Optical Spin Polarization Measurements on InAs

Optical Spin Polarization Measurements on InAs-based Light Emitting Diodes

by

Andreas Volker Stier

August, 2005

A dissertation submitted to the Faculty of the Graduate School of The State University of New York at Buffalo in partial fulfillment of the requirements for the degree of

Master of Science

Department of Physics

i

Dedicated to my parents Erwin & Christiane Stier

Acknowledgements During my time as an exchange student in Buffalo, I was able to meet lots of extraordinary people all of different kind. It is a pleasure to acknowledge Professor B. D. McCombe for giving me the opportunity and confidence to work in his laboratory on such a great experiment. I was able to learn so much about physics, no classes and books could teach me that. I also want to thank my committee member Prof. H. Luo for useful discussions during my stay. I also want to express my thanks to Prof. J. Cerne for giving me advice concerning questions about the anti-reflection coating. I am pleased to thank Dr. C. Meining for his never ending support and criticism, challenging me constantly and making me think about problems on a new, higher level. I am proud and honored to be able to work with you. This work would have not been possible without the efforts of our many collaborators. Prof. Laurens Molenkamp and his group (Dr. Peter Grabs, Dr. Idriss Chado) at my Alma Mater, the University of W¨ urzburg, Germany, provided the samples for the spin-injection measurements. For tremendous help with technical questions and setting up the experiment, as well for his mental support during frustrating times, I want to thank Vincent Whiteside.

ii

iii I am grateful to MaryAnn LaMilia for smoothing the sometimes stony ways in administration processes. My thanks are also to my labmembers of the McCombe’s lab Mustafa Eginligil for making the long hours of data acquisition less boring and to Jason Bowker helping me building the samples. I would have never had the opportunity to come to Buffalo and learn more than just physics without the America exchange programme of the University of W¨ urzburg. May facilities like this be supported in even greater amount to give more people the opportunity I had. Now, my words fade if I want to express my thanks to my parents, that supported me throughout my student life and especially in America so that I could concentrate my whole time on physics. I hope I could pay back what you invested in me. Thank you, Anita, for your never ending love.

Contents Acknowledgements

ii

List of Figures

vi

List of Tables

viii

1 Introduction

1

2 General Background

4

2.1

Methods of Spin Injection . . . . . . . . . . . . . . . . . . . . . . . .

4

2.2

Diluted Magnetic Semiconductors . . . . . . . . . . . . . . . . . . . .

12

3 Theory

18

3.1

InAs Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.2

Optical Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.3

Spin Relaxation Mechanisms . . . . . . . . . . . . . . . . . . . . . . .

34

4 Experimental Details

45

4.1

Fabrication of the Anti-Reflection Coating . . . . . . . . . . . . . . .

45

4.2

Sample Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

iv

CONTENTS

v

4.3

Light Emission Measurements . . . . . . . . . . . . . . . . . . . . . .

55

4.4

I(V) Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

4.5

Polarization Measurements . . . . . . . . . . . . . . . . . . . . . . . .

57

5 Experimental Results and Discussion

64

5.1

Anti Reflection Coating

. . . . . . . . . . . . . . . . . . . . . . . . .

64

5.2

I(V) Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

5.3

Optical Polarization Degree Measurements . . . . . . . . . . . . . . .

84

6 Summary

95

A Fourier Analysis and Interferometry

97

B 10 T Magnet

104

C Sample Batch Details

105

List of Figures 2.1

Optical Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.2

Spin injection with circular polarized laser . . . . . . . . . . . . . . .

6

2.3

Optical polarization degree . . . . . . . . . . . . . . . . . . . . . . . .

7

2.4

Resistor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.5

Spin injection with DMS . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.6

Spin injection in AlGaAs/GaAs QW . . . . . . . . . . . . . . . . . .

10

2.7

Optical interband transitions in GaAs . . . . . . . . . . . . . . . . . .

11

2.8

Transition to degenerate and non degenerate VB level in GaAs . . . .

12

2.9

Energy level in CdMnSe . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.1

InAs bandstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.2

Envelope function . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.3

Landau level in InAs . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

3.4

Energy levels and optical transitions . . . . . . . . . . . . . . . . . .

30

3.5

Spin relaxation mechanism . . . . . . . . . . . . . . . . . . . . . . . .

42

4.1

Evaporation system . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

4.2

Band alignment in the heterostructure . . . . . . . . . . . . . . . . .

49

4.3

Sample structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

vi

LIST OF FIGURES

vii

4.4

Band offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

4.5

Calculated bandstructure . . . . . . . . . . . . . . . . . . . . . . . . .

53

4.6

Polarization measurement setup . . . . . . . . . . . . . . . . . . . . .

58

4.7

Light path inside the FTIR . . . . . . . . . . . . . . . . . . . . . . .

59

4.8

Tilt angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

4.9

AC vs. DC PL spectra . . . . . . . . . . . . . . . . . . . . . . . . . .

62

5.1

SiO film on GaAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.2

Cut through the ARC layer . . . . . . . . . . . . . . . . . . . . . . .

66

5.3

Transmission spectra of Si-O compounds . . . . . . . . . . . . . . . .

67

5.4

Transmission spectra of the test film . . . . . . . . . . . . . . . . . .

68

5.5

Internal reflection at the top boundary . . . . . . . . . . . . . . . . .

69

5.6

Schematic of the InAs/SiO boundary . . . . . . . . . . . . . . . . . .

72

5.7

Light gain measurement results . . . . . . . . . . . . . . . . . . . . .

75

5.8

Room temperature I(V) . . . . . . . . . . . . . . . . . . . . . . . . .

77

5.9

Liquid helium temperature I(V) . . . . . . . . . . . . . . . . . . . . .

78

5.10 I(V) at RT and LHe . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

5.11 Band diagram of a Esaki diode . . . . . . . . . . . . . . . . . . . . .

81

5.12 I(V) curves in forward bias . . . . . . . . . . . . . . . . . . . . . . . .

83

5.13 EL spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

5.14 Optical polarization degree . . . . . . . . . . . . . . . . . . . . . . . .

87

5.15 Simulated Po vs. measured Po . . . . . . . . . . . . . . . . . . . . . .

89

5.16 ∆E(B) for different manganese concentrations . . . . . . . . . . . . .

90

5.17 Temperature dependence of Po . . . . . . . . . . . . . . . . . . . . . .

91

B.1 Schematic of Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

List of Tables 4.1

Bandparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

C.1 Sample Batch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

viii

Abstract The general approach for examining the large variety of spin-related phenomena in metals and semiconductors is to introduce or otherwise prepare a collection of aligned spins and study the response of that system to external conditions like an asymmetric potential, or an applied electric or magnetic field. This work focuses on measuring the injection of spins into the narrow gap semiconductor Indium Arsenide (InAs) from a CdMnSe spin-aligner by the optical polarization degree of the radiation emitted from a light emitting diode structure with InAs as the active layer material. In order to improve the signal-to-noise ratio of the very weak electro-luminescence (EL) from these diodes, a single layer anti-reflection coating (ARC) of silicon monoxide (SiO) was developed, and applied on the samples. A positive optical circular polarization degree was found in the polarization measurements on recent samples grown at the University of W¨ urzburg, suggestive of significant spin injection from the CdMnSe spin-aligner. These results indicate that we have successfully injected spins into InAs for the first time.

ix

Chapter 1 Introduction Semiconductor nanostructures are often designated as ”artificial materials”: If the extension of such materials is comparable to characteristic length scales, like the de Broglie wavelength of the carrier, electronic, optical and magnetic properties can indeed be artificially tailored. The need to control the electronic properties at smallest length scales is well-known from microelectronics. Huge progresses is the field of molecular beam epitaxy (MBE) over the past decade enables people to build devices with an accuracy of an atomic layer. But up to now the functionality of the devices involves a huge amount of electrons which dissipate more and more energy heating these devices up to a self destructive level. Moreover, a high potential for future applications is predicted for devices, which make use of the particle’s spin instead of its charge. This new research field is called spintronics. The idea is to enhance the features of conventional electronic circuits by utilizing the spin degree of freedom. Thus, people hope to provide the basis for enhanced technologies used in future devices (Prinz, 1995, 1998). A number of requirements have to be met to make realistic and useful objects that

1

CHAPTER 1. INTRODUCTION

2

utilize the spin rather than the charge. The spin system is prepared by spin-aligners like diluted magnetic semiconductors (Furdyna, 1988) or ferromagnetic semiconductors (Ohno, 1999a). The latter material class is highly desirable as they are able to spin-polarize carriers at high temperature (Jiang et al., 2005) without the application of an external magnetic field. Aligned spins can now be manipulated either optically (Rashba and Efros, 2003a,b) or electrostatically by a gate voltage in a transistor structure (Datta and Das, 1990) via the spin-orbit interaction (Winkler, 2003). The spin-manipulation normally takes place in an area of the device spatially separated from the spin-aligner and thus the decay of the spin-information with transport has to be minimized in spin-devices. So far, this could only be achieved by cooling the structures beyond temperatures reasonable for useful applications. After the spins are aligned, they have to be injected into the manipulation layer. This key component is crucial for the functionality and efficiency of the device. The feasibility of this concept was shown first for spin-injection of electrons into the wide gap semiconductor GaAs by our collaborators at the University of W¨ urzburg (Fiederling et al., 1999) (see also Jonker et al., 2000). In a test structure similar to the samples used in this work, the groups showed that it is possible to inject spins from a diluted magnetic semiconductor in a nonmagnetic layer and measure the spin polarization of the carrier optically. The radiation comes from the recombination of spin-polarized electrons with unpolarized holes in a GaAs/AlGaAs quantum well. Since spin-orbit interaction couples orbital and spin degrees of freedom, the associated interband transitions are circularly polarized (Meier and Zakharchenya, 1984). Thus, the polarization of recombination emission together with the knowledge about the involved states serves as tool to investigate the spin-polarization of the injected electrons and hence the spin-injection efficiency.

CHAPTER 1. INTRODUCTION

3

However, most of the studies utilized wide-gap semiconductors such as GaAsbased QWs or InAs-based quantum dots (with a large effective gap due to quantum confinement in all spatial directions) as spin analyzers. Spin-orbit (SO) coupling effects in these systems are negligibly small for conduction band electrons compared to narrow-gap semiconductors such as InAs. The enhanced SO coupling effects due to strong coupling of conduction and valence bands, and in particular the (bulk and structural) inversion-asymmetry-induced effects (Dresselhaus, 1955) give rise to a number of spin manipulation schemes, which are, in addition to spin-injection, desirable for spintronic device applications. As electrical detection, still proves difficult and exhibits only small spin-injection efficiencies (Hammar and Johnson, 2002), it is therefore important to study whether spin-injection into InAs and optical detection is possible. Because of the enhanced spin-orbit interaction effects in this narrow gap semiconductor, spin relaxation is enhanced and large intrinsic g-factors lead to thermal population effects that have to be taken into account by determining the spin-injection efficiency. Optical detection of spin-injection into the narrow-gap semiconductor InAs from the diluted magnetic semiconductor CdMnSe is the subject of this dissertation. The following chapter provides the background necessary to place the present work in context, and Chapter 3 outlines the theory needed to understand the results. This is followed in Chapter 4 by a description of the samples and experimental details. The results are presented and discussed in Chapter 5, and finally a summary is given in Chapter 6.

Chapter 2 General Background In this chapter, I present an overview about the basic concepts that underlie the optical polarization degree (OPD) measurements. I review previous experiments and techniques to inject spins in semiconductors.

2.1

Methods of Spin Injection

The oldest way of creating spin polarized carriers is due to the principle of symmetry in physics. Figure 2.1 shows a simple schematic of spin-split (the spin quantum number is indicated as ±1/2) conduction band and valence band, assuming positive band g-factors, in a semiconductor. The population of the bands can be changed from their equilibrium distribution by optically pumping the system. Electrons from the valence band are excited into CB states. These transitions obey quantum mechanical selection rules1 . If the laser beam, for example, is σ + (right-hand rule) polarized, then the electron will be excited into a s = + 21 , the hole in a s = − 12 state for a total 1

The selection rules are examined in more detail in chapter 3.2.

4

CHAPTER 2. GENERAL BACKGROUND

5

Figure 2.1: Simple schematic of the spin-split conduction band (CB) and valence band (VB) of a semiconductor in a magnetic field assuming positive band g-factors. The optical absorption transitions and their polarization properties are indicated with arrows.

4m = +1. The helicity of the photon is transferred to the electron. As only certain states are allowed, the optical pumping leads to a spin polarization of the CB electrons depending on the excitation power and the spin-lifetime τs in the semiconductor. Assuming, that the spin-lifetime is large compared to the recombination time τr , the emitted radiation from the semiconductor contains the information about the involved states in the emission process. The energy difference of the states is contained in the wavelength of the radiation via ∆E = ~ω, and the spin-information can be detected by examining the optical polarization degree. An experiment, including the optical spin-polarization and detection has been done by Hägele et.al. (Hagele et al., 1998). Figure 2.2 shows the schematic of their experimental setup. A circular polarized laser pulse is used to create electro-hole pairs. The spin-polarized


6

Figure 2.2: Schematic of the spin-injection experiment by Hägele et al., taken from (Hagele et al., 1998).

electrons are separated from the holes by an applied electric field. They diffuse into a AlGaAs/GaInAs quantum well where they recombine with unpolarized holes. The result of the experiment can be seen in figure 2.3. The optical polarization degree, defined as Po =

I+ − I− I+ + I−

(2.1)

can be calculated from the measured intensity and is shown in the inset of the figure. The major disadvantage of optical injection is the need of a laser which is unsuitable in the design of integrated circuits. A major driving force behind spin-injection is the possibility to use the spin-degree of freedom for information processing2 ; thus it is desired to find a way of injecting spins from a spin-aligner directly in a 2DEG of a semiconductor. 2

for a review about semiconductor spintronics and quantum information, see e.g. Awschalom

et al. (2002); for quantum information see Alber et al. (2001) and references within


7

Figure 2.3: Intensity of σ + (solid line) and σ − (dashed line) as a function of time for an excitation power of 4 mW. The inset in the graph shows the optical polarization degree of the photoluminescence.

One approach is to inject electrons via a ferromagnetic metal contact into the semiconductor (for theoretical work, see e.g. Aronov and Pikus (1976)) and use another ferromagnetic metal contact to measure the spin dependent voltage drop across the device. In this setup, a spin polarization of the charge carriers comes from the different conductivities due to the difference in the density of states (DOS) for the two spin directions in the metal layer. The conductance of the full device depends on the relative magnetization of the contacts as the DOS in the 2DEG is constant and equal for spin up and spin down states when no magnetic field is applied. Nevertheless, the spin polarization measured in samples like these is small due to fundamental obstacles (Schmidt et al., 2000). In a simple model, describing the different spinchannels as resistors (see fig2.4) Schmidt et al. proved, that spin polarization can only be measured when the magnetization of the contacts is essentially 100%. The


8

Figure 2.4: Resistor Model for the two spin channels. R1,3 stand for the FM contacts; their spin state is indicated by arrows. Rsc represents the semiconductor layer. The resistance of both spin channels are equal as a 2DEG is considered. Taken from (Schmidt et al., 2000).

spin-polarization degree (SPD) in one of the layers αi (x) ≡

ji↑ (x) − ji↓ (x) , ji↑ (x) + ji↓ (x)

(2.2)

where ji↑,↓ (x) are the current densities in the i-th layer with either spin-up or spindown. For parallel magnetization of the ferromagnetic contacts (β1 = β3 = β, defined by 2.2), the finite spin-polarization in the semiconductor can be calculated under the condition of charge conservation as α2 = β

λf m σsc 2 λ σ sc f m σf m x0 (2 + 1) − β 2 x 0 σf m

(2.3)

where λf m is the spin-flip length in the ferromagnetic layer, σsc,f m are the conductivities of the respective layers and x0 is the layer thickness of the semiconductor. The polarization degree is independent of x, as the spin-flip length is assumed to be much larger than the size of the device3 . Theoretically, the maximum obtainable value for the spin polarization in the semiconductor is β. But this can only be achieved 3

This can be assumed in GaAs as spin-flip length of about 100µm have been reported (Kikkawa

and Awschalom, 1998).


9

Figure 2.5: Schematics of spin-alignment with a diluted magnetic semiconductor, from (Oestreich et al., 1999)

if

σsc σf m

→ ∞, x0 → 0 and λf m → ∞, which is far away from practical situations.

Especially bad is the conductivity mismatch between the ferromagnetic contacts and the semiconductor. A typical value for σsc /σf m = 10−4 is given by Schmidt et al. and thus, the spin polarization degree in the semiconductor layer can only reach 10−3 %. For any useful applications utilizing the spin degree of freedom, this spin polarization degree is far too low! Ideally, the spin-aligner is a semiconducting material that exhibits large spinsplitting at room temperature at very low magnetic fields. The problem in most semiconducting materials is that the intrinsic g-factors are too small to achieve a large enough spin splitting of the states at experimentally reasonable magnetic fields. A new type of material, the so-called diluted magnetic semiconductors (DMS, examined in more detail in chapter 2.2) exhibit large band g-factors due to introduced additional magnetic moments. A schematic diagram showing how DMS can be used as the spin-aligning material has been given by Oestreich et al. (see fig. 2.5). The current is introduced by a metal contact into the DMS and further driven by a bias


10

Figure 2.6: Sample structure and band offsets of the GaAs spin-injection experiment. Spin-polarized electrons are injected from the left (BeMnZnSe spin aligner) and unpolarized holes from the right. The schematic depicts the forward bias only. No band bending is drawn. (Fiederling et al., 1999)

voltage into a non magnetic semiconductor. Up to today, this material class still needs low temperatures and relatively high magnetic fields to yield a satisfying spinpolarization degree. These are impractical for building devices for normal use (at room temperature), but useful materials to make test structures, helping to understand the physics behind spin-injection. Fiederling et al. (1999) used an arrangement utilizing a DMS to inject a spinpolarized current in a AlGaAs/GaAs quantum-well structure. This experiment was the first to use optical detection of spin-injection in GaAs and can be viewed as the predecessor to our spin-injection measurements. Figure 2.6 shows the sample structure and the band alignment of the experiment. As a spin-aliger Fiederling et al. used a layer of the diluted magnetic semiconductor BeMnZeSe. The spin-aligned electrons are injected into the AlGaAs layer and diffuse further to the GaAs QW.


11

Figure 2.7: Allowed interband transitions in GaAs.the total angular momentum electron quantum number mj is indicated. The numbers 3 and 1 next to the arrows denote the relative strength of the transition.

They maintain most of their spin alignment and thus the circular polarization of light emitted from the quantum-well can be used to measure (at least approximately) the spin injected from the AlGaAs layer. The long spin-lifetime in GaAs, as well as the small band g-factors, make it relatively easy to determine the spin polarization degree in the GaAs QW from the optical polarization degree. In figure 2.7 the allowed optical interband transitions are shown and their relative intensity due to the relative strength of the transition matrix elements are indicated. Fiederling et al. determined the spin polarization degree from the optical polarization degree with the 3:1 rule and by assuming that the valence band states were degenerate because of the small HH-LH splitting4 . For a similar structure, but with stronger confinement, Jonker and Petrou (Jonker et al., 2000) calculated a HH/LH-band splitting at 4.2 K of about 5 meV such that the light hole states are not occupied and the transitions contributing to the optical polarization degree are dominantly the heavy hole like ones (see fig. 2.8(b)). 4

in the order of kB T at 4.2 K


12

Figure 2.8: Intraband transitions in GaAs for degenerate (a) and non degenerate (b) valence band levels, after (Jonker et al., 2000).

2.2

Diluted Magnetic Semiconductors

In this section I briefly describe the physics that leads to spin alignment in the diluted magnetic semiconductors (DMS). Semiconducting alloys whose lattice is made up in part of magnetic atoms subsidiary for the cation or anion are called diluted magnetic semiconductors or semi magnetic semiconductors. As the variety of these materials is large, I base this discussion on Cd1−x M nx Se, the material used in the samples presented in this work. VI alloy, in which the fraction x of the group Cd1−x M nx Se is a type AII 1−x M nx B

II sublattice atoms is replaced by Mn. An advantage of this particular type of DMS is its ternary nature. In principle, it is possible to tune all the parameters characterizing the crystal and its electronic structure in the range between AMn and MnB


13

by adjusting the composition of the compound. In that way, DMS can be grown lattice-matched to III-V semiconductors to reduce strain effects. In the presented case, we are interested in the large magnetic effects occuring in DMS. They are due to the exchange interaction between the sp-hybridized band electrons of the ternary alloy and the half filled 3d5 shell of the M n2+ ions. If a magnetic field is applied, the conduction and valence bands split into Landau levels, each Landau level being further split into sub levels corresponding to the spin orientation of the electron. The additional magnetic moment coming from the 3d5 electrons of the localized M n2+ ions modifies the Landau levels depending on the magnitude of the exchange interaction. In general, the total Hamiltonian HT can be written as HT = HL + Hex = HL +

X

~ i )Sî · σ J(~r − R ˆ,

(2.4)

i

~ i ) is the exchange coupling constant where HL describes the Landau levels, J(~r − R and Sî and σ ˆ are the spin operators of the M n2+ and the band electrons, respectively. ~ i that are occupied with M n2+ ions. The sum goes over all lattice sites R Two approximations can be made to simplify Hex . They both come from the fact that the electrons in the conduction and in the valence band can be described by extended Bloch functions, which are so large in extent in terms of the size of unit cells of the crystal that the electron always ”sees” a large number of M n2+ ions. Applying this so called ”mean field approximation”, one can replace Sî in equation 2.4 by the thermal average along the magnetic field direction hSz i = Sef f B 5 { 2

5gM n µB B }, 2k(T + Tef f )

(2.5)

where Sef f is the effective spin saturation. The magnitude of Sef f depends on the Mn concentration; Sef f = S0 =

5 2

for low Mn concentrations and |Sef f |