Inelastic Light Scattering of Semiconductor Nanostructures: Fundamentals and Recent Advances

181 Pages·2006·7.97 MB·English

by  Christian Schüller (auth.)

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Christian Schüller
Inelastic Light Scattering
of Semiconductor
Nanostructures
Fundamentals and Recent Advances
With105Figures
ABC
ChristianSchüller
PhysikII
InstitutfürExperimentelle
undAngewandtePhysik
UniversitätRegensburg
Universitätsstr.31
93053Regensburg
Germany
Email:[email protected]
LibraryofCongressControlNumber:2006930613
PhysicsandAstronomyClassificationScheme(PACS):
78.30.-j,68.65.-k,73.21-b,78.67.-n,81.07.-b
ISSNprintedition:0081-3869
ISSNelectronicedition:1615-0430
ISBN-10 3-540-36525-7SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-36525-9SpringerBerlinHeidelbergNewYork
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To Claudia, Sarah, Alina,
and my dear father, Hans Schu¨ller,
who passed away during
preparation of this book.
Preface
Semiconductornanostructuresarecurrentlyoneofthelargestandmostexcit-
ingareasinsolidstatephysics.Low-dimensionalelectronsystems(realizedin
semiconductor quantum structures) are particularly appealing because they
allowonetostudymany-particleeffectsinreduceddimensions.Inelasticlight
scattering gives direct access to the elementary excitations of those systems.
Afteranoverviewofthebasicconceptsandfabricationtechniquesfornanos-
tructures on an introductory level, and an introduction into the method of
inelastic light scattering, this monograph presents a collection of recent ad-
vances in the investigation of electronic elementary excitations in semicon-
ductor nanostructures. Experiments on quantum wells, quantum wires, and
quasiatomicstructures,realizedinquantumdots,arediscussed.Theoriesare
presented to explain the experimental results. Special chapters are also de-
voted to recent developments concerning tunneling – coupled systems and
nanostructures embedded inside semiconductor microcavities. I have tried
to make the chapters as self-containing as possible so that readers who are
already familiar with the basics can directly read selected chapters.
With this book I have tried to fill the gap between research articles and
contributed book chapters on special topics of the field on one hand, and
morestandardsemiconductortextbooks(whichcoveramuchbroaderrange)
on the other hand. The book should therefore be interesting for experimen-
talists,theorists,andresearchstudentsworkinginthefieldofsemiconductor
nanostructures,aswellasforgraduatestudentswithknowledgeinsolidstate
physics and quantum mechanics.
Most of the experimental and theoretical results presented in this book
comprise a good part of the research that we have done at the Institute of
Applied Physics and Microstructure Research Center of the University of
Hamburgduringthepastdecade.Thisworkwasonlypossibleduetothecol-
laboration with many excellent Diploma and Ph.D students. It is with plea-
sure that I thank Dr. Gernot Biese, Katharina Keller, Dr. Roman Krahne,
Dr. Edzard Ulrichs, Dr. Lucia Rolf, Dr. Tobias Kipp, Dr. Maik-Thomas
Bootsmann, Thomas Brocke, Gerwin Chilla, and Dr. Annelene Dethlefsen
for an excellent and enjoyable collaboration in the Raman laboratory. Spe-
cial thanks go to Professor Dirk Grundler and Professor Can-Ming Hu, my
fellow postdocs in the Hamburg group, for many inspiring discussions. Very
VIII Preface
special thanks, however, go to Professor Detlef Heitmann, my mentor dur-
ingmytimeinHamburg.Amongallmyscientificteachers,hehadbyfarthe
greatestimpactonmyscientificlifeandcareer.Ourworkimmenselybenefited
from his enthusiasm and deep knowledge and I appreciate the many lively
discussions which took place in a very friendly and convenient atmosphere.
Regensburg Christian Schu¨ller
May 2006
Contents
1 Introduction.............................................. 1
References ................................................. 4
Part I Basic Concepts
2 Fundamentals of Semiconductors and Nanostructures..... 9
2.1 III-V Semiconductors: Crystal and Band Structure ......... 9
2.1.1 Phenomenology .................................. 9
2.1.2 k∗p Theory...................................... 13
2.2 Electrons in Three, Two, One, and Zero Dimensions ........ 16
2.3 Layered Growth of Semiconductors: Vertical Nanostructures . 18
2.3.1 Molecular–Beam Epitaxy (MBE) ................... 19
2.4 Electronic Ground State of Vertical Nanostructures ......... 22
2.4.1 Envelope Function Approximation (EFA)............ 22
2.4.2 Self–Consistent Band Structure Calculation.......... 25
2.5 Lateral Micro- and Nanostructures ....................... 30
2.5.1 General Remarks................................. 30
2.5.2 Lithography and Etching .......................... 31
2.5.3 Self–Assembled Quantum Dots..................... 35
2.6 Electronic Ground State of Lateral Nanostructures ......... 37
References ................................................. 38
3 Electronic Elementary Excitations ........................ 41
3.1 Single–Particle Continua ................................ 42
3.2 Electron–Density Waves: Phenomenology of Collective
Charge– and Spin–Density Excitations .................... 43
3.3 Collective Excitations: Theoretical Models ................. 48
3.3.1 Basic Ideas of RPA and TDLDA ................... 49
3.3.2 Application to Two–Subband System ............... 50
3.3.3 Plasmon–LO Phonon Coupling .................... 53
References ................................................. 54
X Contents
4 Basic Concepts of Inelastic Light Scattering, Experiments
on Quantum Wells........................................ 57
4.1 Macroscopic Approach .................................. 57
4.1.1 General Remarks................................. 57
4.1.2 Macroscopic Point of View ........................ 59
4.1.3 Dissipation–Fluctuation Analysis ................... 61
4.2 Microscopic Approach, Polarization Selection Rules ......... 62
4.2.1 Two- and Three-Step Scattering Processes .......... 62
4.2.2 Scattering Cross Section: General Considerations .... 68
4.2.3 Scattering by Crystal Electrons:
Polarization Selection Rules ....................... 71
4.2.4 Parity Selection Rules in Nanostructures ............ 75
4.2.5 Intrasubband Excitations, Grating Coupler–Assisted
Scattering ....................................... 76
4.2.6 Multiple Cyclotron Resonance Excitations
in Quantum Wells ............................... 79
References ................................................. 83
Part II Recent Advances
5 Quantum Dots: Spectroscopy of Artificial Atoms ......... 87
5.1 Introduction ........................................... 87
5.2 Semiconductor Quantum Dots ........................... 90
5.2.1 Preparation of Quantum Dots...................... 90
5.2.2 Electronic Ground State and Excitations ............ 91
5.3 GaAs–AlGaAs Deep-Etched Quantum Dots................ 95
5.3.1 Parity Selection Rules in Quantum Dots............. 96
5.3.2 Fine Structure in Quantum Dots ................... 98
5.3.3 The Important Role of Extreme Resonance .......... 104
5.3.4 Calculations for Few-Electron Quantum Dots ........ 109
5.4 InAs Self-Assembled Quantum Dots ...................... 112
5.4.1 Few–Electron Quantum–Dot Atoms ................ 112
5.4.2 Electronic Excitations in InAs SAQD ............... 113
5.4.3 Comparison with Exact Calculations................ 114
References ................................................. 118
6 Quantum Wires: Interacting Quantum Liquids ........... 121
6.1 Introduction ........................................... 121
6.2 Electronic Elementary Excitations in Quantum Wires ....... 122
6.2.1 Ground State and Excitations ..................... 122
6.2.2 Experimental Spectra and Wave–Vector Dependence.. 125
6.3 Confined and Propagating 1D Plasmons in a Magnetic Field 130
6.3.1 Microscopic Picture for Confined Plasmons .......... 130
6.3.2 Coupling with Bernstein Modes .................... 134
Contents XI
6.4 Towards the Tomonaga–Luttinger Liquid? ................. 138
References ................................................. 142
7 Tunneling–Coupled Systems ............................. 145
7.1 Introduction ........................................... 145
7.2 Charge–Density Excitation Spectrum in Tunneling–Coupled
Double Quantum Wells.................................. 146
7.3 Experiments on Tunable GaAs–AlGaAs Double Quantum
Wells ................................................. 150
7.4 Vertically–Coupled Quantum Wires....................... 153
References ................................................. 158
8 Inelastic Light Scattering in Microcavities ............... 161
8.1 Introduction ........................................... 161
8.2 2DES Inside a Semiconductor Microcavity ................. 162
8.3 Optical Double–Resonance Experiments ................... 163
References ................................................. 168
Part III Appendix
Kronecker Products of Dipole Matrix Elements I ............ 171
Kronecker Products of Dipole Matrix Elements II ........... 173
Index......................................................... 175