopy with pump and

probe pulses ranging from 1.2-2 µm and 650-850 nm, respectively [12, 13, 14, 15]. In the re-

ported measurements, rapid change of the differential reflectivity was observed and ascribed

to a fast disappearance of photoinduced free carriers through ultra-fast trapping by mid gap

states. The carrier relaxation time reported in the MBE grown InMnAs [14] demonstrated

a similar time scale as an InAs film under identical experimental conditions [16]. Fast re-

laxation in the differential reflectivity patterns of relaxation dynamics are commonly seen in

low-temperature-grown III-V semiconductors. The extracted information from the differen-

tial reflectivity measurements can be affected by multi-reflections in multi-layer structures.

In this work, several time-resolved differential transmission (TRDT) schemes were employed

to provide insight into the time scales and the nature of the interactions in MOVPE grown

ferromagnetic InMnAs and InMnSb films [29, 30, 31]. We demonstrate the sensitivity and

tunability of the carrier dynamics to the initial excitation region as well as the final states

that are probed. The MOVPE-grown InMnAs structure is an 800 nm thick film with a Mn

content of 4%, a hole concentration p = 1.35 × 1018 cm−3, and a mobility of 142 cm2/V s

with the Tc above room temperature. The samples used in this study were provided by the

group of Prof. Wessels of Northwestern University. The details of the growth conditions

are described in Refs. [32] and [33]. In these materials, probing the dynamical behavior

of non-equilibrium carriers created by intense laser pulses can provide valuable information

about different scattering mechanisms and the band structure. Time-resolved spectroscopy

can help us to understand the relaxation of photo-excited carriers; where after the initial


excitation, the non-equilibrium population of carriers can relax by a series of scattering

processes.

1.3 InSb Quantum Well Structures

Solid-state physics, particularly the area which deals with semiconductors, have undergone a

rapid development during the last few decades. With a primary goal of exploiting quantum

mechanics in design and functionality of the semiconductor devices, this branch of condensed

matter physics has grown to massive heights in all directions. Aided by advancements in

terms of fabrication techniques and efficient light sources, material scientists were able to

provide exotic structures such as quantum wells, quantum wires, and quantum dots. Until

the 80’s, only bulk materials were used to realize devices. These sources suffered heavily

for the electrical and optical losses [34]. The remedy came from pioneers such as Alferov

and Kroamer, who independently proposed a construction technique which would produce

double heterostructures by incorporating an active layer of semiconductor with a narrower

bandgap between two layers of a wider gap material [35].

This design is advantageous for several reasons due to the confinement of the carriers and led

to significant improvement in terms of losses. Later it was also realized that the confinement

of the carriers were instrumental to give rise new optoelectronic properties which were not

present in bulk materials. Using the concept of de Broglie wavelength, it was also found that

the energy-momentum relations in a quantum well structure could be drastically changed


Figure 1.5: InSb/AlInSb Quantum Well heterostructures. Adapted from www.quantum-

algorithms.html.

by simply making one of the dimensions of the semiconductor sufficiently small (lesser than

or equal to the de Broglie wavelength, to be precise). III-V semiconductors were always a

primary candidate material for devising quantum wells, and thus became subject of extensive

studies quite rapidly. In the early 90’s, a new direction was added to the already existing

list of interests in terms of III-V compounds. In 1990, for the first time, a device employing

electronic spin was proposed by a paper of Dutta and Das, and a totally new field of research

called ”spintronics” was born [36].

Thus, the recent interest in the science and engineering of Narrow Gap Semiconductors


Figure 1.6: Spin polarized field effect transistor (SFET), as proposed by Dutta and Das in

1990. Adapted from www.nims.go.jp/apfim/SpinFET.html.

(NGS), (e.g. III-V compound semiconductors) is consistent with the early developments of

semiconductor electronics. These structures have the potential to lead to revolutionary de-

vices like spin transistors, infrared spin-photonics, and novel switches for the next generation

of computing. NGS offer several unique electronic features such as a small effective mass, a

large g-factor, a high intrinsic mobility, and large spin-orbit coupling effects. With smallest

band-gap among other NGS materials, InSb heterostructures enjoy a privileged position, and

preference in the list of potential materials when it comes to potential charge and spin based

applications. The room temperature mobility in InSb two-dimensional structures is higher

than that of other similar semiconductors. Besides, the combination of large Rashba split-

ting and a huge g-factor have a potential to generate strong spin splitting even in absence


of externally applied magnetic field.

The fabrication of InSb based QWs into specialized high speed electronic devices demon-

strated promising progress where the integration of InSb QW transistors onto silicon sub-

strates has been investigated. The performance of field effect transistors (FETs) suitable for

digital logic circuits was demonstrated on material with a buffer just 1.8 µm thick which is

an initial step towards integrating InSb FETs with Si-CMOS for high-speed, energy-efficient

logic applications [37]. As the switching rates in electronic devices are pushed to higher

frequencies, it is important to understand the carrier dynamics in semiconductors on fem-

tosecond time-scales.

Among other properties, shape of a quantum well influences material properties in several

manner. Heterostructures with parabolic confinement are important systems to study for

many reasons. In a perfect Parabolic Quantum Well (PQW), the subbands are equally

spaced and electron-electron interactions are very small, allowing coupling of long-wavelength

radiation only to the center-of-mass coordinate of the electron system. The combination

of designability in transition frequency, stability at higher temperatures, and narrow-band

emission makes PQW systems suitable for THz devices. The InSb quantum wells involved

in this work have been grown by the group of Prof. Santos at University of Oklahoma.


1.4 Publications

The findings of this project appeared in the form of articles in following scientific journals

and proceedings. The theoretical calculations were performed in collaboration with Prof.

Stanton’s group at University of Florida. A part of the project was completed at National

High Magnetic Field Laboratory (Florida) in collaboration with Dr. Stephen McGill.

1. M. Bhowmick, T. R. Merritt, G. A. Khodaparast, Bruce W. Wessels, Stephen A. McGill,

D. Saha, X. Pan, G. D. Sanders, C. J. Stanton,”Time Resolved Differential Transmission

Measurements in Ferromagnetic MOVPE Grown InMnAs” Physical Review B, 85, 125313

(2012).

2. Proceedings of 15th International Conference on Narrow Gap Systems: Mithun Bhowmick,

Travis Merritt, Giti A. Khodaparast, Tetsuya D. Mishima, Michael B. Santos, Carrier Dy-

namics in Parabolic InSb Based Multi Quantum Wells AIP Conference Proceedings, Vol.

1416 (2011).

3. Invited Paper, Photonic West Conference: Giti A. Khodaparast, Mithun Bhowmick,

Matthew Frazier, Rajeev N. Kini, Kanokwan Nontapot, Tetsuya D. Mishima, Michael San-

tos, Bruce W. Wessels, Probe of Coherent and Quantum States in Narrow-Gap Semicon-

ductors in the presence of strong Spin-Orbit Coupling. Proc. of SPIE: Vol. 7608 76080O-1

(2010). Peer Reviewed.

4. M. Bhowmick, R. N. Kini, K. Nontapot, N. Goel, S. J. Chung, T. D. Mishima, M. B.

Santos, G. A. Khodaparast, Probe of Interband Relaxations of Photo-excited and Carriers


and Spins in InSb Based Quantum Wells, Physics Procedia (3) 1161-1165 (2010). Peer

Reviewed.

5. M. Bhowmick, T. R. Merritt, K. Nontapot, B. W. Wessels, O. Drachenko, G. A. Khoda-

parast, Time Resolved Spectroscopy of InMnAs Using Differential Transmission Technique

in Mid-Infrared , Physics Procedia, (3) 1167-1170 (2010). Peer Reviewed.

6. Invited Paper SPIE-Spintronics III conference: Giti A. Khodaparast, Mithun Bhowmick,

Tetsuya D. Mishima, Michael Santos, C. Feaser, Bruce W. Wessels, Y. Matsuda Probe of

Coherent and Quantum States in Narrow-Gap Based Semiconductors with strong Spin-Orbit

Coupling. Spintronics III, Proc. of SPIE Vol 77600x-1 (2010), Peer Reviewed.

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Furdyna, Appl. Phys. Lett. 92, 06191(2008).


[25] K. Nontapot, R. N. Kini, A. Gifford, T. R. Merritt, G. A. Khodaparast, T. Wojtowicz,

X. Liu, J. K. Furdyna, Appl. Phys. Lett. 90, 143109 (2007).

[26] J. Wang, C. Sun, Y. Hashimoto, Y., Kono, J. , Khodaparast, G. A., Cywinski, L., Sham,

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ferromagnetic III-V semiconductors,” Journal of Physics: Condens. Matter, 18, R501

(2006).

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Optics 51, 2771 (2004).

[28] R. N. Kini,K. Nontapot, G. A. Khodaparast, R. E. Welser, and L. J. Guido, Journal of

Applied Physics 103, 064318 (2008).

[29] G. A. Khodaparast, M. Frazier, R. N. Kini, K. Nontapot, T. D. Mishima, M. B. Santos,

and B. W. Wessels, Proc. SPIE 7608,76080O (2010).

[30] G. A. Khodaparast, M. Bhowmick, T. D. Mishima, M. B. Santos, C. Feaser, and B. W.

Wessels, Spintronics III, Proc. SPIE 7760, 77600X (2010).

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Khodaparast, Physics Procedia 3, 1167 (2010).

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[34] E. U. Rafailov, M. A. Cataluna, and E. A. Avrutin Ultrafast Lasers Based on Quantum

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(2007).

Chapter 2

Narrow Gap based Materials

Narrow gap III-V compound semiconductors are primary focus of this work. Probing carrier

and spin dynamics in these materials is of utter importance due to their unique properties.

Two different genres of samples were used in this study: 1) Ferromagnetic thin films of

InMnAs and InMnSb using Metalorganic Vapor Phase Epitaxy (MOVPE), and 2) InSb

quantum well heterostructures grown by Molecular Beam Epitaxy (MBE). This chapter

briefly discusses the growth and properties of the materials, followed by an overview of

earlier work performed on similar or equivalent systems.

20

Mithun Bhowmick Chapter 2. Narrow Gap Based Materials 21

2.1 MOVPE grown InMnAs and InMnSb thin films

2.1.1 Growth and Basic Properties

Ferromagnetic semiconductors have always been sought after materials for their unique blend

of semiconducting and magnetic properties. As mentioned in chapter 1, extensive work was

done on II-VI compounds at the very beginning, only to realize the resulting films are

antiferromagnetic. After the synthesis of first ferromagnetic III-V compound, a great deal of

interest was shifted to develop ferromagnetic films from III-V through Mn doping [1]. The

main challenge in making ferromagnetic III-V compounds is surface segregations that occur

when magnetic elements such as Mn are introduced into the material. Significant work on

the growth continued through low temperature MBE, with issues were raised in terms of

phase integrity, low Curie temperature (Tc), anomalies between theoretical calculations, and

experimental observations [2]. The mean field approach, successful in GaMnAs and other

similar compounds, was found to have huge deviations while predicting Tc values for newly

formed or proposed III-Mn-V compounds.

A new approach, known as metalorganic vapor phase epitaxy (MOVPE), was taken in de-

positing InMnAs in search of a better material in terms of Tc. Exploration of this technique

gradually showed promise by enabling preparation of a wide variety of transition metal

doped III-V compound semiconductors [2]. The corresponding growth temperatures were

much higher than that in MBE methods used earlier, and a very high (330 K) Tc was demon-

strated by single phase ferromagnetic InMnAs films [3, 4]. MOVPE grown samples added


the flexibility of having both p and n type materials, and also the growth temperature was

200-300 0C higher than that in the case of MBE grown materials (i.e around 500 0C) [2].

X-ray diffraction (XRD) and transmission electron microscopy (TEM) analysis of the layers

were performed to investigate the presence of a second phase with a different crystal structure

in the system, but no evidence was found [4]. The anomalous Hall effect was demonstrated

by the MOVPE grown InMnAs films through variable Hall measurements, and Tc was de-

termined by magnetization measurements [3]. A series of In1−xMnxAs films with (x= 0.01-

0.10) showed room temperature ferromagnetism, with Curie temperature Tc= 333 K. Lack

of XRD or STEM evidence of MnAs nanoprecipitates proved that MnAs was not the source

of room temperature ferromagnetism. A theory was proposed based on formation of Mn

dimers at nearest-neighbor cation sites in the thin films to explain the observed high Tc in

these materials [4].

Details of the electronic and magnetic properties for MOVPE grown InMnAs and InMnSb

thin films are given in table 2.1.

2.1.2 Earlier Work

Most of the understanding of carrier relaxation in MBE grown narrow gap (III,Mn)V ferro-

magnetic structures has been based on two-color differential reflectivity spectroscopy with

pump and probe pulses ranging from 1.2 to 2 µm and 650 to 850 nm, respectively [5, 7].

In the reported measurements, rapid change of the differential reflectivity was observed and


Figure 2.1: X-ray diffraction and STEM images for MOVPE grown InMnAs thin film.

Adapted from A.J. Blattner, B.W. Wessels, Applied Surface Science 221 155159 (2004).

ascribed to a fast disappearance of photoinduced free carriers through ultrafast trapping by

midgap states. The carrier relaxation time reported in the MBE grown InMnAs demon-

strated a similar time scale as an InAs film would show under similar experimental condi-

tions [6, 8]. Fast relaxation in the differential reflectivity patterns of relaxation dynamics

are commonly seen in low-temperature-grown III-V semiconductors. The extracted infor-

mation from the differential reflectivity measurements can be affected by multireflections in

multilayer structures.

In contrast to the previously reported measurements, carrier dynamics studied in this work

was based on differential transmission technique [9]. The very unique nature of the samples


Table 2.1: A few electronic and magnetic properties of MOVPE grown InMnAs and InMnSb

thin fims.

Specifications InMnAs InMnSb

Thickness (nm) 800 200

Mn content (%) 4 3.7

Hole concentration (cm−3) 1.35 × 1018 3 × 1019

Mobility (cm2/Vs) 142 198

Figure 2.2: Band gap vs. Lattice constants for III-V compounds. Clearly, InSb

has the narrowest band gap among all the III-V semiconductors. Adapted from

www.ecse.rpi.edu/schubert/LightEmittingDiodes.org/chap12/chap12.htm.


(thin films grown directly on GaAs by MOVPE technique as shown in fig. 2.3, ferromagnetic

at room temperature) and measurement schemes make the work more crucial and valuable.

Figure 2.3: MOVPE grown InMnAs samples.

2.2 MBE grown InSb heterostructures

2.2.1 Growth and Properties

Narrow band gap semiconductors such as InSb offer exciting prospect in terms of charge

and spin based devices, and several unique properties. Among all bulk III-V compounds,

InSb offer smallest effective mass (0.0139 m0) and smallest band gap (0.24 eV at 300 K, as

shown in Fig. 2.2), which are of particular interest. The small effective mass also gives rise

to a large intrinsic mobility of the carriers, and thus important for realizing energy efficient

fast devices. InSb also has the largest g-factor (-51), largest lattice constant (6.479 A), and

largest spin orbit interaction among the III-V binary materials for which it has attracted a

lot of attention in recent times. Moreover, with the most non parabolic structure among the


III-V’s, InSb is an ideal candidate for carreir transport and spintronic devices.

InSb quantum well (QW) structures are known for increased sensitivity than that of the uni-

formly doped InSb epilayers [10]. However, fabrication of InSb QWs was always challenging

because of the unavailability of a suitable barrier material in terms of lattice constant. A

close match was found with CdTe, but the resulting two dimensional (2D) systems showed

low mobilities due to poor interfaces [11]. Later on, AlxIn1−xSb (x is the concentration of

Al) was employed as barrier material and the quality of InSb QWs improved [12, 13]. The

lattice constant of AlSb is 5% smaller than InSb, but a larger band gap (≈ 1.4 eV at room

temperature) ensures the confinement of the electrons when the concentration of Al (i.e, x)

is small enough.

The InSb/AlxIn1−xSb structures studied in this work were grown at University of Oklahoma

by Professor Santos’s group. The growth technique has been molecular beam epitaxy (MBE),

using semi-insulating GaAs (001) substrates to eradicate electrical conduction through the

substrate layer [10]. Fig. 2.2 represents a comparison of a few III-V semiconductors of

interest. Since the lattice constant of GaAs is 14% smaller than that of InSb and AlxIn1−xSb,

several buffer layers with graded lattice constants were used. The neculeation layer was

formed with AlSb, which has an intermediate lattice constant, and was proved to be effective

for growing InSb on GaAs substrate. The doping, if present, was achieved by Si δ-doped

layers, leading to either symmetric, or asymmetric QWs. The strain in the InSb QWs can


remove the degeneracy of the heavy hole and light hole bands, resulting in two different

gaps at the Γ point with the light hole gap being larger. The QWs used in this work had

different shapes, widths, doping profiles, and number of layers. A total of eight QWs were

studied, including single and multi QWs with either square or parabolic shapes. Each of

the multi QWs contained 25 wells. The square, undoped QWs were comprised of nominally

undoped InSb layers of 300 A, 325 A, and 500 A well thickness with AlxIn1−xSb barriers

of 500 A thickness and 9-15% Al concentration. The parabolic multi QWs were grown by

following Miller’s technique. In this technique the wells are grown digitally to achieve an

effective parabolic Al compositional gradient inside [14]. Summary of structural, growth,

and electronic properties of the QWs are presented in table 2.2.

Figure 2.4: Example of a typical MBE grown symmetrically doped InSb QW.


Table 2.2: Characteristics of the samples studied in this work. The densities and mobilities

are from the measurements at 4.2 K. In the doped samples, only the first subband is occupied

and the Fermi levels, EF , are with respect to the bottom of conduction band.

Sample Density Mobility QW Width x CB1 EF

cm−2 cm2/Vs nm % meV meV

S1(769) 2.0×1011 97,000 30 1.4 9 33

S2(S939) 4.4×1011 96,000 11.5 15 53 72

A1(S360) 2.2×1011 73,000 30 9 14.4 36

MQW1(S591) Undoped 30 9

MQW2(S592) Undoped 32.5 9

MQW3(676) Undoped 5 20

MPQW(607) Undoped 40 12


2.2.2 Earlier Work

Carrier and spin relaxation measurements performed in InSb QW heterostructures are his-

torically rare. Previously, a set of measurements carried on Te-doped, n-type InSb/AlInSb

QWs reported relaxation times close to 0.5 ps [15, 16]. Investigation of carrier relaxation

dynamics remain scarce, with almost no information available on InSb QW heterostructures.

In this work, extensive carrier relaxation dynamics were studied on MBE grown InSb/AlInSb


QWs grown on GaAs(001), employing time resolved differential transmission technique. The

effect of number of layers (single vs. multi QWs), shapes (parabolic vs. square QWs), doping

profile (undoped, symmetrically doped, and asymmetrically doped QWs) on carrier relax-

ation dynamics were investigated in this work. In each of the cases mentioned above, effect

of temperature were studied as well by comparing room temperature (290 K) measurements

with the 77 K counterparts. Understanding the dynamical behavior of nonequilibrium car-

riers can provide new information about the band structures of the material, and several

different scattering mechanisms.

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30


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Harris, L. F. Cohen Blackett, T. Ashley, L. Buckle, Phys. Rev. Lett., 96 096603 (2006).

[16] K. L. Litvinenko, B. N. Murdin, J. Allam, C. R. Pidgeon, M. Bird, K. Morris, W.

Branford, S. K. Clowes, L. F. Cohen, T. Ashley and L. Buckle, New Journal of Physics,

8 491 (2006).

Chapter 3

Experimental Methods

3.1 Introduction

Optical spectroscopy involving techniques such as absorption, reflection, luminescence, and

light-scattering has always been known for extracting invaluable information regarding the

structures and properties of solids. It has also contributed to the overall understanding of

some other unique fundamental properties related to non linear or non equilibrium, or even

transport mechanisms [1]. Among other techniques, time resolved spectroscopy is a powerful

tool to investigate relaxation dynamics in semiconductors. In this chapter, experimental

techniques will be discussed, along with a brief overview of the components employed for the

measurements.

32

Mithun Bhowmick Chapter 3. Experimental Methods 33

3.2 Time Resolved Differential Transmission technique

Time resolved differential transmission (TRDT) technique is a direct method to measure the

dynamics of photo-excited carriers. Like all other spectroscopy techniques, it also has three

distinct parts: creation of non-equilibrium distribution functions in the material by photo-

excitation, detection of the distribution function through proper channel, and recording the

signal after translating it to usable form electronically.

TRDT is a pump-probe technique with the laser pulses are divided into two parts. The part

with a larger power is called pump, and is responsible for the photo-excitation. The other

part, commonly known as probe, is a significantly weaker pulse. Probe is suitably delayed by

adding an optical delay before it reaches the sample, and eventually to the detector (Fig. 3.1).

A change of specific property of the probe is measured and subsequently recorded through

the detector. The additional optical delay in the probe path ensures that the information

about the system before and after the excitation could be extracted.

In general, the time scale clearly shows when the two pulses reached simultaneously to the

sample, and regarded as zero delay. Accordingly, the times before and after zero delay are

called negative and positive delays respectively. Zero delay essentially notes the start of

excitation with the positive delay recording the relaxation dynamics of the corresponding

excitation.

Another variation of pump-probe, known as non degenerate or two color technique, is some-

times used depending on the requirements of the experiment (Fig. 3.1). In this type, a


Figure 3.1: Degenerate and Non degenerate differential transmission schemes.

second laser pulse with a different wavelength is used as probe. Even if the two wavelengths

are different, the probe needs to be in sync with the pump. Non degenerate technique adds

to the versatility of the experiment.


3.3 Time Resolved Magneto Optical Kerr Effect tech-

nique

In time resolved MOKE, a circularly-polarized beam from a pulsed laser source can be used

as pump pulses to selectively excite either spin-up or spin-down electrons in a sample by

taking advantage of the selection rules of the inter-band absorption in semiconductors. The

spin relaxation time is then directly measured from the Kerr rotation of a linearly-polarized

probe pulse as a function of the time delay between the pump and the probe beams.

3.4 Carrier and Spin Relaxation Measurement Schemes

As mentioned before, carrier relaxation could be probed using either a degenerate or a non

degenerate scheme. In the degenerate scheme most of our measurements were focused in the

mid-infrared (MIR) region, tuned in the vicinity of desired transitions. The details of the

laser sources will be discussed in the next section. In our non degenerate scheme, 800 nm

pump pulses with the MIR probe pulses, were used. A Mercury Cadmium Telluride (MCT)

to detect the MIR and a Silicon detector to detect NIR pulses, were employed.

In probing the spin dynamics, the samples were excited with circularly polarized pump

pulses, and probed with either a same, or an opposite circular polarized pulse. Accordingly,

the signal is named as Same Circular Polarization (SCP) or Opposite Circular Polarization

(OCP). The difference of the two, normalized with the sum of the two, is studied as a


function of time delay between the pump and probe pulses. This normalized signal gives the

degree of spin polarization. Since polarization of the laser sources is used to distinguish the

two opposite scenarios, the spin relaxation measurements are often known as polarization

resolved differential transmission (PRDT) measurements.

A few spin relaxation measurements were also performed using magneto optical Kerr ro-

tation, or MOKE measurements. As a result of selection rules for interband transitions,

spin-polarized carriers can be created using circularly polarized pump beams. The MOKE

signal arises from the difference between the optical coefficients of a material for left-and

right-circularly polarized light, which is proportional to the magnetization M [2]. Hence, a

MOKE signal can be induced by: an external magnetic field, an optically induced magneti-

zation, or a spontaneously induced magnetization [2].

3.5 Experimental Components

3.5.1 Laser sources

Ti:Sapphire laser

A Ti:Sapphire (titanium sapphire) laser contains a Sapphire (Al2O3) crystal doped with

Titanium ions. Ti:Sapphire lasers are typically pumped with another laser such as Argon

ion laser or frequency-doubled Nd:YAG. The Ti-sapphire laser used in this work (Mai Tai,

manufactured by Spectra physics, Inc.) generates near infra red (NIR) pulses with duration


of 100 fs, tunable from 750 nm to 850 nm, with a repetition rate of 80 MHz, and an average

power of about 900 mW. In all measurements, the NIR pulse was fixed to 800 nm.

Chirped pulse amplifier(CPA)

Chirped pulse amplification (CPA) is a widely used technique to amplify femtosecond pulses.

The CPA used in this work (Legend-F, manufactured by Coherent Inc.) stretches 800 nm

laser pulses from a Ti:Sapphire laser by a factor of 106 before amplifying the pulses. The

CPA can generate linearly polarized pulses with the wavelength centered at 800 nm and

energy pulses as high as 1 mJ with the repetition rate of 1 kHz. Beam diameter of the

output is typically 6-8 mm.

Optical Parametric Amplifier (OPA)

OPA converts the output laser pulses from a CPA to tunable pulses of wavelengths ranging

from 1.3-10 µm. Inside the OPA, a small fraction of the pump beam (which is the output of

CPA) is focused into a non linear optical material to generate white light. The remaining part

of the beam is focused and recombined with the white light inside a non-centro-symmetric

crystal. This process of nonlinear mixing is called optical parametric amplification (OPA)

where different output wavelengths can be generated by varying the crystal angle. The

output of the OPA consists of two tunable beams called the Signal and the Idler. The Signal

and Idler outputs are tunable from 1150-1600 nm and 1600-2999 nm respectively. It was

important to gauge the optical path length of the beam inside the OPA. From input to

output, the length was measured (and later confirmed by experiments) to be 216 cm.


Figure 3.2: Different components of the Laser sources used.

Difference Frequency Generator (DFG)

The outputs of the OPA are fed to an accessory called DFG. The signal and idler beams

generated in OPA is mixed inside the DFG chamber using a crystal to create output wave-

lengths in the mid infra red (MIR) range. The MIR output from DFG is tunable, and can be

controlled between 2.4-10 µm by changing the angle of the DFG crystal. Total OPA output

travels a 48 cm long optical path inside DFG to produce the desirable output wavelengths

in MIR range.

3.5.2 Optical Components:

Wave plates

Wave plates are important optical component of spin relaxation measurements. Some times


also referred as retarder, a wave plate is made from a birefringent (a material where different

linear polarizations of light propagate with different speeds when passing through it) crystal

with a desired thickness. A wave plate alters the state of polarization of a light beam trav-

eling through it by shifting the phase of the beam between the two orthogonal polarization

components, often referred to as ”fast” and ”slow” components [3]. In principle, the crystal

is designed in such a way that the refractive index is smaller for the light polarized parallel

to the fast axis than it is for the light polarized along the axis perpendicular to the fast

axis (or parallel to the slow axis). As a result, light polarized along the fast axis travels

faster than that of the slow axis, and depending on the thickness of the plate, a light beam

with both the components present emerges with a different polarization state. The formula

corresponding to the phase shift is given as follows:

Γ = 2π∆nL

λ(3.1)

Where Γ denotes the amount of phase shift generated between the components, ∆ n is the

birefringence, and L is the thickness of the crystal [3].

When the phase shift between the two polarized components is made equal to quarter of

the wavelength, the wave plate functions as quarter wave plate, and can convert linearly

polarized light to circularly polarized light beams and vice versa. This conversion can be

done by simply adjusting the plane of the incident light to 45 angle with respect to the fast

axis.


Figure 3.3: Role of a half-wave plate. When a linearly polarized light that is composed of two

components, parallel (green) and perpendicular (blue) to the optical axis of the wave plate,

enters a wave plate, the parallel wave propagates slower than the perpendicular one. At the

other end of the plate, the parallel wave is exactly half of a wavelength delayed relative to

the perpendicular wave. This fact results in output light that is orthogonal to the input

state. Adapted from: http://en.wikipedia.org/wiki/Wave plate.

Wollaston Prism

A Wollaston prism, invented by William Hyde Wollaston [4], can be used to separate ran-

domly polarized or unpolarized light into two orthogonal, s- and p- polarized beams. The

Wollaston prisms are typically made from two orthogonal calcite prisms, glued together into

two right triangle prisms as shown in Figure. After randomly polarized light beams enter

the Wollaston prism, the prism can separate them into two orthogonal polarized rays. The

angle of divergence between the two separated beams depends on the prism’s wedged angle


and the wavelength.

3.5.3 Components employed for data acquisition

Mercury Cadmium Telluride (MCT) detector

The nitrogen-cooled MCT detector has great advantages over detectors that operate at or

near room temperature. For a given scanning time, an MCT detector will produce a spectrum

with a noise level 10 to 100 times lower than the noise from a pyroelectric detector. This

low noise has two important results [5]. (1) It lowers the minimum detection limits for

all compounds being measured. (2) It widens the concentration range over which valid

measurements can be made. A small inconvenience during its operation is to keep the

detector cold with liquid nitrogen, but the accuracy out weighs the inconvenience quite

easily. The exact model used in these measurements was from Electro-Optical systems

(MCT-20-010-E-LN4), which was a cryogenically operated HgCdTe photodetector/amplifier

module [6]. The detector operates at liquid nitrogen temperature in the wavelength range

2-12 microns, with an active area of 1 mm square for receiving the signal. Output of the

module was guided through a BNC-type cable to the lock-in amplifier.

Si detector

These photoconductive detectors typically have a cylindrical housing with approximately 2.5

inches long and 2.5 inches in diameter with an active area of 5 mm square, and an operating

temperature between 0-700 C. The spectral response is in the range 350-950 nm [7].


Lock-in Amplifier

Detection of the amplified voltage was performed using a lock-in amplifier (Stanford Research

Systems, model SR830). The lock-in amplifier can detect the small AC voltage from the

current preamplifier using a reference provided by the laser power supply. A sinusoidal

reference wave was generated from the reference pulses from the laser, and then multiplied

with the amplified signal from the current preamplifier. The result of this multiplication is

two AC signals at the sum and difference frequencies of the signal and reference. Passing these

two signals through a low-pass filter removes all the signals for which the signal frequency

is different from the reference frequency. The remaining signal, where the frequencies are

equal, is a DC signal.

Vout ∝ Vsignal cos(∆ϕ) (3.2)

where ∆ϕ is the difference in phase between the signal and reference. This process of

multiplying and filtering is known as phase-sensitive detection (PSD). Performing PSD on

the output with a new reference (which is out of phase with the original reference) will

remove the phase dependency, giving by [8]:

X = Vsignal cos(ϕsignal) (3.3)

Y = Vsignal sin(ϕsignal) (3.4)

R =√X2 + Y 2 (3.5)

In this work, an SR830 DSP lock in amplifier was used.


3.6 Detailed Description of the Experimental Set ups

3.6.1 Degenerate Differential Transmission Measurements

In the degenerate measurements, a MIR pulse (typically in the range of 3-5 µm) was divided

with a beam splitter into 55% transmitted and 45% reflected beams. The reflected beam

was directed to a moving mirror which adjusts the required delay between the two beams.

Both the beams go through a set of optics to have equal path lengths traveled when they

reach to the sample. Either a parabolic mirror or a pair of CaF2 lenses was employed to

focus the two beams onto the sample.

An MCT detector, placed behind the sample, collected the probe beam and recorded through

a synchronized data acquisition system comprised of a lock-in- amplifier and a computer. In

a typical degenerate carrier relaxation measurement, the ratio of pump and probe fluences

was kept around 1000:1. In case of carrier relaxation studies, the change of the differential

transmission was plotted against the time delay.

For the spin relaxation measurements, a pair of quarter wave plates created circularly po-

larized pump and probe beams. The SCP scenario was created when both the polarizers

were at +450, whereas, OCP represented a situation when the probe had a ”left” circular

polarization through the wave plate reading -450. The net signal, which also was a measure

of the degree of spin polarization (P) in the sample, was calculated through the equation :


Figure 3.4: Schematic diagram of Degenerate Differential Transmission setup for carrier

relaxation measurements. The same setup was used for spin relaxation measurements, in

presence of quarter wave plates.

P =SCP −OCP

SCP +OCP(3.6)

The creation and decay of P was plotted as a function of the time delay between pump and

probe beams. Using the degenerate scheme, carrier and spin dynamics at two particular

temperatures were investigated, one being the room temperature (290 K) and the other

liquid helium temperature (77 K). In all measurement schemes, the sample was housed by

a cryostat for adding the flexibility of temperature dependence studies to the experimental


setup.

3.6.2 Non Degenerate Differential Transmission Measurements

In Non degenerate differential transmission (NDDT) measurements, a NIR pump pulse (800

nm) generated photo excitations, and either a NIR (1.3-2.5 µm), or a MIR (2.7-4.68 µm)

pulse probed the dynamics of the carriers generated. Similar to the degenerate scheme, the

optical path lengths were matched before the two beams reached the samples. Since the

wavelengths were different in this scheme, a lens suitable to each beam was installed for

focusing. The detection scheme was very similar to that of degenerate measurements, and

used an MCT detector for collecting the probe.

Carrier relaxation dynamics were investigated using the NDDT measurements, with varying

several parameters such as probe wavelengths, temperature, externally applied magnetic

field, or pump fluences. The probe wavelengths were tuned in the vicinity of transitions to

be investigated. Using either liquid nitrogen or liquid helium, temperatures ranging from

5-290 K were applied to the sample.

The dependence of carrier dynamics on externally applied magnetic field was studied at

the National High Magnetic Field Laboratory (NHMFL, Florida), in collaboration with Dr.

Stephen McGill, using the DC field facility with filed strengths ranging 0-17 tesla. Lastly,

pump fluences were varied using suitable neutral density filters, and the effect was studied

systematically.


Figure 3.5: Schematic diagram of Non Degenerate Differential Transmission setup for carrier

relaxation measurements.

3.6.3 Non Degenerate Differential Reflectivity Measurements

A few differential reflectivity measurements were also performed, using a MIR (output from

DFG, selected according to the requirement) pulse as pump and 800 nm probe. The scheme

was very similar to the NDDT scheme, with difference in the collection technique and signal

monitoring. Here, reflection of the probe beam in stead of the transmission was collected

through a Si photodiode detector. The net signal was expressed as a function of time delay

between the two beams.


Figure 3.6: Schematic diagram of Non Degenerate Differential Reflectivity setup for carrier

relaxation measurements.

3.6.4 Magneto Optical Kerr Effect (MOKE) Measurements

A limited number of MOKE measurements were done also. For time resolved MOKE mea-

surements, a circularly polarized pump pulse is used to excite a population of spin-polarized

electrons (as a consequence of the selection rules for inter-band absorption in semiconduc-

tors). The spin-polarized electrons act as a net magnetization that decays as the spins relax.

The Kerr rotation of a linearly polarized pump pulse is then measured as a function of

the time delay between pump and probe pulses, which gives the spin relaxation time. The

MOKE signal originates from the difference between the optical coefficients of a material for


left and right circularly polarized light which is proportional to the magnetization produced

by the circularly polarized pump.

Figure 3.7: Schematic diagram of one color MOKE setup for spin relaxation measurements.

The laser sources used as pump and probe in the MOKE experiments were taken from the

CPA beam, with probe being a very small fraction (∼ 10−4) of the pump.

In order to modulate the pump beam at 1 KHz, the reference frequency of CPA was fed to the

Lock-in-amplifier. The pump and the probe beams were focused by a parabolic mirror onto

the sample where the two beams overlaps (at least partially) with a spot diameter of about

100-150 µm (pump being slightly bigger). A quarter wave plate was employed to obtain

circularly polarized pump beam, thereby generating spin polarized photo-excitation in the

sample. The reflected probe beam is guided to a Wollaston prism. The prism separates s-

and p- components of the reflected beam which are orthogonal and have equal intensity in

the equilibrium spin density state. In the presence of non-equilibrium spin polarized carriers,

the MOKE signal represents an intensity difference between the s- and p- components of the


reflected probe pulses. The signals were monitored by using a Si-balanced detector which

was fed into a lock-in amplifier. The carrier dynamics were measured by probing the change

of the transient reflectivity as a function of the time delay between the two beams.

Bibliography

[1] J Shah Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures

Springer Publishing (1996).

[2] A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials

IoP Publishing, Bristol, (1997).

[3] http:en.wikipedia.org/wiki/Waveplate.

[4] http:en.wikipedia.org/wiki/Wollastonprism.

[5] http:www.infraredanalysisinc.com/m2.htm.

[6] http:www.eosystems.com/pdf/MCTCryogenicReceivers.pdf.

[7] http:www.hindsinstruments.com.

[8] http://www.thinksrs.com/products/SR810830.htm.

50

Chapter 4

InMnAs and InMnSb

4.1 Introduction

Narrow gap ferromagnetic semiconductors (NGFS) such as InMnAs have significant poten-

tial for applications in infrared spin photonics and in spin transport devices due to their

small energy gap and much higher electron and hole mobilities, relative to other III-Mn-V

ferromagnetic semiconductors. The first III-V NGFS, InMnAs, was prepared by MBE with

a Curie temperature Tc on the order of 10 K. Subsequent fabrications demonstrated a Tc

close to 90 K [1]. A low temperature MBE technique was nearly exclusively used to prepare

InMnAs thin films; although MOVPE, an alternative technique demonstrated that a single

phase magnetic InMnAs compound could be deposited at 500◦ C, much higher than that

used in MBE [2, 3] .

51

Mithun Bhowmick Chapter 4. InMnAs and InMnSb 52

Furthermore, the MOVPE technique demonstrated that the films are ferromagnetic with

a Tc of 330 K [3, 4]. The Rudermann-Kittel-Kasuya-Yosida (RKKY) mechanism, where

free holes mediate the ferromagnetism, is indeed favored in NGFS while a small hole effec-

tive mass mh results in a long interaction distance and effective exchange coupling. The

hole effective Bohr radius in NGFS suggests a large enough overlap with the Mn induced

hole wave functions to stabilize ferromagnetism even for small Mn contents [5]. The sam-

ples’ ferromagnetic states were measured using several techniques reported earlier [2, 3, 4, 6].

The success with MOVPE grown InMnAs encouraged the same group to search for more

similar materials. A system of interest was InMnSb, where Mn forms a shallow acceptor level

in InSb [7]. Thus, in order to achieve another III-Mn-V material with Tc in excess of 300 K,

and to explore the unique features associated with InMnSb (such as largest lattice constant,

smallest band gap among the class of III-Mn-V, smallest effective mass of the holes thereby

having a much higher hole mobility), a series of In1−xMnxSb films were grown on GaAs(100)

substrates using atmospheric pressure MOVPE method [8]. The alloys were grown at a

substrate temperature of 400 0C. Resulting films were of 350 nm thickness, and of p-type in

nature [8]. Double crystal X-ray diffraction and TEM analysis confirmed the phase purity,

and well defined hysteresis loops proved the existence of room temperature ferromagnetism

in the material, with a very high Tc (in excess of 400 K, predicted by mean field model to be

590 K) [8]. Thus, with the successful growth of InMnSb film with such high-Tc, it became

clear that narrow band III-V semiconductors have huge potential for being excellent hosts


for room temperature ferromagnetic materials.

In this work, several time resolved differential transmission (TRDT) [9, 10, 11] schemes

were employed to provide insight into the time scales and the nature of the interactions in

MOVPE grown ferromagnetic InMnAs and InMnSb films. We demonstrate the sensitivity

and tunability of the carrier dynamics to the initial excitation region as well as to the final

states that are probed. The MOVPE grown InMnAs structure is an 800 nm thick film with a

Mn content of ∼ 4%, a hole concentration p=1.35× 1018 cm−3, and a mobility of 142 cm2/V s

with the Tc above room temperature. In contrast, the 200 nm thick InMnSb film has a hole

concentration p=3×1019 cm−3, and a mobility µ= 198 cm2/Vs with the Mn content of 3.7%.

A summary of the basic features of interest are given in table. The specifications of the

growth conditions, along with detailed electronic and magnetic properties are described in

Refs. [3, 4].

Probing the dynamical behavior of nonequilibrium carriers created by intense laser pulses

can provide valuable information about different scattering mechanisms and the band struc-

ture. Time resolved spectroscopy can help us understand the relaxation of photoexcited

carriers; where after the initial excitation, the nonequilibrium population of electrons and

holes can relax by a series of scattering processes including, carrier-carrier and carrier-phonon

scattering.

Most of the understanding of carrier and spin relaxations in MBE grown narrow gap (III,Mn)V

ferromagnetic structures has been based on two color differential reflectivity spectroscopy

with pump and probe pulses ranging from 1.2-2 µm and 650-850 nm, respectively [12, 13, 14,


15]. In the reported measurements, rapid change of the differential reflectivity was observed

and ascribed to a fast disappearance of photoinduced free carriers through ultrafast trap-

ping by mid-gap states. The carrier relaxation time reported in the MBE grown InMnAs

[14] demonstrated a similar time scale as an InAs film under similar experimental conditions

[16]. Fast relaxation in the differential reflectivity patterns of relaxation dynamic are com-

monly seen in low-temperature-grown III-V semiconductors. The extracted information from

the differential reflectivity measurements can be affected by multi-reflections in multi-layer

structures.

It is important to emphasize and note that our studies are unique in being able to investigate

carrier and spin dynamics in ferromagnetic semiconductors. That is because our InMnAs and

InMnSb samples are on a GaAs substrate. Photoexcitation by the 800 nm pump pulse creates

the majority of carriers in the InMnAs part of the sample with only a few carriers being

excited near the band edge in the GaAs layer. In contrast, previously InMnAs [14] was grown

on a GaSb buffer layer. Photoexcitation by the pump probe created substantial carriers in

this buffer layer making it difficult to separate out the relaxation dynamics of the magnetic

InMnAs layer from the GaSb buffer layer. In addition, GaMnAs samples are grown on a

GaAs substrate. Photoexcitation by the pump pulse creates carriers both in the GaMnAs

layer as well as the GaAs substrate and again, one can not separate out the relaxation

dynamics of the carriers in the magnetic layer from that in the non-magnetic layer. We

demonstrated the tunability of carrier dynamics and relaxation time with characteristics not

reported in the MBE grown InMnAs [14] and InAs [16], the examples of our measurements


are presented here.

4.2 Degenerate Differential Transmission

In our degenerate TRDT pump/probe measurements, the laser source was a Difference Fre-

quency Generator (DFG), which mixes the signal and idler beams from an Optical Parametric

Amplifier (OPA). The OPA itself was pumped by an amplified Ti:sapphire oscillator with

a repetition rate of 1 KHz. The pulses had a duration of ∼ 100 fs, defining the resolution

of the measurements with the ratio of the pump:probe of 1000:1. Both beams were focused

onto the sample with a spot size of around 150-200 µm for probe and slightly larger for the

pump. The differential transmissivity as a function of the time delay between the pump and

probe pulses was measured using a cooled MCT detector.

4.2.1 Degenerate Measurements in InMnAs

Examples of our degenerate TRDT in the InMnAs film with 4% Mn content are shown in Fig.

4.1. The photoexcited carriers were generated/probed at 3.467 µm, close to the fundamental

gap of InMnAs, at 290 K and 77 K and several relaxation regimes, after the initial increase in

the DT were observed. Optical transitions in semiconductors can be strongly influenced by

the distribution of carriers in the conduction and valence bands. The initial sharp increase

in the DT results from free carrier Drude absorption; whereas, the alteration of the dielectric

function of the film through changes in the electron and hole distribution function can be


responsible for the sign change of the Differential Transmission (DT). As shown in Fig. 4.1,

by tuning the pump/probe at 3.1 µm, the DT demonstrated a different pattern, and at 77

K the photo-excited carriers, fully relaxed to its initial value at negative time delay in the

time scale of ∼ 2 ps.

In the presence of point defects and mid-gap states, nonlinear absorption dynamics can in-

fluence the relaxation process, where the observed fast decay could be due to trapping of

carriers in the mid gap states and the slow component could be reflecting the slow recom-

bination of the trapped carriers. In addition, in a degenerate pump-probe scheme when

the pump/probe excitations are from the same source, the optical excitation of the carriers,

followed by the fast relaxation in the bands, can result in a saturation of the band-to-band

absorption [17, 18]. In order to avoid possible nonlinear effects we employed a non-degenerate

differential transmission and examples of the measurements are presented.

4.2.2 Degenerate Measurements in InMnSb

Degenerate measurements in InMnSb were perfomred as well. The experimental condi-

tions were very similar to that used in the measurements on InMnAs sample. With MIR

pump/probe pulses ranging from 3.467-4.3 µm, the differential transmission was studied.

The measurements were focused primarily on probing carrier dynamics in the film, although

a few spin relaxation measurements were performed as well, using polarization resolved

differential transmission (PRDT) scheme. Details of the PRDT technique is discussed in


-DT

/T0

543210 Time Delay (ps)

0

0

InMnAsPump/Probe 3.1mm

77 K x3 290 K

b)

-D

T/T

0


0

0

InMnAs,Pump/Probe3.467 µm

77 K x5 290 K

a)

Figure 4.1: a) DT in MOVPE grown ferromagnetic InMnAs at 290 K and 77 K with

pump/probe fixed at 3.467µ m. b) A different pattern in the relaxation was observed for the

pump/probe at 3.1 µm. Adapted from M. Bhowmick et al, Physical Review B, 85, 125313

(2012).

chapter 3. PRDT allows us to measure the degree of spin polarization in the system, and

also provides the information about the time scale of its decay. Temperature dependence of

the differential transmission was studied by repeating the experiments at room temperature

(290 K) and at temperature of liquid nitrogen (77 K).

Examples of degenerate measurements in InMnSb at 290 K are presented in Fig. 4.2. When

pump/probe beams were fixed to 3.467-4.1 µm, the change in DT was found to be close to

5% in each case. However, a much smaller change in DT was found in case of 4.3 µm, (∼

1%). Fig. 4.3 represents the degenerate measurements at two different temperatures, 77 K

and 290 K, when the pump/probe beams were fixed at 3.8 µm. At both temperatures, the

relaxation pattern was found to be quite similar, with a larger change in DT associated with


the 77 K trace.

-D

T/T

0 (5

% p

er d

iv.)

151050

Time Delay (ps)

0

0

0

0

0

3.467 µm, 3.6 µm3.8 µm, 4.1 µm 4.3 µm ( x 5)

InMnSb, 290K

Pump 1.3 mW,Probe .001 mW

Figure 4.2: Wavelength dependence of degenerate DT in InMnSb at 290 K. The pump/probe

wavelengths were fixed to MIR. The change in DT was found to be much smaller in case of

4.3 µm, (∼ 1%) than that of the other wavelengths.

-D

T/T

0 (1

0% p

er d

iv.)

151050

Time Delay (ps)

0

0 3.8 µm, 77K 3.8 µm, 290K

InMnSb, Deg. DTPump 1.3 mWProbe .001 mW

Figure 4.3: Comparison of degenerate DT in InMnSb at 290 K and 77 K when pump/probe

was tuned to 3.8 µm. At 77 K, the percentage change in DT is larger than that at 290 K.


4.3 Non-degenerate Differential Transmission Measure-

ments

In our Non-Degenerate Differential Transmission (NDDT) scheme the pump pulses were

tuned above the fundamental gap. In this scheme, the photoexcited carriers were created by

NIR pulses fixed at 800 nm above the fundamental gaps of InMnAs and InMnSb, and probed

by laser pulses ranging from 1.3-3.8 µm. The pump fluence was tunable from 1-5 mJ-cm−2

corresponding to a photoexcited carrier density in the range of ∼1×1018 − 5×1019cm−3;

respectively. The band structure calculations, presented in section 4.5, show the optical

transitions for a pump wavelength of 800 nm.

4.3.1 Non-degenerate Differential Transmission in InMnAs

Fig. 4.4 demonstrates the two-color differential transmission measurements in InMnAs fer-

romagnetic film at 290 K for different pump fluences. The fast component of the temporal

evolution can be attributed to the relaxation of the hot electrons and holes, and the slower

component is attributed to the electron-hole recombination across the gap. In the regime

of high electron densities, due to the screening effect and hot phonons, the hot electrons

experience a significant reduction in their energy loss rate through the emissions of longitu-

dinal optical (LO) phonons; therefore, the relaxation time of the hot electrons increase at

higher laser fluences [21]. In addition, some of the photoexcited electrons energetically able

to scatter between the X, L, and Γ valleys in the conduction band resulting in a longer and


more complex relaxation dynamics [22, 23]. The threshold for L-Valley scattering for this

sample is discussed in section 4.5.

The reabsorption of the trapped carriers in the mid gap levels are responsible for the long

relaxation time of the observed photoinduced absorption [24, 25]. The photoexcited electrons

in the conduction band can return to the valence band through the defect and mid-gap

states. The trapped electrons act as additional absorption center and could be reexcited to

the conduction band after absorbing the probe beams. Except for the lowest laser fluence,

the photoinduced carriers were not fully relaxed in a time scale longer than 10 ps.

-D

T/T

0 (1

0 %

per

div

.)


0

0

0

0

Fluence: J/cm2

5x10-3 3.8x10

-3 1.0x10

-3

InMnAs FluencePump 800 nm, Probe 3.467µm

Figure 4.4: Two-color differential transmission measurements in InMnAs ferromagnetic film

at 290 K and different pump fluences. The pump/probe pulses were 800 nm and 3.467 µm,

respectively. The peak of the DT, −∆T/T0 = (T0 − T )/T0, increases from 30% to ∼ 60%,

is suggesting larger photoinduced absorption at higher laser fluences. Adapted from M.

Bhowmick et al, Physical Review B, 85, 125313 (2012).


As shown in Fig. 4.4, for the pump fixed at 800 nm with a fluence of 3.8 mJ-cm−2, tuning

the probe wavelengths in MIR resulted in several differences in the TRDT patterns, where

both the amplitude and the relaxation time demonstrate strong wavelength dependence.

The −∆T/T0 change, at 3.0 µm exceeded 60%, suggesting larger photoinduced absorption

compared to 3.8 µm in which the band filling could be more dominating. The gradual

increase in the amplitude of TRDT peak as a function of the wavelength originated from the

band-gap renormalization important for probe energies around the band gap.

Demonstrated in the inset of Fig. 4.5, lowering the temperature to 77 K increased the

relaxation time. If the reexcitation of the trapped electrons can influence and increase the

relaxation of the photoinduced carriers, then the thermal fluctuations at higher temperatures

make it harder to trap the photogenerated electrons, resulting in a faster relaxation compared

to the observation at 77 K.

Our observations in the NDDT scheme in InMnAs were dominated by photoinduced absorp-

tion only for the wavelengths longer than 2.6 µm. For several NIR probe pulses, ranging from

1.3 to 2.6 µm, we instead observed photoinduced bleaching. Fig. 4.6 demonstrates exam-

ples of the photoinduced bleaching at different temperatures in InMnAs for the pump/probe

tuned at 800 nm/2 µm, respectively. The temperature dependence of the observed photoin-

duced bleaching is not strong and the relaxation in this case lasts longer than the photoin-

duced absorption process. Due to the Pauli exclusion principle, photoexcited electrons in the

conduction band and holes in the valence band can reduce the interband optical transitions

via band and state filling. This leads to a decrease in the absorption, and a corresponding


-D

T/T

0 (

20 %

per

div

)


0

0

0

0

InMnAsPump = 800 nm290 K

Probe: = 3.0 µm = 3.467 µm

1510

50-D

T/T

0 (%

)

80400Time Delay (ps)

77 K

Figure 4.5: Two-color differential transmission measurements in InMnAs ferromagnetic film

at 290 K for different probe wavelengths in MIR. The relaxation dynamic is dominated by

photoinduced absorption. The exponential fits are shifted for clarity. The inset demonstrates

an example of the measurements at 77 K for pump/probe at 800 nm/3.467 µm, respectively.

Adapted from M. Bhowmick et al, Physical Review B, 85, 125313 (2012).

increase in the transmission, which is referred to as bleaching. In a study by Kim et al. [25],

the sign of the differential reflectivity demonstrated a wavelength dependence in GaMnAs

structures where point defect induced absorption is a possible mechanism .

While the TRDT is sensitive to the initial states and the band structure, we have tested

a scheme where the photoexcited carriers were generated by pumping the GaAs substrate

followed by a similar measurement on the ferromagnetic layer side. As shown in Fig. 4.7, the

nature of the relaxations are different suggesting the strong dependence of the dynamics to

the characteristics of the system under study. Unlike the case for Fig. 4.7a, in Fig. 4.7b, the


-D

T/T

0 (2

0 %

per

div

)

100806040200 Time Delay (ps)

0

0

0

0

5K 100K 150 K 290 K

InMnAsPump 800 nm

Probe 2.0 µmField = 0 Tesla

Figure 4.6: Two-color DT measurements of InMnAs ferromagnetic film, at several temper-

atures. The pump/probe pulses were 800 nm and 2 µm. The photoinduced bleaching is

dominating the temporal evolution of the DT. Adapted from M. Bhowmick et al, Physical

Review B, 85, 125313 (2012).

carriers are excited from the GaAs side of the sample and experienced different relaxation

process, compared with carriers originating from the ferromagnetic layer.

The observed wavelength dependence motivated us to probe the possibility of tuning the

nature of the relaxation dynamics in the presence of external magnetic fields. In this case,

the optical components inside the magnet were only compatible for probe pulses tuned below

2 µm with the pump pulses at 800 nm. Examples of our measurements at 5 K are presented

in Fig. 4.8, where the photoinduced bleaching mainly dominated the temporal evolution of

the DT. For external fields of 5 T and 10 T, the photoinduced bleaching changes sign at a

time delay of ∼ 40 ps. Tuning the wavelengths around the band edge (3.0− 3.8µm) did not

result in any change in the DT. However, applying an external field of 5 Tesla, where the


-30

-20

-10

0

-D

T/T

0

403020100-10

Time Delay (ps)

InMnAsPump 800 nmProbe 2 mm

290 K

a)3

2

1

0

-D

T/T

0

403020100-10 Time Delay (ps)

Pump 800 nmProbe 2 mm

290 K

b)

InMnAs filmPumped from GaAs side

Figure 4.7: Two-color DT measurements of the InMnAs ferromagnetic film in two different

configurations and relaxation dynamics. a) When the film is pumped from the ferromagnetic

side. b) When the film is pumped from the GaAs side. Adapted from M. Bhowmick et al,

Physical Review B, 85, 125313 (2012).

band structure is more complicated, caused the switch in the sign.

(T

0 -T

)/T

0 (1

0 %

per

div

)


0

0

0

0InMnAs, 5K

0 T 5T 10 T 15TPump 800 nm

Probe 2.0 µm

Figure 4.8: Two-color DT signals from InMnAs at different applied fields at 5 K. Adapted

from M. Bhowmick et al, Physical Review B, 85, 125313 (2012).


4.3.2 Non-degenerate Measurements in InMnSb

Non-degenerate scheme in InMnSb yielded vital information regarding the time scales and

scattering mechanisms in the material. As in case of the InMnAs film, a 800 nm pump

pulse generated the carriers, and a MIR probe, tuned to several transitions monitored the

relaxation mechanism. The MIR pulses ranged from 2.7-4.6 µm in this case. As before,

measurements carried out at 290 K and 77 K shed light on the temperature dependence

of the carrier relaxation. Fig. 4.9 demonstrates two color DT measurements in InMnSb

performed at 290 K. It was noticed that, as in case of the InMnAs sample, wavelength and

temperature has significant influence on the relaxation dynamics. Fig. 4.10 and Fig. 4.11

represents similar measurements at 77 K, and a comparison of carrier relaxations at two

different temperatures respectively. It is clear that at 77 K, after initial sharp increase of

DT due to free carrier Drude absorption, the relaxation pattern consists of fast and slow

components. As Fig. 4.9 shows, NDDT measurements at 290 K have only one component.

4.4 Spin Relaxation Measurements in InMnAs

4.4.1 Polarization Resolved Differential Transmission Measure-

ments (PRDT)

Fig. 4.12 demonstrates PRDT measurements at 3.467 µm, close to the fundamental gap

of InMnAs. The optical polarization P is related to the spin lifetime through the following


-D

T/T

0 (5

0 %

per

div

.)

2520151050

Time Delay (ps)

0

0

0

0

0

Probe 3.0µm,3.467µm, 3.6µm, 3.8µm, 4.1µm

Pump Power = 1.26 mWProbe Power =0.001 mW

InMnSb, 290K, Pump 800 nm

Figure 4.9: Two-color DT signals from InMnSb at different wavelengths. The exponential

fits are shifted for clarity. For all wavelengths, photo-excited carriers did not fully relax in a

time scale of 25 ps.

-D

T/T

0 (2

0% p

er d

iv.)

302520151050

Time Delay (ps)

0

0

0

0

3.0 µm, 3.467 µm, 3.6 µm, 3.8 µm

InMnSb, NDDT, 77K

Pump 800 nm (1.23 mW),Probe .002mW

Figure 4.10: Two-color DT from InMnSb at 77K demonstrated no significant difference in

the relaxation pattern.

Mithun Bhowmick Chapter 4. InMnAs and InMnSb 67 -D

T/T

0 (2

0% p

er d

iv.)

302520151050

Time Delay (ps)

0

0

3.467µm, 290K 3.467µm, 77K

InMnSb, NDDT Pump 800 nm (1.23 mW)Probe .002mW

-D

T/T

0 (2

0% p

er d

iv.)

302520151050

Time Delay (ps)

0

0

3.6 µm, 290K 3.6 µm, 77K

InMnSb, NDDTPump 800 nm (1.23 mW),Probe .002mW

Figure 4.11: Two-color DT from InMnSb at 77K and 290K for two wavelengths. Clearly,

77K traces show a combination of fast and slow relaxation components after initial sharp

change due to free carrier Drude absorption.

equation: P=P0 exp(-t/T1) where the magnitude of P0 is a constant and can be 0.25 at best

for bulk III-V semiconductors [12]. The relaxation of the optical polarization suggested a

spin relaxation time (T1) of ∼ 1 ps at 290 K, on the same order of magnitude compared to

the MOKE measurements on the same sample.

4.4.2 MOKE Measurements

Spin relaxation in InMnAs was measured at room temperature employing one color Magneto

optical Kerr effect (MOKE) technique. Both the pump/probe were fixed to 800 nm in this

scheme. The MOKE signal arises from the difference between the optical coefficients of a

material for left and right circularly polarized light which is proportional to the magnetization


-D

T/T

0 (

2% p

er d

iv.)

43210-1-2

Time Delay (ps)

a)

0

OCP SCP

InMnAs, 3.467 µm290 K

4

3

2

1

0

-1 (S

CP

- O

CP

)/(S

CP

+ O

CP

) %

3.02.01.00.0 Time Delay (ps)

InMnAs, 3.467mm290 K

b)

Figure 4.12: (a) Polarization-resolved differential transmission measurements at 3.467 µm.

(b) The subtraction represents the degree of spin polarization, and demonstrates an expo-

nential decay of about 1 ps through the fitting curve. Adapted from M. Bhowmick et al,

Physics Procedia, (3) 1167-1170 (2010).

produced by the circularly polarized pump [20]. Using a Wollaston prism, the reflected

NIR signal was separated into s- and p- components which are orthogonal and have equal

intensity in the equilibrium spin density state. In the presence of non-equilibrium spin

polarized carriers, the MOKE signal reflects as an intensity difference between the s- and p-

components of the reflected probe pulses. The signals were monitored using a Si balanced

detector and were fed into a lock-in amplifier. Fig. 4.13 demonstrates the MOKE signal

at 290 K with pump/probe fixed at 800 nm. The pump fluence was ∼ 50 mJ/cm2, which

resulted in a photo-excited carrier density of ∼ 5×1016 cm−3. The MOKE measurement

demonstrated a spin relaxation of ∼ 2 ps, where in this context, the relaxation time is

referred to as the time the signal at positive time delay takes to approximately reach the


value at negative time delays.

MO

KE

(A

rb. U

nit

)

543210-1Time Delay (ps)

InMnAs, MOKEPump/Probe 800 nm290 K

Figure 4.13: MOKE measurements on InMnAs with pump/probe fixed at 800 nm. The

measurement demonstrated a spin relaxation ∼ 2 ps. Adapted from Giti A. Khodaparast et

al, Proc. of SPIE: Vol. 7608 76080O-1 (2010).

4.5 Calculation of Electronic Structure

To understand the effects of the ferromagnetic order on the electronic structure and subse-

quently the carrier relaxation dynamics, the electronic structure for bulk InMnAs has been

calculated at the University of Florida in collaboration with Prof. Stanton’s group. Our pre-

liminary calculations were focused on the band structure. By calculating the electronic band

structure, we can determine where photo-excited carriers are generated by the pump pulse

and which regions of the electronic structure are sampled by the probe pulse. Later, we will

focus on the carrier dynamics. The calculations are based on an 8 band k·p model which in-

cludes the conduction and valence band mixing. The model is similar to the Pidgeon-Brown


model which we have previously used to calculate electron states and to interpret cyclotron

resonance experiments. In this situation, however, there is no external magnetic field but

we allow for kx and ky dependence. We use the standard eight k =0 Bloch basis states (two

spin states each for the conduction band, heavy-hole, light hole and spin-split valence band

states) with no external magnetic field. We however include the effects of the spontaneous

magnetization of the Mn ions and the sp-d coupling of this magnetization to the electrons

and holes. This will spin-split the bands even with no external magnetic field, provided

the Mn ions are ferromagnetically ordered. The magnetization of the Mn ions is calculated

through mean-field theory [29], and the z -component of the average Mn spin < Sz > is

determined by solving

< Sz >= SBs{gS

kT[µBB − 3kTc < Sz >

gS(S + 1)]} (4.1)

where g is the free electron g-factor, Bs is the Brillouin function, S = 5/2 is the spin of the

magnetic Mn ion and Tc = 330 K is the Curie temperature for the InMnAs film. Figure 4.14

shows the calculated band structure for In0.96Mn0.04As at 290 K for Tc = 300 K. We see that

the ferromagnetic order of the Mn ions causes spin splitting of the bands. The red arrows

in Fig. 4.14 show the optical transitions that are possible for an 800 nm pump pulse. We

see that transitions are possible from the heavy-hole, light-hole and spin-orbit split valence

bands. Furthermore, the transitions from the heavy and light hole create photoexcited

electrons in the conduction band that are above the energy threshhold for scattering into

the satellite L valleys. These electrons rapidly scatter into the satellite valleys (which have


a larger effective mass and hence a greater density of states) and take comparatively longer

time to return to the Γ valley and then relax to the bottom of the Γ valley, similar to the

620 nm photoexcitation in GaAs [30, 31, 32].

4.6 Contributions to the differential transmission spec-

tra

The time resolved differential transmission (DT) measures changes to the absorption of the

probe pulse that result from the pump pulse. For thin samples, ∆T/T ≈ −∆αL where L

is the thickness of the sample and ∆α is the change in the absorption coefficient. While

a detailed understanding of the absorption changes requires using the semiconductor Bloch

equations [33], one can gain insight into what types of processes influence the DT signal by

looking at a simplified, approximate expression for the absorption coefficient:

α(ω, t) =1

ω

∫dω′

∫dt′N(ω′, t− t′)

∑transitions

∫dk |Hk|2︸︷︷︸

opticalmatrixelement

×δ(εc(k)− εv(k)︸︷︷︸electron and hole

energies

−ω′)[1− f ec (k, t

′)− fhv (k, t

′)︸︷︷︸electron and hole

distribution functions

]. (4.2)

Here, α (ω, t) is the absorption of the probe pulse centered at frequency ω as a function


of delay time t with respect to the pump pulse, N(ω′, t) is the transient photon energy

density of the probe pulse, Hkk′ is the optical matrix element between conduction and valence

band states, and f ec (k, t

′), fhv (k, t

′) are the electron and hole distribution functions in the

conduction and valence bands respectively.

There are four main contributions to the differential transmission signal −∆T/T0 = (T0 −

T )/T0 [34]. These can be understood by looking at changes in the absorption coefficent

of the probe, eq. 4.2 above, and seeing what changes as a result of the pump pulse. The

four main contributions are: 1)Phase-Space Filling: This comes from the probe pulse

creating additional electrons and holes that block the absorption of additional carriers from

the probe pulse by the Pauli exclusion principle. One can not create an additional electron-

hole pair with the probe pulse if the pump pulse has already created one since the Pauli

principle excludes two electrons from being in the same state. As the photoexcited carriers

relax, the absorption of the probe pulse increases with time. Phase space filling gives a

negative contribution to −∆T/T0 (provided there is no carrier inversion before the pump

pulse). 2) Band Gap Renormalization: This results from the pump pulse photoexciting

electron-hole pairs, which through the many-body interactions, cause the electron and hole

energies (in the delta function in eq. 4.2) to change. This causes the band gap to shrink.

Band gap renormalization gives a positive contribution for probe laser energies below the

pump-induced photoexcited carriers and a negative contribution at energies above the pump-

induced photoexcited carriers. This effect tends to be strong just below and near the band

edge. With no pump-pulse, probing below the band edge will not lead to absorption of


Figure 4.14: Electronic structure of In0.96Mn0.04As at T= 290 K for B =0. The energy

bands are spin-split due to the ferromagnetism. The allowed optical transitions for a pump

wavelength of 800 nm (1.55 eV) are shown by the (red) arrows. The dotted line at 1.08 eV

shows the threshold for Γ valley electrons to scatter to the satellite L valley. Adapted from

M. Bhowmick et al, Physical Review B, 85, 125313 (2012).


the probe pulse. However, with a pump-pulse, the band-gap narrows and the probe pulse

will now be absorbed. 3) Local Field Effects: Photoexcited electon-hole pairs interact

through the Coulomb interaction. This leads to the formation of excitons and changes to

the electron and hole wavefunctions. (Even states excited above the band gap are unbound

excitons). These changes to the wavefunctions will change the optical matrix elements in

eq. 4.2, and lead to a Coulomb Enhancement of the absorption of the probe pulse. Now,

with a pump-pulse on, additional electron-hole pairs are created which screen the Coulomb

interaction and change the optical matrix elements. This gives a negative contribution at

energies below the photoexcited carriers and a positive contribution at energies above the

photoexcited carries. 4) Free Carrier Absorption: This is due to the intraband absorption

of the photoexcited carriers (which must be assisted by phonons or impurities). This will

give a positive contribution to −∆T/T0 due to the photoinduced absorption.

Figure 4.15 shows the calculated bands of In 0.96Mn0.04As at 290 K for Tc = 300 K. This

time we show the transitions from the probe pulse. This allows us to see which regions are

being monitored by the probe pulse. Transitions are shown for probe wavelengths of 3.5 µm

(black arrows) and 2 µm (red arrows). We see that the 3.5 µm probe primarily probes the

states at or near the band edge while the 2.0 µm probe is deep into the bands. This can

explain the sign change in the differential transmission signal shown in Fig. 4.6.

From Fig. 4.15, we see the reason for the change of the sign between 3.5 µm and 2 µm. The

2 µm probes deep into the bands where the phase space filling contribution to −∆T/T0 is

dominant. However, the 3.5 µm transitions probe close to and slightly below the band edge.


In this case, the band gap renormalization term will dominate and give a positive signal to

−∆T/T0 . In addition, free carrier absorption can also contribute to the observed positive

signal at 3.5 µm.

Figure 4.15: Electronic structure of In0.96Mn0.04As at T= 290 K for B =0. The energy

bands are spin-split due to the ferromagnetism. The allowed optical transitions are shown

for a probe wavelength of 3.5 µm (black arrows) and 2.0 µm (red arrows). Adapted from M.

Bhowmick et al, Physical Review B, 85, 125313 (2012).


4.7 Terahertz Time-Domain Spectroscopy

Terahertz time-domain spectroscopy (THz-TDS), with its broad fractional bandwidth and

sub-picosecond time resolution (Fig. 4.16), offers an effective method of characterizing a

semiconductor’s frequency dependent absorption and refractive index. This is an attractive

technique as the electric field is measured as a direct function of time (Fig. 4.16, allowing

for both the amplitude and phase of the pulse to be recorded. Extraction of the complex

refractive index from the time-domain data is accomplished by comparison of the transmitted

(or reflected) complex spectrum of the pulse that interacted with the sample to the spectrum

of the pulse that traveled through air or vacuum (reference). This complex transmittance (or

reflection) function is compared to the Fresnel conditions for transmission or reflection at the

sample interfaces [35]. The complex refractive index can be related to the complex dielectric

permittivity of the sample. For most semiconductors, it is not the complex permittivity

that is sought, but instead the frequency-dependent conductivity which is derived from the

permittivity. The conductivity data is then fit to one of several charge transport models,

such as the Smith-Drude [36] model, where the fitting parameters are optical constants of

the sample such as the plasma frequency and the characteristic relaxation time.

As this overall effort is a study of the growth and characterization of III-Mn-V semiconduc-

tor alloys, a vital component of such a study is the determination of the basic frequency-

dependent electronic/optical properties such as the refractive index, absorption, and con-

ductivity as a function of various factors. Such factors will include semiconductor alloy


Figure 4.16: Terahertz time-domain spectroscopy (TDS) allows for non-contact evaluation

of the frequency-dependent electronic/optical properties of novel materials. Obtained from

Prof. Jason Deibel of Wright State University through personal communication.

TH

z E

lect

ric

Fie

lds

(arb

. un

it)

Time (ps)

2000

0

-2000

0

2000

-2000

0

-2000

Signal (p-p) = 4738

Signal (p-p) = 4134

Signal (p-p) = 3550

0 2 4 6

InMnAs

5K 77K 250K

TH

z E

lect

ric

Fie

lds

(arb

. un

it)

Time (ps)

2000

0

-2000

0

0

2000

-2000

-2000

2000

2 4 60

Signal (p-p) = 5557

Signal (p-p) = 5376

Signal (p-p) = 5316

InMnSb

77K 160 K 290K

Figure 4.17: Terahertz time-domain spectroscopy (TDS) in MOVPE grown InMnAs and

InMnSb films.


4800

4600

4400

4200

4000

3800

3600

3400

Pea

k to

Pea

k T

Hz

Sig

nal

(ar

b. u

nit

)

250200150100500 Temperature (K)

InMnAs

5500

5400

5300

5200

Pea

k to

Pea

k T

Hz

Sig

nal

(ar

b. u

it)

24020016012080

Temperature (K)

InMnSb

Figure 4.18: Temperature dependence of THz peak-to-peak signals in MOVPE grown InM-

nAs and InMnSb films.

composition and growth parameters and external conditions such as temperature (T > 10

K) and applied electromagnetic fields. III-Mn-V semiconductor alloys will be characterized

using both a commercial THz time-domain spectroscopy system that covers 0.1 to 3 THz in

bandwidth and a laboratory-constructed ultra broadband THz-TDS system that spans from

0.3 to 10 THz [37]. The use of multiple THz systems for this characterization effort will

insure the veracity of the results. An example of temperature-dependence measurement can

be seen in Fig. 4.17, performed in collaboration with Prof. Deibel’s group at Wright State

University, where the transmission properties of InMnAs at THz frequencies are investigated.

An additional experiment will study the transient photoconductivity of InMnAs semicon-

ductor alloys. Such a measurement can be accomplished via what is known as Time-resolved

THz-TDS in which the THz transmission or reflection properties of the sample under study


are monitored temporally during excitation by a secondary ultrafast laser pulse [38]. The

experiments proposed here will not only provide feedback to the growth segment of this

collaboration team, but will also characterize the required basic electronic/optical properties

of these materials that are necessary for any future device or application development that

is to be associated with III-Mn-V materials.

4.8 Summary

In summary, carrier and spin relaxation dynamics were probed in MOVPE grown InM-

nAs and InMnSb thin films employing several degenerate and non degenerate pump/probe

schemes. The carrier relaxation measurements demonstrated tunability in time scales, and

could be longer than a few picoseconds. A change in nature of the dynamical processes in

these ferromagnetic semiconductors was noted when the differential transmission changed

sign and a photo-induced bleaching, in stead of absorption, was observed. To explain the

switch, electronic structure was calculated for InMnAs using eight-band k.p model that in-

cludes the nonparabolicity and coupling of the electrons and holes to the Mn impurities.

The calculated band structure with the bands splitting due to the Mn impurities shows :

(1) The NIR (800 nm) pump pulse creates photo-excited carriers from all the hole bands

and some of the photo-excited electrons can scatter to the satellite L valleys which slows

down their relaxation. (2) The sign change between probing with 3.5 and 2.0 µm can be

explained by what regions of the bands are sampled by the probe pulses. At 2.0 µm, the


probe is deep into the bands where the phase-space-filling term dominates. However, at

3.5 µm, the probe is at the band-edge or slightly below it, where band-gap renormalization

term dominates. Spin relaxation dynamics were investigated through polarization resolved

differential transmission (PRDT) and magneto optical Kerr effect (MOKE) measurmeents.

A spin relaxation time of 1-2 ps was obtained in both cases. Finally, a THZ time domain

spectroscopy was performed in the same MOVPE grown InMnAs and InMnSb films to ex-

tract valuable information (such as the refractive indices, absorption spectra) of the systems.

More work regarding this project is underway, and will be reported in due course.

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Chapter 5

InSb based Quantum Wells

5.1 Introduction

As the switching rates in electronic and optoelectronic devices are pushed to even higher

frequencies, it is crucial to probe carrier dynamics in semiconductors on femtosecond time-

scales. Time resolved spectroscopy will allow us understand the relaxation of photoexcited

carriers; where after the initial photoexcitation, the nonequilibrium population of electrons

and holes relax by a series of scattering processes; including carrier-carrier and carrier-

phonon scattering. Using femtosecond short pulses, a narrow band of states can be excited,

and as time progresses, the carrier-carrier interaction results in thermalization of the carrier

distribution. In a longer time scale, by lattice-carrier interaction, the photoexcited carriers

can reach to equilibrium.

85

Mithun Bhowmick Chapter 5. InSb based Quantum Wells 86

Narrow gap semiconductors based quantum wells (QWs) such as InSb offer exciting prospect

in terms of charge and spin based devices, compared to the uniformly doped epilayers [1].

5.2 Samples

The InSb quantum wells (QWs) were grown through molecular beam epitaxy (MBE) by the

group of Prof. Santos at the University of Oklahoma. For the doped samples, the AlxIn1−xSb

barrier layers were δ-doped with Si, either on one side of the QW (asymmetric sample) or

equidistant on both sides of the QW (symmetric sample). The δ doped layers within the

barrier layers were typically located 70 nm from the well center. The shape and symmetry

of the wells were determined by the doping profiles of the wells. Both square and parabolic

QWs were studied in the measurements.

The square multi-quantum-well (SMQW) InSb/AlxIn1−xSb heterostructures were grown on

GaAs substrates. For the measurements described here, we have chosen a sequence of 25

nominally undoped InSb MQWs with different well thicknesses and the alloy barriers are 500

A thick. The remotely δ- doped InSb single QWs had electron concentrations in the wells

ranging from ∼1− 4.4×1011cm−2, where only the ground-state subband is occupied and the

mobility is in the range ∼70, 000−100, 000 cm2/Vs at 4.2 K. Detailed growth conditions were

described previously [2, 3]. The characteristics of the samples are summarized in Table 5.1,

where samples S1, S3, and A1 are modulation doped single QWs and the rest are undoped

multi-QW (MQW) structures either square or parabolic wells.


The two InSb undoped parabolic multi-quantum-well (PMQW) structures studied in this

work consisted of 25 nominally undoped 40 nm and 100 nm wide wells with AlxIn1−xSb

barriers grown on GaAs substrates. In order to achieve an effective parabolic profile inside

each well, the QWs were grown using the recipe of Miller it et al., with barrier thickness of

500 A. In this digital technique, the wells were divided into 50 A-thick segments containing

InSb and AlxIn1−xSb layers, where the relative thickness of each layer was dependent on the

segment’s distance from the center of the well. Details of the growth can be found in Ref.

[1, 2].

Heterostructures with parabolic confinements are important systems to study. In a per-

fect parabolic quantum well (PQW), the subbands are equally spaced and electron-electron

interactions are weak. This fact allows coupling of long-wavelength radiation only to the

center-of-mass coordinate of the electron system, as explained by the generalized Kohn the-

orem [4]. The combination of designability in transition frequency, temperature stability,

and narrow-band emission makes PQW systems suitable for THz devices. Coherent THz

emission (1.5-2.8 THz) from optically pumped intersubband plasmons in modulation doped

GaAs/AlGaAs PQW with a narrowband emission (FWHM ∼0.3 THz) was observed [5].

The corresponding narrowband emission was found to be dependent on the well width, thus

motivating us to investigate well width dependence in similar systems.

The knowledge of detailed band structure and accurate band gap is inevitable for the assess-

ment of a material system, and its design compatibility for devices. One such way to model

the band structure of two dimensional InSb systems is band offset calculations. The band


offsets in this system has been determined earlier [6] and the interband transition energies

were calculated using a four-band model described by Bastard [4]. Band-edge effective mass

values in the alloy barrier are considered to change with the band gap Exg according to the

Kane [7] model. The energy gap (in eV) of the alloy at 4.0 K can be calculated from the

known variation of the alloy gap with concentration x: Exg = E0

g +2.06x [8]. To calculate the

subband energies, the effect of strain in determination of the band gap in InSb QWs E0g , [9],

has been included. Below 77 K, the variation in the bandgap of both InSb and AlxIn1−xSb

below 77 K is about 3% [8], resulting in negligible variation of the confinement potentials

and therefore the interband transition energies.

5.3 Experimental Results:

We probed the interband relaxation dynamics of photo-excited carriers and spins in doped

and undoped InSb based QWs by employing several pump/probe DT schemes in MIR. The

laser pulses were from an optical parametric amplifier (OPA) pumped by a chirped pulse

amplifier (CPA) or from a difference frequency generator (DFG), which mixes the signal and

idler beams from an OPA. The pulses had a repetition rate of 1 KHz and duration of ∼ 100

fs.The pump fluence is on the order of 5 mJ− cm−2 corresponding to a photo-excited carrier

density of ∼ 5 ×1018 cm−3.


Table 5.1: Characteristics of the samples studied in this work. The densities and mobilities

are from the measurements at 4.2 K. In the doped samples, only the first subband is occupied

and the Fermi levels, EF , are with respect to the bottom of conduction band.

Sample Density Mobility QW Width x CB1 EF

cm−2 cm2/Vs nm % meV meV

S1(769) 2.0×1011 97,000 30 1.4 9 33

S2(S939) 4.4×1011 96,000 11.5 15 53 72

A1(S360) 2.2×1011 73,000 30 9 14.4 36

MQW1(S591) Undoped 30 9

MQW2(S592) Undoped 32.5 9

MQW3(676) Undoped 5 20



5.3.1 Degenerate pump/probe scheme

A degenerate pump-probe approach was employed for probing time scales of carrier and spin

relaxations in several InSb based QWs. In a degenerate time resolved pump/probe scheme,

after the optical injection, the fast relaxation of the carriers in the bands can result in a

saturation of the band-to-band absorption. Here we present examples of the relaxation dy-

namics in samples with different design structures, and close to several interband transitions


Table 5.2: Possible interband transitions in a 30 nm square quantum well with with 9% alloy

concentration.

Interband Wavelength

Transitions µm

HH1→ CB1 4.68

HH2→ CB2 4.0

HH3→ CB3 3.46

LH1→ CB1 4.1

LH2→ CB2 3.45

were probed.

Figures 5.1 and 5.2 demonstrate the photo-induced carrier dynamics through degenerate

pump/probe scheme in the vicinity of several interband transitions in a MQW sample (S592).

We observed an initial increase in the differential transmission which can be attributed to

the free carrier Drude absorption. The initial relaxation lasts for ∼ 1 ps followed by a longer

component in the time scale of ∼ 6 ps. As shown in Fig. 5.2 for the same measurements on

sample S592, at 77 K, the temperature dependence of the relaxation dynamic is weak.

Figure 5.3 demonstrates the carrier dynamics in a parabolic multi quantum well (S607),

where much faster relaxation times were observed. The observed fast relaxations motivated

us to probe a scheme where the carriers are created above the gap and probed in the vicinity


Table 5.3: Possible interband transitions in a 11.5 nm square quantum well with with 15%

alloy concentration.


Transitions µm

HH1→ CB1 3.9

HH2→ CB2 2.8

LH1→ CB1 3.2

-D

T/T

0 (1

0% p

er d

iv.)

6543210

Time Delay (ps)

0

0

0

t7, 3.467 micron t6, 3.6 micron t8, 3.8 micron

S592, 290K, Deg, 04/10/12Pump 1.3 mW, Probe .001mW

Figure 5.1: Carrier relaxation in a degenerate MIR pump/probe scheme close to interband

transitions at room temperature. The initial relaxation time lasts for ∼ 1 ps followed by a

slower component.


Table 5.4: Possible interband transitions in a 32.5 nm square quantum well with with 9%

alloy concentration.


Transitions µm

HH1→ CB1 4.7

HH2→ CB2 4.1

HH3→ CB3 3.5

LH1→ CB1 4.1

LH2→ CB2 3.5

of several interband transitions; examples of the measurements are presented in the next

section.

5.3.2 Non-degenerate pump/probe scheme

In order to explore the possibility of tuning the relaxation time, a non-degenerate differential

transmission scheme was employed. In this scheme, the carriers are created by NIR pulses

fixed at 800 nm above the band gap of AlxIn1−xSb and InSb and probed by MIR pulses.

The pump fluence was similar to the measurements in degenerate scheme. The carriers were

captured in the QW on a time scale of ∼ 1 ps. In these measurements, the selected MIR

probe pulses allowed us to probe the optical transitions only in the InSb QWs, avoiding


-D

T/T

0 (2

% p

er d

iv.)

1086420

Time Delay (ps)

0

0

0

t9, 3.467 micron t8, 3.6 micron t12, 3.8 micron

S592, Degenerate, 77K,04/11/12Pump 1.3 mW, Probe .001 mW


transitions at 77 K. The dynamic is similar to the measurements at room temperature.

the AlxIn1−xSb barrier layer. This fact can be supported by earlier measurements that

determined the concentration and temperature dependence of the fundamental energy gap

in AlxIn1−xSb [10].

Figures 5.4 and 5.5 represent examples of non degenerate differential Transmission (NDDT)

measurements in S592 InSb QW structures where a much slower dynamics have been ob-

served, compared to the degenerate measurements. In the carrier relaxation process in a

two-dimensional system and its neighboring barrier region, the carriers can experience sev-

eral scattering mechanisms including both intrasubband and intersubband scattering with

phonons [8]. In addition, electrons that are sufficiently energetic have some possibility to


-D

T/T

0 (1

0% p

er d

iv.)

3.02.01.00.0 Time Delay (ps)

0

0

0

3.467 mic 3.6 mic 4.1 mic

S607, 290K, Pump 1.3 mWProbe .001 mW 11/29/11


transitions at 290 K.

scatter between the X, L, and Γ valleys in the conduction band, resulting in a more com-

plex relaxation dynamics [9]. Our observations provide information on the carrier relaxation

which are important for the limit of quantum well lasers based on this material system.

In addition, Figures 5.6 and 5.7 show examples of the carrier dynamics at 290 K us-

ing two-color time-resolved differential transmission (TRDT) in InSb/Al0.04In0.96Sb and

InSb/Al0.12In0.88Sb multi PQW structures with 25 parabolic wells of 100 and 40 nm width,

respectively. The pump excitation was fixed at 800 nm and MIR probe pulses were tuned to

3.467, 3.6, 3.8, 4.0, and 4.1 µm. The pump fluence was tunable of the order of 1-5 mJ/cm2

corresponding to a photo-excited carrier density of ∼ 1×1018-1×1019 cm−3. For the selected


-D

T/T

0 (1

0% p

er d

iv.)

35302520151050

Time Delay (ps)

0

0

0

S592,Pump 800 nm (1.23 mW)Probe (0.002mW), 290K, 07/28/11

Probe 3.2 micron 3.467 micron 3.6 micron

Figure 5.4: Carrier relaxation in a Non degenerate pump/probe scheme tuned to NIR/MIR

respectively, at 290 K.

wavelengths, the probe pulses can avoid the barriers except for the case of the PQW with

4% alloy content. Considering the absorption length for InSb at 800 nm, we expect ap-

proximately 6 wells were optically populated for the 100 nm PQWs and 10 wells for the 40

nm PQWs. In an earlier study, ”forbidden” interband transitions with n=2 were observed,

where n is the subband index, in addition to the allowed interband transitions with n=0.

Possible interband transitions were identified using numerical calculations based on the Bas-

tard four-band model formalism [4]. The calculations included band non-parabolicity and

took into account the digital composition of the PQWs [5]. To calculate the interband tran-

sitions in the PQWs, we used band-edge masses of 0.0139m0, 0.015m0, and 0.25m0 for the


-D

T/T

0 (5

% p

er d

iv.)

3020100

Time Delay(ps)

0

0

S592, Pump 800 nm (1.23 mw) Probe 3.6mic (.002mW)

290K 77K

Figure 5.5: Temperature dependence in S592 employing Non degenerate scheme. No signif-

icant difference was observed between 77 K and 290 K traces.

electrons, light holes (LH), and heavy holes (HH), respectively, where m0 is the free electron

mass.

Figure 5.6 demonstrates the relaxation dynamics in the 100 nm wide PQWs where the initial

increase in the differential transmission can be attributed to free carrier Drude absorption

due to the intraband absorption of the photoexcited carriers. The carriers were captured in

the QWs in a time scale of ∼ 1 ps and the signal changed sign for all the probe wavelengths

with insignificant temperature dependence. For the 100 nm PQW with 4% alloy content,

the probe wavelength of 4.1 µm was tuned in the vicinity of the CB4-HH4 and CB4-HH6

transitions, whereas the other possible MIR probes were tuned close to the top of the PQWs.


The alteration of the dielectric function through changes in the electron and hole distribution

functions could be responsible for the sign change of the differential transmission.

-D

T/T

0 (2

0% p

er d

iv.)


0

0

0

Probe 3.467 µm 3.6 µm 3.8 µm

S625, Pump 800nm (1.26 mW)Probe .001 mW, 290K, 11/11/10

Figure 5.6: Carrier relaxation in a Non degenerate pump/probe scheme, with 800 nm pump

and MIR probe.

For the 40 nm wide wells, the probe wavelengths were tuned in the vicinity of the CB1-HH3

(for probe wavelength of 3.8 µm), CB1-LH1 and CB2-HH2 (for probe wavelength of 3.6 µm),

along with HH4-CB2 (for probe wavelength of 3.467 µm) transitions. An example of the

measurements is presented in Fig. 5.7 for three different probe wavelengths. In this case,

the carriers fully relaxed in the time scale of 40 ps without any change in the sign of TRDT.


-D

T/T

0 (2

0% p

er d

iv.)

6050403020100

Time Delay (ps)

0

0

0

0

Probe 3.2 µm, 3.467µm 3.6 µm, 3.8 µm

S607, Pump 800 nm290K, 07/15/10

Pump = 1.26 mW, Probe = .001 mW

Figure 5.7: Carrier relaxation in a Non degenerate pump/probe scheme , with 800 nm pump

and MIR porbe.

5.3.3 Fluence Dependence

The effect of pump fluence was studied in many of the InSb based quantum wells. The pump

fluence was varied in the range 1.7 to 9.62 mJ/cm−2, with the temperature ranging from

290 K and 77 K. Fig. 5.8 represents example of the fluence dependence measurements in a

parabolic quantum well used in this work.


-D

T/T

0 (2

0% p

er d

iv.)


0

0

0

0

1.4 mW,1.26 mW0.5 mW,0.3 mW

S607,Pump 800 nm, Probe 3.467µm, 290K, 07/15/10

Figure 5.8: Fluence dependence of carrier relaxation in a non degenerate pump/probe scheme

in the 100 nm PQW with 4% alloy (S607).

5.3.4 Polarization Resolved Differential Transmission(PRDT)

In order to probe the relaxation of photo-induced spin polarized carriers in the InSb QWs,

pump/probe pulses were tuned close to several interband transitions of the InSb QWs. As a

result of selection rules for interband transitions, spin-polarized carriers can be created using

circularly polarized pump beams. By monitoring the transmission of a weaker, delayed

probe pulse that has the same circular polarization (SCP) or opposite circular polarization

(OCP) as the pump pulse, the optical polarization P = (SCP −OCP )/(SCP +OCP ) can

be extracted. The optical polarization P is decaying exponentially with a decay constant

related to the spin lifetime as following: P=P0 exp(-t/τ s), where the magnitude of P0 is a


constant and can be 0.25 at best for bulk III-V semiconductors [12]. In order to measure the

optical polarization, the differential transmissivity was recorded as a function of the time

delay between the pump and probe pulses, using a liquid nitrogen cooled mercury cadmium

telluride (MCT) detector.

Figures 5.9 and 5.10 are examples of the polarization-resolved differential transmission mea-

surements at 4.1 µm, to extract T1. A similar measurement is presented in Fig. 5.11,

with a parabolic sample, where the pump/probe was tuned to 3.6 µm. We observe spin

relaxation times ranging from 1-4 ps, longer than the earlier observations in Te-doped

InSb/Al0.15In0.85Sb QWs at room temperature [13, 14]. The measured T1 in our samples

is consistent with the theoretical calculations in two dimensional systems based on the

Dyakonov-Perel (DP) relaxation mechanism [15, 16].

5

4

3

2

1

0

-1

(S

CP

- O

CP

)/(S

CP

+ O

CP

) %

2.01.51.00.50.0 Time Delay (ps)

S9394.1µm

290 K

Figure 5.9: The optical polarization for a symmetric QW at 290 K (S939), employing the

spin polarized differential transmission technique. The optical polarization is decaying ex-

ponentially with a decay constant related to the spin lifetime.


5

4

3

2

1

0

(S

CP

- O

CP

)/(S

CP

+ O

CP

) %

3.02.52.01.51.00.50.0 Time Delay (ps)

S591, Pump/Probe = 4.1 µm

Figure 5.10: The optical polarization at 290 K for an undoped MQW (S591) employing the

spin polarized differential transmission technique.

5.4 Summary

In summary, interband relaxation dynamics of photo-induced carriers and spins were probed

in doped and undoped InSb based quantum wells with different structures through several

pump/probe differential transmission schemes employing either degenerate or non degenerate

approach. In a degenerate scheme (pump/probe both MIR), initial increase in the differential

transmission was observed in all the measurements. The sharp increase can be attributed

to the free carrier Drude absorption. The relaxation dynamics comprised of a fast (∼ 1 ps),

and a comparatively slower component (∼ 6 ps). Temperature dependence of the relxation

dynamics was found to be weak. In search of tunability of the time scale, a non degenerate

differential transmission approach with NIR pump and MIR probe was also employed on the


-2

-1

0

1

(S

CP

-OC

P)/

(SC

P+O

CP

) %

2.01.51.00.50.0

Time Delay (ps)

S607, 3.6 micron

Figure 5.11: The optical polarization at 290 K for a parabolic sample (S607) employing the

spin polarized differential transmission technique.

same set of samples. Compared to the degenerate measurements, carrier relaxation dynamics

in non degenerate measurements were proved to be much slower. In this case, the initial sharp

increase was followed by a more complex relaxation dynamics lasting approximately 20-60

ps. In case of non degenerate measurements (when the pump was in the NIR), it is possible

that the electrons can get sufficiently energetic to scatter between X, L, and Γ valleys in the

conduction band, resulting in a complex and long relaxation dynamics. A thorough study

of pump fluence and temperature dependence were performed. To probe the photo-induced

spin polarized carriers, circularly polarized MIR pump/probe pulses were employed on the

same set of InSb based quantum wells. The optical polarization decayed exponentially with

relaxation times ranging from 1-4 ps, longer than earlier observations reported in Te-doped

InSb/AlInSb quantum wells at room temperature [13, 14]. Our observations are consistent


with the theoretical calculations in two dimensional systems based on Dyakonov-Perel (DP)

model [15, 16].

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