ivchenko_bookreg

E.L. Ivchenko

OPTICAL SPECTROSCOPY OF SEMICONDUCTOR NANOSTRUCTURES

SPIN Springer’s internal project number, if known

– Monograph –

April 1, 2004

Springer

Berlin Heidelberg NewYork

Hong Kong London

Milan Paris Tokyo

To Alla and Konstantin

Preface

What is the way to the abode of light?

And where does darkness reside?

Can you take them to their places?

Do you know the paths to their dwellings?

Job 38: 19,20

The present book is an attempt to create an impression of the contemporary optical spectroscopy of semiconductor nanostructures. It reviews new trends and notable progress attained in the field at the beginning of the third millennium. Nearly a decade ago G.E. Pikus and I published the book

Superlattices and Other Heterostructures: Symmetry and Optical Phenomena. It had been written at the time of rapid transformation of research activities in semiconductor physics from bulk materials to systems of low dimensionality. At present nanophysics has become an established area which continues to accelerate and provides a fundamental base for tremendous technological developments. In order to keep pace, I decided to write a completely new book on optics of semiconductor nanostructures.

The new book reflects the success achieved during the recent decade in various optical studies of semiconductor nanostructures. Now the oneand zero-dimensional structures, quantum wires and quantum dots, are presented on an equal footing, alongside of superlattices and two-dimensional systems, heterojunctions and quantum wells. New concepts and phenomena included into consideration are exciton polaritons in resonant Bragg structures and photonic crystals, the strong Rabi splitting in quantum microcavities, trions, micro-photoluminescence of localized excitons in quantum wells, zero-dimensional excitons in quantum dots, giant magneto-optical e ects in semimagnetic nanostructures, interface-induced lateral optical anisotropy, quantum-confined Pockels e ect, chirality e ects in carbon nanotubes, pola- riton-polariton scattering in the microcavities, etc. Moreover, in connection with the increasing interest in spintronics, special attention is paid to spinrelated concepts and spin-dependent phenomena, including the spin splitting of electron and hole subbands, fine structure of excitonic levels, optical orientation of free-carrier spins and exciton angular momenta under interand intraband photoexcitation, sensitivity of the Zeeman spin splitting to the content, size and shape of a nanostructure, spin relaxation mechanisms, spin quantum beats, spin dynamics of exciton polaritons in the microcavities, circular photogalvanic and spin-galvanic e ects in quantum wells. The organization of the book consisting of eight chapters is presented in Sect. 1.4.

Naturally, the present treatment was inspired by the book Symmetry and Strained-Induced E ects in Semiconductors by G.L. Bir and G.E. Pikus as

VIII Preface

well as by my previous book with G.E. Pikus. For me, these three books are aligned in a kind of trilogy. Firstly, this is so because I feel greatly priviledged to belong to the physical school founded by my teacher G.E. Pikus who, together with A.G. Aronov and G.L. Bir, after introducing me to the world of theoretical physics taught, guided and supported me. Secondly, because, in each of the books, both the phenomenological and the microscopical description of physical phenomena is performed with emphasis on the symmetry analysis and the method of invariants, and the power of symmetry considerations is demonstrated.

I gratefully acknowledge that I learned and understood much of what follows due to my close research cooperation with M.M. Glazov, L.E. Golub, S.V. Goupalov, A.V. Kavokin, A.Yu. Kaminskii, A.A. Kiselev, A.I. Nesvizhskii, M.O. Nestoklon, S.A Tarasenko and M.M. Voronov, having grown up within the same school of theoretical physics; they represent the younger generations of physicists. Who knows, maybe some of them will write a book on sophisticated “nano-opto-bio-electronic” systems of the future. Then the trilogy would convert into a tetralogy.

Special thanks goes to my coauthors of the short textbook Optical Properties of Semiconductor Nanostructures by L.E. Vorobjev, E.L. Ivchenko, D.A. Firsov and V.A. Shalygin, published a few years ago in Russian. Perhaps, without that encouraging experience I would never made a decision to write this monograph.

St.-Petersburg	E.L. Ivchenko
February 2004

Contents

1 Kingdom of Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Multilayered Heterostructures: Quantum Wells and

Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Quantum Wires and Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Nanocrystals and Quantum Dot Structures . . . . . . . . . . . . . . . . 9 1.4 Structure of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Quantum Confinement in Low-Dimensional Systems . . . . . . 15 2.1 Charge Carriers in Quantum Wells . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.1 Size-Quantization of Electrons with Simple Parabolic Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.2 Luttinger Hamiltonian. Heavyand Light-Hole

Subbands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.3 E ect of Nonparabolicity on the Confinement Energy . 30 2.2 Electron States in Quantum Wires and Nanotubes . . . . . . . . . . 32 2.2.1 Cylindrical and Rectangular Quantum Wires . . . . . . . . 32 2.2.2 T-shaped Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.3 Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Size Quantization in Quantum Dots . . . . . . . . . . . . . . . . . . . . . . 42 2.3.1 Rectangular and Spherical Quantum Dots . . . . . . . . . . . 42 2.3.2 Parabolic Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3.3 Cone-, Lensand Pyramid-Shaped Quantum Dots . . . . 47

2.4 Spin Splitting of Electron Subbands: Bulkand Structure-Inversion Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.5 Electrons, Photons and Phonons in Superlattices . . . . . . . . . . . 57 2.6 Interband Optical Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.6.1 Transition Probability Rate . . . . . . . . . . . . . . . . . . . . . . . . 66 2.6.2 Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.7 Excitons in Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.7.1 Free Excitons in Bulk Crystals . . . . . . . . . . . . . . . . . . . . . 70 2.7.2 Free Exciton in a Quantum Well . . . . . . . . . . . . . . . . . . . 72 2.7.3 Excitons in Various Nanostructures . . . . . . . . . . . . . . . . . 77 2.7.4 Biexcitons and Trions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.7.5 Dielectric Response of an Exciton . . . . . . . . . . . . . . . . . . 84

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3 Resonant Light Reflection and Transmission . . . . . . . . . . . . . . 87 3.1 Optical Reflection from Quantum Wells and Superlattices . . . 88 3.1.1 Single Quantum Well Structure . . . . . . . . . . . . . . . . . . . . 88 3.1.2 Periodic Quantum Well Structure . . . . . . . . . . . . . . . . . . 101

3.1.3 E ective Dielectric Function of Short-Period Multiple Quantum Wells and Superlattices . . . . . . . . . . . . . . . . . . 104

3.1.4 Resonant Bragg Structures . . . . . . . . . . . . . . . . . . . . . . . . 107 3.1.5 Finite Quantum Well Structure . . . . . . . . . . . . . . . . . . . . 110 3.1.6 Quantum Wells Grown along the Low-Symmetry

Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.1.7 Interface Optical Anisotropy of Heterostructures

without a Common Atom . . . . . . . . . . . . . . . . . . . . . . . . . 120 3.2 Reflection and Di raction of Light from Arrays of Quantum

Wires and Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.2.1 Rayleigh Scattering of Light by a Single Quantum

Wire or Dot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.2.2 Periodic Arrays of Isolated Quantum Dots . . . . . . . . . . . 130 3.2.3 Di raction by a Planar Array of Quantum Dots . . . . . . 133 3.2.4 Two-Dimensional Quantum-Dot Superlattices . . . . . . . . 137 3.3 Electro-Optics of Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . 143 3.3.1 Quantum-Confined Stark E ect . . . . . . . . . . . . . . . . . . . . 144 3.3.2 Stark Ladder in a Superlattice . . . . . . . . . . . . . . . . . . . . . 147 3.3.3 Quantum-Confined Pockels E ect . . . . . . . . . . . . . . . . . . 153

3.4 Magneto-Optics of Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . 159 3.4.1 Magneto-Excitons in Quantum Well Structures . . . . . . . 159 3.4.2 Polarized Reflection Spectra in an External Magnetic

Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 3.4.3 Giant Magneto-Optical E ects in Semimagnetic

Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

4 Intraband Optical Spectroscopy of Nanostructures . . . . . . . . 171 4.1 Intersubband Optical Transitions. Simple Band Structure . . . . 171 4.1.1 Intersubband Light Absorption in a Quantum Well . . . 171 4.1.2 Interminiband Light Absorption in a Superlattice . . . . . 183 4.2 Intersubband Optical Transitions. Complicated Band Structure185

4.3 Intrasubband Optical Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 190 4.3.1 Intrasubband Light Absorption in a Quantum Well . . . 190 4.3.2 Electron Cyclotron Resonance in a Superlattice . . . . . . 193 4.4 Infrared Reflection from Quantum Wells and Superlattices . . . 199

5 Photoluminescence Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 203

5.1 Mechanisms of Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . 203

5.2 Emission Spectra of Localized Excitons . . . . . . . . . . . . . . . . . . . . 205

5.2.1 Stokes Shift of the Low-Temperature

Photoluminescence Peak . . . . . . . . . . . . . . . . . . . . . . . . . . 205

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5.2.2 Nonmonotoneous Behavior of the Stokes Shift with Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

5.2.3 Micro-Photoluminescence Spectroscopy . . . . . . . . . . . . . . 216 5.2.4 Excitons in Quantum Wells Containing Free Carriers . 219 5.3 Optical Spin Orientation of Free Carriers . . . . . . . . . . . . . . . . . . 225 5.3.1 Principles of Optical Orientation . . . . . . . . . . . . . . . . . . . 225 5.3.2 Spin-Relaxation Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 228

5.3.3 E ect of Quantum Confinement on the Electron g

Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 5.3.4 Spin Quantum Beats in Photoluminescence . . . . . . . . . . 246 5.4 Hot Photoluminescence in Quantum-Well Structures . . . . . . . . 248

5.5 Polarized Photoluminescence of Excitons . . . . . . . . . . . . . . . . . . 251 5.5.1 Fine Structure of Exciton Levels in Nanostructures . . . 251 5.5.2 Optical Orientation and Alignment of Free Excitons

in Quantum Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 5.5.3 Optical Orientation and Alignment of Zero-

Dimensional Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 5.5.4 Photoluminescence of Neutral and Charged Quantum

Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 5.6 Interface-Induced Linear Polarization of

Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

6 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 6.1 The Physics of Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 287 6.2 Light Scattering in Bulk Semiconductors . . . . . . . . . . . . . . . . . . 291 6.2.1 Scattering by Free Carriers . . . . . . . . . . . . . . . . . . . . . . . . 291 6.2.2 Scattering by Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 6.3 Scattering by Intersubband and Intrasubband Excitations . . . 300

6.4 Scattering by Folded Acoustic Phonons . . . . . . . . . . . . . . . . . . . . 305 6.5 Scattering by Confined and Interface Optical Phonons . . . . . . 310 6.6 Spin-Flip Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 6.7 Double Resonance in Raman Scattering . . . . . . . . . . . . . . . . . . . 320

7 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

7.1 Two-Photon Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

7.2 Biexcitonic Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

7.3 Degenerate Four-Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

7.4 Second-Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

7.5 Nonlinear Optical Phenomena in Quantum Microcavities . . . . 343

7.5.1 Exciton Polaritons in a Quantum Microcavity . . . . . . . . 343

7.5.2 Four-Wave Mixing in Microcavities . . . . . . . . . . . . . . . . . 351

7.5.3 Angle-Resonant Stimulated Polariton-Polariton

Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

7.5.4 Stimulated Spin Dynamics of Polaritons . . . . . . . . . . . . . 358

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8 Photogalvanic E ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 8.1 Circular Photogalvanic E ect in Quantum Well Structures . . . 362 8.2 Spin-Galvanic E ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 8.3 Photon Drag E ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 8.4 Linear Photogalvanic E ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 8.5 Saturation of Photocurrents at High Light Intensities . . . . . . . 388 8.6 Chirality E ects in Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . 391

8.6.1 Circular Photocurrent in Nanotubes . . . . . . . . . . . . . . . . 392 8.6.2 Magneto-Chiral Currents and Optical Absorption . . . . 394

9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423