Graduate Texts in Physics

Graduate Texts in Physics

Graduate Texts in Physics publishes core learning/teaching material for graduate- andadvanced-level undergraduate courses on topics of current and emerging fields withinphysics, both pure and applied. These textbooks serve students at the MS- or PhD-level andtheir instructors as comprehensive sources of principles, definitions, derivations, experi-ments and applications (as relevant) for their mastery and teaching, respectively. Interna-tional in scope and relevance, the textbooks correspond to course syllabi sufficiently to serveas required reading. Their didactic style, comprehensiveness and coverage of fundamentalmaterial also make them suitable as introductions or references for scientists entering, orrequiring timely knowledge of, a research field.

Series Editors

Professor William T. RhodesFlorida Atlantic UniversityDepartment of Computer and Electrical Engineering and Computer ScienceImaging Science and Technology Center777 Glades Road SE, Room 456Boca Raton, FL 33431, USAE-mail: wrhodes@fau.edu

Professor H. Eugene StanleyBoston UniversityCenter for Polymer StudiesDepartment of Physics590 Commonwealth Avenue, Room 204BBoston, MA 02215, USAE-mail: hes@bu.edu

Professor Richard NeedsCavendish LaboratoryJJ Thomson AvenueCambridge CB3 0HE, UKE-mail: rn11@cam.ac.uk

Please view available titles in Graduate Texts in Physics on series homepagehttp://www.springer.com/series/8431/

123

Claus F. Klingshirn

Fourth Edition

With 369 Figures and 18 Tables

OpticsSemiconductor

Professor Claus F. Klingshirnü ü

KarlsruheGermany

Karlsruher Institut für Technologie (KIT)

recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission

dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part

or information storage and retrieval, electronic adaptation, computer software, or by similar or

Springer-Verlag Berlin Heidelberg 1995 , 2005 , 2007, 2012

ISSN 1868-4521 (electronic)ISBN 978-3-642-28362-8 (eBook)

ISSN 1868-4513

DOI 10.1007/978-3-642-28362-8Springer Heidelberg New York Dordrecht London

of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,

Springer-Verlag Heidelberg.

ISBN 978-3-642-28361-1

Chapter 25 was taken from Londolt-Börnstein, Group III, Volume 34/Subvolume C1: “Semi- conductor Quantum Structures -- Optical Properties” (edited by C. Klingshirn), 2001,

©

Institut fü r Angewandte Physik

Library of Congress Control Number: 2012940411

To my parents(�), my wife and our children

•

Wahrheit und Klarheit sind komplementar.E. MOLLWO

This aphorism was coined in the 1950s by E. MOLLWO, Professor of Physics at theInstitut fur Angewandte Physik of the Universitat Erlangen during a discussion withW. HEISENBERG. The author hopes that, with respect to his book, the deviationsfrom exact scientific truth (Wahrheit) and perfect understandability (Klarheit) are ina reasonable balance.

Just as an illustration of the above statement, the attention of the author hasbeen drawn to the fact, that the same statement has been reported even in Germanlanguage also from NIELS BOHR. See Steven Weinberg, Dreams of a Final Theory,Vintage Books, New York (1994) p. 74.

A slightly different view on this problem can be gained by comparing thefollowing two statements:

There are more things in heaven and on earth, Horatio, than are dreamt of in yourphilosophy

(William Shakespeare, Hamlet, Act 1, Scene 5)

Ein etwas vorschnippischer Philosoph, ich glaube, Hamlet, Prinz von Danemark,hat gesagt, es gabe eine Menge Dinge im Himmel und auf der Erde, wovon nichtsin unseren Kompendien (Lehrbucher, textbooks; Anm. des Autors) stande. Hatder einfaltige Mensch, der bekanntlich nicht recht bei Troste war, damit auf dieKompendien der Physik gestichelt, so kann man ihm getrost antworten: Gut, dafurstehen auch wieder eine Menge von Dingen in unseren Kompendien, wovon wederim Himmel noch auf der Erde etwas vorkommt.

(Georg Christoph Lichtenberg, Sudelbucher)

•

Preface to the Fourth Edition

The third edition of “Semiconductor Optics” and a reprint of it for the Chinesemarket, which appeared both in 2007, were again very well received by studentsand the scientific community world wide.

As a consequence, this fourth edition became necessary. In many of its chaptersthere are only minor changes and amendments. On the other hand, importantprogress in this field of research and development made significant updates andamendments in other chapters necessary. Some prominent examples are listedbelow:

• The progress in the field of Bose-Einstein condensation, especially of cavitypolaritons, resulted in a significantly up-dated and enlarged Sect. 20.5.

• The ongoing discussion on the value of the Mott density in an electron-hole plasma addressed already in the third edition resulted in modifications ofChap. 21.

• Random lasing in semiconductors is now treated in some detail in Chap. 22.• The research boom on ZnO with more than 2,000 publications per year lasts now

already for several years. Consequently we present more examples for the opticalproperties of this semiconductor in various sections. This includes also a moredetailed discussion on how the band gap can be deduced form absorption spectrain Sect. 13.1.

• Photonic crystals and meta-materials tend to develop more and more away fromsemiconductor physics. The same holds partly for THz sources and spectroscopy.Therefore the corresponding sections are up-dated essentially only by addingsome new references. Similar arguments hold also for optical computing and forspintronics.

• Finally the author tried again, to reduce the number of misprints, to removeunclear formulations etc. In this context he thanks all readers, who drew hisattention on such points.

I conclude this preface with a personal statement. I retired in spring 2010.Though I liked my profession as professor over the last almost 30 years verymuch, especially research and teaching, I decided not to continue after retirement

ix

x Preface to the Fourth Edition

to do essentially what I did before (as many other colleagues do), but to abandongradually science and to accept in my pension age new challenges, mainly in fieldsof social activities. These activities deem to me more reasonable and rewardingthan to increase the number of my publications from more than 450 (from whichscientific data bases find generally about 380, which are cited more than 5,800times) by another 10 or 20. Consequently, this edition of “Semiconductor Optics”will be the last one written and edited by myself. In this sense it is together withsome other books and review articles cited in the following chapters my scientificlegacy. I hope that students and colleagues will enjoy seeing this book.

Karlsruhe C.F. KlingshirnMay 2012

Preface to the Third Edition

The second edition, which appeared in 2005 and contains substantial up-datesand amendments compared to the first one and its corrected reprints, was againfavourably received by the students and the scientific community worldwide.

As a consequence, the present third edition became necessary. The changesintroduced are, compared to the second edition, more limited, among others becausethe time elapsed between second and third edition is much shorter than the timebetween first and second one.

The main chances concern the following points: The discussion about the density,at which an electron-hole plasma is formed, has been up-dated, in the section aboutphotonic crystals a few comments on meta-materials have been added, several newand timely references have been included and some of the misprints have beenremoved.

Karlsruhe C.F. KlingshirnAugust 2006

xi

•

Preface to the Second Edition

The book on Semiconductor Optics has been favourably received by the studentsand the scientific community worldwide. After the first edition, which appeared in1995 several reprints became necessary starting from 1997, one of them for theChinese market. They contained only rather limited updates of the material andcorrections.

In the meantime scientific progress brought a lot of new results, which necessitatea new, seriously revised edition. This progress includes bulk semiconductors,but especially structures of reduced dimensionality. These new trends and resultsare partly included in existing chapters e.g. for phonons or for time-resolvedspectroscopy, partly new chapters have been introduced like the ones on cavitypolaritons and photonic structures.

We based the description of the optical properties again on the simple andintuitively clear model of the Lorentz-oscillators and the concept of polaritonsas the quanta of light in matter. But since there is presently a trend to describeat least the optical properties of the electronic system of semiconductors by theoptical or the semiconductor Bloch equations, a chapter has been added on thistopic written by Prof. Dr. R. v. Baltz (Karlsruhe) to familiarize the reader with thisconcept, too, which needs a bit more quantum mechanics compared the approachused here. The chapter on group theory has been revised by Prof.Dr. K. Hummer(Karlsruhe/Forchheim)

Karlsruhe C.F. KlingshirnSeptember 2004

xiii

•

Preface to the First Edition

One of the most prominent senses of many animals and, of course, of human beingsis sight or vision. As a consequence, all phenomena which are connected with lightand color, or with the optical properties of matter, have been focal points of interestthroughout the history of mankind. Natural light sources such as the Sun, the Moonand stars, or fire, were worshipped as gods or goddesses in many ancient religions.Fire, which gives light and heat, was for many centuries thought to be one of the fourelements – together with earth, water, and air. In alchemy, which marks the dawn ofour modern science, the Sun and the Moon appeared as symbols of gold and silver,respectively, and many people tried to produce these metals artificially. Some timelater, Johann Wolfgang von Goethe (1749–1832) considered his “Farbenlehre” asmore important than his poetry. In the last two centuries a considerable fraction ofmodern science has been devoted to the investigation and understanding of lightand the optical properties of matter. Many scientists all over the world have addedto our understanding of this topic. As representatives of the many we should liketo mention here only a few of them: I. Newton (1643–1727), J.C. Maxwell (1831–1879), M. Planck (1858–1947), A. Einstein (1879–1955), N. Bohr (1885–1962),and W. Heisenberg (1901–1976).

The aim of this book is more modest. It seeks to elucidate one of the numerousaspects in the field of light and the optical properties of matter, namely the inter-action of light with semiconductors, i.e., semiconductor optics. The investigationof the properties of semiconductors has, in turn, its own history, which has beensummarized recently by H.J. Queisser [85Q1]. In Queisser’s book one can find earlyexamples of semiconductor optics, namely the observation of artificially createdluminescence by V. Cascariolo in Bologna at the beginning of the seventeenthcentury, or by K.F. Braun (1850–1918), inventor of the “Braun’sche Rohre” (Braun’stube) now usually called CRT (cathode ray tube), at the beginning of this century.

Another root of semiconductor optics comes from the investigation of the opticalproperties of insulators, especially of the color (Farb- or F-) centers in alkali halides.This story has been written down recently by J. Teichmann [88T1]. It is inseparablyconnected with names such as Sir Nelville Mott and A. Smakula, but especially withR.W. Pohl (1884–1976) and his school in Gottingen.

xv

xvi Preface to the First Edition

Together with J. Franck (1882–1964) and M. Born (1882–1970) R.W. Pohl wasone of the outstanding physicists of the “golden years of physics” at Gottingenbefore 1933 [77B1, 84M1, 88H1]. The present author considers himself a scientificgrandson of Pohl, with E. Mollwo (1909–1993), F. Stockmann (1918–1998) andW. Martienssen (*1926) as the intermediate generation, and he owes to them a largepart of his scientific education.

Scientific interest in semiconductor optics comprises both fundamental andapplied research. It has been an extremely lively, rapidly developing area of researchfor the last five decades and more, as can be seen from the contributions to theseries of International Conferences on the Physics of Semiconductors [50I1] andon Luminescence [81I1] or on Non-linear Optics and Excitation Kinetics [87N1].It does not need much of a prophetic gift to predict that semiconductor optics willcontinue to be a major topic of solid state physics far into the next century. Manyapplications of semiconductor optics are known from everyday life such as light-emitting diodes (LED) in displays, laser diodes in compact-disk (CD) players, laserprinters and laser scanners or solar cells.

Karlsruhe C.F. KlingshirnFebruary 1995

References (up-dated)

[50I1] The Series of International Conferences on the Physics of Semiconductors (ICPS) wasstarted in 1950 in Reading. Proceedings of the more recent ones are

a. M.H. Pilkuhn (ed.), 12th ICPS, Stuttgart, 1974 (Teubner, Stuttgart, 1974)b. F.G. Fumi (ed.), 13th ICPS, Rome, 1976 (Tipographia Marves, Rome, 1976)c. B.L.H. Wilson (ed.), 14th ICPS, Edinburgh, 1978 (The Institute of Physics, Bristol,

1979)d. S. Tanaka, Y. Toyozawa (ed.), 15th ICPS, Kyoto, 1980; J. Phys. Soc. Jpn. 49(Suppl.

A), (1980)e. M. Averous (ed.), 16th ICPS, Montpellier, 1982. Physica B, vols. 117+118 (North-

Holland, Amsterdam, 1983)f. J.M. Chadi, W.A. Harrison (ed.), 17th ICPS, San Francisco, 1984 (Springer,

Berlin/Heidelberg, 1984)g. O. Engstrom (ed.), 18th ICPS, Stockholm, 1986 (World Scientific, Singapore, 1987)h. W. Zawadzki (ed.), 19th ICPS, Warsaw, 1988 (The Institute of Physics, Polish

Academy of Sciences, Warsaw, 1988)i. E.M. Anastassakis, J.D. Joannopoulos (ed.), 20th ICPS, Thessaloniki, 1990 (World

Scientific, Singapore, 1990)j. P. Jiang, H.-Z. Zheng (ed.), 21st ICPS, Beijing, 1992 (World Scientific, Singapore,

1993)k. D.J. Loockwood (ed.), 22nd ICPS, Vancouver, 1994 (World Scientific, Singapore,

1995)l. M. Scheffler, R. Zimmermann (eds.), 23rd ICPS, Berlin, 1996 (World Scientific,

Singapore, 1996)m. D. Gershoni (ed.), 24th ICPS, Jerusalem, 1998 (World Scientific, Singapore, 1999)

References (up-dated) xvii

n. N. Miura, T. Ando (eds.), 25th ICPS, Osaka, 2000. Springer Proceedings in Physics,vol. 87 (Springer, Berlin, 2001)

o. A.R. Long, J.H. Davies (eds.), 26th ICPS, Edinburgh, 2002. Institute of PhysicsConference Series, vol. 171 (IOP Publishing, Bristol, 2003)

p. J. Menendez, Ch. Van de Walle (eds.), 27th ICPS, Flagstaff, 2004. AIP ConferenceProceedings, vol. 772 (American Institute of Physics, Melville, 2005)

q. W. Jantsch, F.Schaffler (eds.), 28th ICPS, Vienna, 2006. AIP Conference Proceedings,vol. 893 (American Institute of Physics, Melville, 2007)

r. M.J. Caldas, N. Studart (eds.), 29th ICPS, Rio de Janero, 2008. AIP ConferenceProceedings, vol. 1199 (American Institute of Physics, Melville, 2010)

s. Z. Ihm, H. Cheong (eds.), 30th ICPS, Seoul, 2010. AIP Conf. Proc. vol 1399(American Institute of Physics, Melville 2012)

t. 31th ICPS, Zurich (2012), to be published by AIP

[77B1] A.D. Beyerchen, Scientists Under Hitler (Yale University Press, New Haven, 1977)[81I1] The proceedings of the Series of Internationl Conferences of Luminescence (ICL) are

published in J. Lumin. The more recent ones were

a. I. Broser, H.-E. Gumlich, R. Broser (eds.), ICL, Berlin, 1981. Journal of Luminescence,vol. 24/25 (North-Holland, Amsterdam, 1981)

b. W.M. Yen, J.C. Wright (eds.), ICL, Madison, 1984. Journal of Luminescence, vol.31/32 (North-Holland, Amsterdam, 1984)

c. X. Xurong (ed.), ICL, Beijing, 1987. Journal of Luminescence, vol. 40/41 (North-Holland, Amsterdam, 1987)

d. S.J. Formosinho, M.D. Sturge (eds.), ICL, Lisbon, 1990. Journal of Luminescence, vol.48/49 (North-Holland, Amsterdam, 1990)

e. D.S. Hamilton, R.S. Meltzer, M.D. Sturge (eds.), ICL, Storrs, 1993. Journal ofLuminescence, vol. 60/61 (North-Holland, Amsterdam, 1995)

f. J. Hala, P. Reinecker (eds.), ICL, Prague, 1996. Journal of Luminescence, vols. 72–74(Elsevier, Amsterdam, 1997)

g. K. Cho (ed.), ICL, Osaka, 1999. Journal of Luminescence, vols. 87–89 (North-Holland,Amsterdam, 2000)

h. S. Speiser (ed.), ICL, Budapest, 2002. Journal of Luminescence, vols. 102–103(Elsevier, Amsterdam, 2003)

i. S. Huang, Z. He, X. Wanf, H. Zhang (eds.), ICL, Beijing, 2005. Journal of Lumines-cence, vols. 122–133 (Elsevier, Amsterdam, 2007)

j. G. Boulon (ed.), ICL, Lyon, 2008. Journal of Luminescence, vol. 129 (Elsevier,Amsterdam, 2009)

k. Proc. 16th ICL Ann Arbor, 2011 (in press)

[84M1] E. Mollwo, Phys. unserer Z. 15, 110 (1984)[85Q1] H.-J. Queisser, Kristallene Krisen (Piper, Munchen, 1985)[87N1] The Series of International conferences/workshops on Nonlinear Optics and Excitation

Kinetics ( NOEKS ) has been started in the former German Democratic Republic (DDR)and continued successfully after the reunification of Germany. The proceedings have so farbeen published in

a. NOEKS I, Bad Stuer, November 1987. Physica Status Solidi (b), vols. 146, 147(Akademie-Verlag, Berlin, 1988)

b. NOEKS II, Bad Stuer, December 1989, Physica Status Solidi (b), vol. 159(1)(Akademie-Verlag, Berlin, 1990)

c. NOEKS III, Bad Honnef, May 1992, Physica Status Solidi (b), vol. 173(1) (Akademie-Verlag, Berlin, 1992)

d. NOEKS IV, Gosen, November 1994, Physica Status Solidi (b), vol. 188(1) (Akademie-Verlag, Berlin, 1995)

xviii Preface to the First Edition

e. NOEKS V, Graal-Muritz, September 1997, Physica Status Solidi (b), vol. 206(1)(Wiley, Chichester, 1998)

f. NOEKS VI, Marburg, April 2000, Physica Status Solidi (b), vol. 221(1) (Wiley,Chichester, 2000)

g. NOEKS VII, Karlsruhe, February 2003, Physica Status Solidi (c), vol.0(5) (Wiley,Chichester, 2003)

h. NOEKS VIII, Munster, February 2006, Physica Status Solidi (c), vol. 3(7) (Wiley,Weinheim, 2006)

i. NOEKS IX, Klink-Muritz, May 2008, Physica Status Solidi C, vol. 6(2) (Wiley,Weinheim, 2009)

j. NOEKS X, Paderborn, August 2010, Physica Status Solidi C, vol. 8(4) (Wiley,Weinheim, 2011)

[88H1] F. Hund, H. Maier-Leibnitz, E. Mollwo, Eur. J. Phys. 9, 188 (1988)[88T1] J. Teichmann, Zur Geschichte der Festkorperphysik-Farbzentrenforschung bis 1940

(Steiner, Wiesbaden, 1988)

Acknowledgements

This book is based on various lectures given by the author at the Universitiesof Karlsruhe (now Karlsruher Institut fur Technologie (KIT)), Frankfurt am Mainand Kaiserslautern, at Harvard University and the University of Metz and oncontributions given at several of the Summer Schools on Atomic and MolecularSpectroscopy organised by Prof. Dr. B. Di Bartolo in Erice, Sicily.

The sources of the scientific information presented here are partly the referencesgiven. Of equal importance, however, is the physics, which I learned from myacademic teachers during my studies and PhD work at the University of Erlangen,my post-doc time at the Laboratoire de Spectroscopie et d’Optique du CorpsSoilide in Strasbourg and my Habilitation at the University of Karlsruhe, andlater on from fruitful discussions with many colleagues and co-workers at theplaces where I was or still am as Professor (Frankfurt am Main, Kaiserslauternand Karlsruhe) and abroad including guest scientists in my group. Without tryingto be complete, I should like to mention my academic teachers Profs. Drs.R. Fleischmann (�), H. Volz (�), E. Mollwo (�), R. Helbig(�) and K. Hummer(Erlangen) and F. Stockmann (�), W. Ruppel and W. Stoßel (Karlsruhe).

From the colleagues I should like to mention with great pleasure fruitful and stim-ulating discussions e.g. with Profs. Drs. H. Haug, W. Martienssen(�), E. Mohler andL. Banyai (Frankfurt am Main), J.B. Grun, B. Honerlage and R. Levy (Strasbourg),B. Stebe (Metz), U. Rossler (Regensburg), E. Gobel, S.W. Koch, S. Schmitt-Rink (�)and P. Thomas (Marburg), J.M. Hvam (Lyngby), D.S. Chemla(�) (Berkeley),K.P. O’Donnel (Glasgow), E. Mazur (Cambridge), I. Bar-Joseph and R. Reisfeld(Israel), I. Broser, R. Zimmermann and F. Henneberger (Berlin), H. Stolz andK. Henneberger (Rostock), A. Reznitsky, A. Klochikhin and S. Permogorov(St. Petersburg), V. Lyssenko (Chernogolovka), O. Gogolin and E. Tsitisishvili(Tiblissi), M. Brodyn and S. Shevel (�) (Kiev), S. Gaponenko and S. Apanasevich(Minsk), H. Kalt, M. Wegener, R. v. Baltz and K. Busch (Karlsruhe), U. Woggon(Berlin), H. Giessen (Stuttgart) and last but not least B. Di Bartolo (Boston), also forrunning the school in Erice and the special and comfortable atmosphere he createsthere for all participants.

xix

xx Acknowledgements

My special thanks are due to all my former and present students and co-workers,who produced their Diploma, PhD or Habilitation thesis in my research groupand many of the fine results presented in this book and who partly hold in themeantime professorships or equivalent positions of their own (H. Kalt (Karlsruhe),M. Wegener (Karlsruhe), U. Woggon (Berlin). H. Giessen (Stuttgart), M. Kuball(Bristol), S. Petillon (Landau) and W. Langbein (Cardiff)). Beyond that I do not wantto give names here, because they are too many and I am afraid to forget somebody.

In this context the financial support for my research is gratefully acknowl-edged especially from the Deutsche Forschungsgemeinschaft, the Lander Hessen,Rheinland-Pfalz and Baden-Wurttemberg, the Stiftung Volkswagenwerk, the Bun-desministerium fur Bildung und Forschung (BMBF) and the European Community.

A lot of thanks also to all, who tried to solve “the final problem” on p. 782 of thesecond edition. Without trying to be complete, I should like to mention my colleagueProf. Dr. R. v. Baltz and my diploma student M. Hauser in Karlsruhe.

Last but not least, I should like to thank the Publishing House Springer and thereespecially Dr. Th. Schneider for the excellent cooperation in the production of thisnew edition.

Karlsruhe, Claus F. KlingshirnMay 2012

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Aims and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Outline of the Book and a Lot of References . . . . . . . . . . . . . . . . . . . . . . . 21.3 Some Personal Thoughts .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Maxwell’s Equations, Photons and the Density of States . . . . . . . . . . . . . . 112.1 Maxwell’s Equations .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Electromagnetic Radiation in Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Electromagnetic Radiation in Matter; Linear Optics . . . . . . . . . . . . . . . 182.4 Transverse, Longitudinal and Surface Waves . . . . . . . . . . . . . . . . . . . . . . . 222.5 Photons and Some Aspects of Quantum Mechanics

and of Dispersion Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6 Density of States and Occupation Probabilities. . . . . . . . . . . . . . . . . . . . . 282.7 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3 Interaction of Light with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.1 Macroscopic Aspects for Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.1 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.1.2 Laws of Reflection and Refraction. . . . . . . . . . . . . . . . . . . . . . . . . 423.1.3 Noether’s Theorem and Some Aspects of

Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.1.4 Reflection and Transmission at an Interface

and Fresnel’s Formulae .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.1.5 Extinction and Absorption of Light. . . . . . . . . . . . . . . . . . . . . . . . 503.1.6 Transmission Through a Slab of Matter and

Fabry Perot Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.1.7 Birefringence and Dichroism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.1.8 Optical Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

xxi

xxii Contents

3.2 Microscopic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.1 Absorption, Stimulated and Spontaneous

Emission, Virtual Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.2 Perturbative Treatment of the Linear

Interaction of Light with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.3 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4 Ensemble of Uncoupled Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.1 Equations of Motion and the Dielectric Function.. . . . . . . . . . . . . . . . . . 784.2 Corrections Due to Quantum Mechanics and Local Fields . . . . . . . . 814.3 Spectra of the Dielectric Function and of the Complex

Index of Refraction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.4 The Spectra of Reflection and Transmission . . . . . . . . . . . . . . . . . . . . . . . . 894.5 Interaction of Close Lying Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.6 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5 The Concept of Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.1 Polaritons as New Quasiparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.2 Dispersion Relation of Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.3 Polaritons in Solids, Liquids and Gases and From the

IR to the X-ray Region .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.3.1 Common Optical Properties of Polaritons .. . . . . . . . . . . . . . . . 1055.3.2 How the k-vector Develops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.4 Coupled Oscillators and Polaritons with Spatial Dispersion .. . . . . . 1135.4.1 Dielectric Function and the Polariton States

with Spatial Dispersion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.4.2 Reflection and Transmission and Additional

Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.5 Real and Imaginary Parts of Wave Vector and Frequency.. . . . . . . . . 1225.6 Surface Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.7 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6 Kramers–Kronig Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.1 General Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.2 Problem .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7 Crystals, Lattices, Lattice Vibrations and Phonons . . . . . . . . . . . . . . . . . . . . 1357.1 Adiabatic Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.2 Lattices and Crystal Structures in Real and Reciprocal Space . . . . . 1377.3 Vibrations of a String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.4 Linear Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1447.5 Three-Dimensional Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Contents xxiii

7.6 Quantization of Lattice Vibrations:Phonons and the Concept of Quasiparticles. . . . . . . . . . . . . . . . . . . . . . . . . 151

7.7 The Density of States and Phonon Statistics . . . . . . . . . . . . . . . . . . . . . . . . 1557.8 Phonons in Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1587.9 Defects and Localized Phonon Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1597.10 Phonons in Superlattices and in Other Structures

of Reduced Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1617.11 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8 Electrons in a Periodic Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1678.1 Bloch’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1688.2 Metals, Semiconductors, Insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1718.3 An Overview of Semiconducting Materials . . . . . . . . . . . . . . . . . . . . . . . . . 1748.4 Electrons and Holes in Crystals as New Quasiparticles . . . . . . . . . . . . 1788.5 The Effective-Mass Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1808.6 The Polaron Concept and Other Electron–Phonon

Interaction Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1848.7 Some Basic Approaches to Band Structure Calculations. . . . . . . . . . . 1878.8 Bandstructures of Real Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1968.9 Density of States, Occupation Probability and Critical Points . . . . . 2038.10 Electrons and Holes in Quantum Wells and Superlattices. . . . . . . . . . 2078.11 Growth of Quantum Wells and of Superlattices . . . . . . . . . . . . . . . . . . . . 2178.12 Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2228.13 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2248.14 Defects, Defect States and Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2288.15 Disordered Systems and Localization .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2338.16 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

9 Excitons, Biexcitons and Trions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2499.1 Wannier and Frenkel Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2509.2 Corrections to the Simple Exciton Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2559.3 The Influence of Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2589.4 Biexcitons and Trions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2639.5 Bound Exciton Complexes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2649.6 Excitons in Disordered Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2659.7 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

10 Plasmons, Magnons and Some Further Elementary Excitations . . . . . . 27310.1 Plasmons, Pair Excitations and Plasmon–Phonon

Mixed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27310.2 Magnons and Magnetic Polarons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27910.3 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

xxiv Contents

11 Optical Properties of Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28311.1 Phonons in Bulk Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

11.1.1 Reflection Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28311.1.2 Raman Scattering .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28511.1.3 Phonon Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28811.1.4 Brillouin Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29011.1.5 Surface Phonon Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29011.1.6 Phonons in Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29211.1.7 Defects and Localized Phonon Modes. . . . . . . . . . . . . . . . . . . . . 293

11.2 Phonons in Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29311.2.1 Backfolded Acoustic Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29411.2.2 Confined Optic Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29411.2.3 Interface Phonons.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

11.3 Phonons in Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29711.4 Phonon Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29711.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

12 Optical Properties of Plasmons, Plasmon–Phonon MixedStates and of Magnons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30112.1 Surface Plasmons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30112.2 Plasmon–Phonon Mixed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30312.3 Plasmons in Systems of Reduced Dimensionality . . . . . . . . . . . . . . . . . . 30412.4 Optical Properties of Magnons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30612.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

13 Optical Properties of Intrinsic Excitons in Bulk Semiconductors. . . . . 30913.1 Excitons with Strong Oscillator Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

13.1.1 Exciton–Photon Coupling .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31013.1.2 Consequences of Spatial Dispersion . . . . . . . . . . . . . . . . . . . . . . . 31313.1.3 Spectra of Reflection, Transmission and

Luminescence .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31413.1.4 Spectroscopy in Momentum Space . . . . . . . . . . . . . . . . . . . . . . . . 33113.1.5 Surface-Exciton Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33813.1.6 Excitons in Organic Semiconductors and in Insulators . . . 33913.1.7 Optical Transitions Above the Fundamental

Gap and Core Excitons .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34213.2 Forbidden Exciton Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

13.2.1 Direct Gap Semiconductors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34713.2.2 Indirect Gap Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

13.3 Intraexcitonic Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35513.4 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

Contents xxv

14 Optical Properties of Bound and Localized Excitons andof Defect States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36314.1 Bound-Exciton and Multi-exciton Complexes . . . . . . . . . . . . . . . . . . . . . . 36314.2 Donor–Acceptor Pairs and Related Transitions .. . . . . . . . . . . . . . . . . . . . 37114.3 Internal Transitions and Deep Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37314.4 Excitons in Disordered Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37514.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

15 Optical Properties of Excitons in Structures of ReducedDimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38315.1 Qantum Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38315.2 Coupled Quantum Wells and Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . 39315.3 Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40015.4 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40315.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

16 Excitons Under the Influence of External Fields . . . . . . . . . . . . . . . . . . . . . . . . 42316.1 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

16.1.1 Nonmagnetic Bulk Semiconductors . . . . . . . . . . . . . . . . . . . . . . . 42616.1.2 Diluted Magnetic Bulk Semiconductors.. . . . . . . . . . . . . . . . . . 43216.1.3 Semiconductor Structures of Reduced Dimensionality . . . 43416.1.4 Spin Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

16.2 Electric Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43916.2.1 Bulk Semiconductors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43916.2.2 Semiconductor Structures of Reduced Dimensionality . . . 441

16.3 Strain Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44516.3.1 Bulk Semiconductors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44516.3.2 Structures of Reduced Dimensionality . . . . . . . . . . . . . . . . . . . . 448

16.4 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

17 From Cavity Polaritons to Photonic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 45717.1 Cavity Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

17.1.1 The Empty Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45717.1.2 Cavity Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

17.2 Photonic Crystals and Photonic Band Gap Structures . . . . . . . . . . . . . . 46417.2.1 Introduction to the Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . 46517.2.2 Realization of Photonic Crystals and Applications . . . . . . . 469

17.3 Photonic Atoms, Molecules and Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 47217.4 Present and Further Developments of Photonic Crystals . . . . . . . . . . . 47617.5 A Few Words about Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47717.6 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

xxvi Contents

18 Review of the Linear Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48518.1 Review of the Linear Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48518.2 Problem .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

19 High Excitation Effects and Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 49119.1 Introduction and Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49119.2 General Scenario for High Excitation Effects. . . . . . . . . . . . . . . . . . . . . . . 50019.3 Beyond the �.n/ Approximations .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50319.4 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505

20 The Intermediate Density Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50720.1 Two-Photon Absorption by Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50720.2 Elastic and Inelastic Scattering Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 50820.3 Biexcitons and Trions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

20.3.1 Bulk Semiconductors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51320.3.2 Structures of Reduced Dimensionality . . . . . . . . . . . . . . . . . . . . 522

20.4 Optical or ac Stark Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52820.5 Excitonic Bose–Einstein Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

20.5.1 Basic Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53220.5.2 Attempts to Find BEC in Bulk Semiconductors . . . . . . . . . . 53420.5.3 Structures of Reduced Dimensionality . . . . . . . . . . . . . . . . . . . . 53920.5.4 Driven Excitonic Bose–Einstein

Condensations and Some Further Systems . . . . . . . . . . . . . . . . 54720.6 Photo-thermal Optical Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54920.7 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

21 The Electron-Hole Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56121.1 The Mott Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56121.2 Band Gap Renormalization and Phase Diagram .. . . . . . . . . . . . . . . . . . . 56721.3 Electron-Hole Plasmas in Bulk Semiconductors . . . . . . . . . . . . . . . . . . . 574

21.3.1 Indirect Gap Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57421.3.2 Electron-Hole Plasmas in Direct-Gap Semiconductors .. . 577

21.4 Electron-Hole Plasma in Structures of ReducedDimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

21.5 Inter-subband Transitions in Unipolar and Bipolar Plasmas . . . . . . . 59021.5.1 Bulk Semiconductors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59121.5.2 Structures of Reduced Dimensionality . . . . . . . . . . . . . . . . . . . . 592

21.6 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

22 Stimulated Emission and Laser Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59922.1 Excitonic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60022.2 Electron–Hole Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60822.3 Cavity Lasing .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

Contents xxvii

22.4 Random Lasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61122.5 Basic Concepts of Laser Diodes and Present

Research Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61222.6 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

23 Time Resolved Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62323.1 The Basic Time Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62423.2 Decoherence and Phase Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630

23.2.1 Determination of the Phase Relaxation Times . . . . . . . . . . . . 63023.2.2 Quantum Coherence, Coherent Control

and Non-Markovian Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66323.3 Intra-Subband and Inter-Subband Relaxation . . . . . . . . . . . . . . . . . . . . . . . 672

23.3.1 Formation Times of Various Collective Excitations . . . . . . 67223.3.2 Intraband and Inter-Subband Relaxation . . . . . . . . . . . . . . . . . . 67423.3.3 Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

23.4 Interband Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68023.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691

24 Optical Bistability, Optical Computing, Spintronicsand Quantum Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70124.1 Optical Bistability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

24.1.1 Basic Concepts and Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 70224.1.2 Dispersive Optical Bistability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70324.1.3 Optical Bistability Due to Bleaching . . . . . . . . . . . . . . . . . . . . . . 70624.1.4 Induced Absorptive Bistability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70824.1.5 Electro-Optic Bistability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71124.1.6 Nonlinear Dynamics .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713

24.2 Device Ideas, Digital Optical Computingand Why It Failed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720

24.3 Spintronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72424.4 Quantum Computing .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72424.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726

25 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73125.1 Linear Optical Spectroscopy .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732

25.1.1 Equipment for Linear Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 73325.1.2 Techniques and Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735

25.2 Nonlinear Optical Spectroscopy .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74025.2.1 Equipment for Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 74125.2.2 Experimental Techniques and Results . . . . . . . . . . . . . . . . . . . . . 744

25.3 Time-Resolved Spectroscopy .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75325.3.1 Equipment for Time-Resolved Spectroscopy . . . . . . . . . . . . . 75325.3.2 Experimental Techniques and Results . . . . . . . . . . . . . . . . . . . . . 757

xxviii Contents

25.4 Spatially Resolved Spectroscopy .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76225.4.1 Equipment for Spatially Resolved Spectroscopy . . . . . . . . . 76225.4.2 Experimental Techniques and Results . . . . . . . . . . . . . . . . . . . . . 765

25.5 Spectroscopy Under the Influence of External Fields . . . . . . . . . . . . . . 76725.5.1 Equipment for Spectroscopy Under the

Influence of External Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76825.5.2 Experimental Techniques and Results . . . . . . . . . . . . . . . . . . . . . 769

25.6 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772

26 Group Theory in Semiconductor Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77926.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77926.2 Some Aspects of Abstract Group Theory for Crystals . . . . . . . . . . . . . 780

26.2.1 Some Abstract Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78126.2.2 Classification of the Group Elements . . . . . . . . . . . . . . . . . . . . . . 78126.2.3 Isomorphism and Homomorphism of Groups .. . . . . . . . . . . . 78226.2.4 Some Examples of Groups .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782

26.3 Theory of Representations and of Characters . . . . . . . . . . . . . . . . . . . . . . . 78726.4 Hamilton Operator and Group Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79226.5 Applications to Semiconductors Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79426.6 Some Selected Group Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80426.7 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812

27 Semiconductor Bloch Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81327.1 Dynamics of a Two-Level System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814

27.1.1 Wave-Function Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81527.1.2 Polarization and Inversion as State Variables . . . . . . . . . . . . . 81727.1.3 Pseudo-spin Formulation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81827.1.4 Linear Response of a Two Level System .. . . . . . . . . . . . . . . . . 820

27.2 Optical Bloch Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82127.2.1 Interband Susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822

27.3 Semiconductor Bloch Equations.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82327.3.1 Excitons .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824

27.4 Some Selected Coherent Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82627.4.1 Pump-Probe .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82727.4.2 Four-Wave Mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82827.4.3 Photon Echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828

27.5 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833

The Final Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837