Basic semiconductor physics

723 Pages·2017·28.666 MB·English

by  Chihiro Hamaguchi

Graduate Texts in Physics
Chihiro Hamaguchi
Basic
Semiconductor
Physics
Third Edition
Graduate Texts in Physics
Series editors
Kurt H. Becker, Polytechnic School of Engineering, Brooklyn, USA
Jean-Marc Di Meglio, Université Paris Diderot, Paris, France
Sadri Hassani, Illinois State University, Normal, USA
Bill Munro, NTT Basic Research Laboratories, Kanagawa, Japan
Richard Needs, University of Cambridge, Cambridge, UK
William T. Rhodes, Georgia Institute of Technology, Boca Raton, USA
Susan Scott, Australian National University, Acton, Australia
H. Eugene Stanley, Boston University, Boston, USA
Martin Stutzmann, TU München, Garching, Germany
Andreas Wipf, Friedrich-Schiller-Universität Jena, Jena, Germany
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Chihiro Hamaguchi
Basic Semiconductor Physics
Third Edition
123
Chihiro Hamaguchi
Osaka University
Suita,Osaka
Japan
ISSN 1868-4513 ISSN 1868-4521 (electronic)
Graduate Textsin Physics
ISBN978-3-319-66859-8 ISBN978-3-319-66860-4 (eBook)
DOI 10.1007/978-3-319-66860-4
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Preface to the Third Edition
The first edition of Basic Semiconductor Physics was published in 2001 and the
second edition in 2010. After the publication of the first edition, many typo-
graphical errors have been pointed out and the corrected version was published in
2006. The publisher and my friends persuade me to revise the book adding new
chapters,keepingthesubjectattheappropriatelevel.WhenIstartedwritingthefirst
edition, I decided not to include the physics of semiconductor devices such as p-n
junction diode, bipolar transistor, and metal oxide semiconductor field-effect tran-
sistor (MOSFET). This decision is kept in the new (third) edition.
Although many books on semiconductor physics and technology have been
published,thebasicphysicsofsemiconductorlaserisnotproperlydescribed.When
the readers of my book understand the characteristics of two-dimensional electron
gas and strain effect of semiconductors, they feel easy to understand double
heterostructurelasersandstrainedquantumwelllasers,butitiseasieriftheystudy
some more detailed discussion on the laser action. Another subject is physics of
low-dimensional semiconductors. Basic Semiconductor Physics, second edition,
deals with two-dimensional electron gas and zero dimensional or quantum dot
structure. The physics of quantum dot includes very important physics of artificial
atoms and gives a good information of few electron systems. These subjects are
included in the second edition published in 2010. Some new topics are also
included in the second edition such as electron motion in an external field dis-
cussing the derivation of effective mass (Sect. 3.5), the physics of quantum dots
(Sect. 8.8), and new Chap. 9 devoted to the discussion on the physics of semi-
conductor laser, where Einstein coefficients A and B, spontaneous and stimulated
emission, luminescence, double heterostructure, and quantum well lasers are dis-
cussed.Thestraineffectofthequantumwelllaserisdescribedindetailbecauseitis
well known that the effect is very important to understand the modes (TE and TM
modes) of quantum well laser oscillations.
v
vi PrefacetotheThirdEdition
This new edition (third edition) is revised in various aspects of semiconductor
physics as described below.
1. This third edition deals very in detail with the most important subjects of
semiconductor physics such as the energy band calculations, transport of car-
riers,andsemiconductorlasers.InChap.1,energybandcalculationsofvarious
semiconductors with spin-orbit interaction are discussed in the full band zone
using the local pseudopotential method, nonlocal pseudopotential method, and
k (cid:1) pperturbationmethod.Oncethereadersunderstandthemethods,numerical
calculationsarestraightforwardbecauseallthematrixelementsaregiveninthis
textbook.
2. Spin-orbit interactionplays an important role intheelectronic states, especially
the valence band splitting. The effect is described in Appendix and the matrix
elements of the spin-orbit interaction are properly included in the energy band
calculations.
3. In Chap. 6, we present the numerical calculations of relaxation times and
mobilities limited by the scattering processes as a function of electron energy
and temperature, including scatterings by various kinds of phonons (lattice
vibrations), impurity density, electron density, and so on. In addition, deter-
mination of the deformation potentials is discussed by comparing the calcula-
tionswiththeexperimentaldata.Theresultshelpourunderstandingofelectron
transport and help to understand semiconductor device physics.
4. Recently, LED’s and LD’s based on nitrides such as GaN and GaInN are
playing the most important role in the optical devices. However, the energy
bandstructuresofthenitridesarenotwelldetermined.InChap.9,energyband
calculations of the nitrides, GaN, InN, and AlN are discussed by using the
pseudopotentialmethod.Inaddition,newmethodtocalculatetheenergybands
of ternary alloys of nitrides such as GaInN, AlGaN, and AlInN is discussed in
which the bowing of the band gaps is well explained by introducing only one
additional parameter.
5. Entirelynewsetsofabout70problems(exercises)anddetailedtreatmentsofthe
answers are provided for better understanding. In order to avoid misleading,
most of the curves in this book have been carefully computed and plotted.
Calculations use SI units throughout.
Inadditiontothesesubjects,errorsinthesecondeditionarecorrectedproperly.
Especially,actualcalculationsofelectronmobilitiesareveryimportantandprovide
detailed information on the transport in semiconductors. Therefore, calculations
oftherelaxationtimesandmobilitiesduetovariousscatteringprocessesarecarried
out. These results will provide readers to manage calculations of the electron
mobilities in various semiconductors. Also, the physical properties of semicon-
ductors are tabulated in the text.
The author would like to express his special thanks to Professor Nobuya Mori,
Osaka University, for his contribution to the energy band calculations of nitrides
andformanystimulateddiscussionsonthebasicphysics.Theauthoristhankfulto
PrefacetotheThirdEdition vii
his wife Wakiko for her patience during the work of this textbook and also his
parentsMasaruandSaiyeHamaguchifortheirsupporttohishighereducation.The
author expresses his gratitude to Professor Dr. Klaus von Klitzing for inviting him
to Max Planck Institute, Stuttgart, to finish the full band k (cid:1) p perturbation theory,
providinghimachancetodiscussthissubjectwithProfessorDr.ManuelCardona.
Finally, we want to thank Dr. Claus E. Ascheron and the staff of the Springer
Verlagfortheirhelpandforthevaluablesuggestionsforclarificationofthisbook.
Osaka, Japan Chihiro Hamaguchi
March 2017
Preface to the Second Edition
WhenthefirsteditionofBasicSemiconductorPhysicswaspublishedin2001,there
were already many books, review papers, and scientific journals dealing with
various aspects of semiconductor physics. Since many of them were dealing with
specialaspectsofnewlyobservedphenomenaorwithveryfundamentalphysics,it
was very difficult to understand the advanced physics of semiconductors without
the detailed knowledge of semiconductor physics. For this purpose, the author
published the first edition for the readers who are involved with semiconductor
research and development. Basic Semiconductor Physics deals with details of
energy band structures, effective mass equation, and k (cid:1) p perturbation, and then
describes very important phenomena in semiconductors such as optical, transport,
magnetoresistance,andquantumphenomena.Someofmyfriendswrotetomethat
thetextbookisnotonlybasic butadvanced, andthat thetitle ofthebook doesnot
reflect the contents. However, I am still convinced that the title is appropriate
because the advanced physics of semiconductor may be understood with the
knowledgeofthefundamentalphysics.Inaddition,newandadvancedphenomena
observed in semiconductors at an early time are becoming well known and thus
classified in basic physics.
After the publication of the first edition, many typographical errors have been
pointedoutandthecorrectedversionwaspublishedin2006.Thepublisherandmy
friendspersuademetorevisethebookaddingnewchapters,keepingthesubjectat
the appropriate level. When I started writing the first edition, I decided not to
include physics of semiconductor devices such as p-n junction diode, bipolar
transistor,andmetaloxidesemiconductorfield-effecttransistor(MOSFET).Thisis
becausethelargenumbersofbooksdealingwiththesubjectsareavailableandabig
or bulky volume is not accepted by readers. On the other hand, many researchers
are involved with optoelectronic devices such as LED (Light Emitting Diode) and
LD (Laser Diode) because memory devices such as DVD and blue ray disks are
becoming important for writing and reading memory devices. In such devices,
semiconductor laser diodes areused.Inaddition,thecommunication system based
ontheopticalfiberplaysaveryimportantroleinnetwork,wherelaserdiodeisthe
key device. Although many books on semiconductor physics and technology have
ix
x PrefacetotheSecondEdition
beenpublished,thebasicphysicsofsemiconductorlaserisnotproperlydescribed.
When the readers of my book understand the characteristics of two-dimensional
electrongasandstraineffectofsemiconductors,theyfeeleasytounderstanddouble
heterostructurelasersandstrainedquantumwelllasers,butitiseasieriftheystudy
some more detailed discussion on the laser action. Another subject is physics of
low-dimensional semiconductors. Basic Semiconductor Physics deals with
two-dimensional electron gasbutzero-dimensional orquantumdotstructure isnot
included. The physics of quantum dot includes very important physics of artificial
atoms, and gives a good information offew electron systems.
In this revised version I included three main topics. The first one is Sect. 3.5,
where electron motion in an external field is discussed with the derivation of
effective mass. The most important relation for transport equation is the velocity
(groupvelocity)ofanelectroninaperiodiccrystal.Inthissection,theexpectation
value of the velocity operator is evaluated and shown to be proportional to the
gradient of the electron energy with respect to the wave vector. Then the classical
motionofequationisprovedtobevalidforanelectroninacrystalwhenweusethe
effective mass. InSect. 8.8 thephysicsofquantumdots isdiscussed inconnection
with the charging energy (addition energy) required to add an extra electron in a
quantumdot.ThetreatmentisveryimportanttounderstandCoulombinteractionof
many electron system. In this section the exact diagonalization method based on
Slaterdeterminantsisdiscussedindetail.Chapter9isdevotedtothediscussionon
the physics of semiconductor laser, where Einstein coefficients A and B, sponta-
neousandstimulatedemission,luminescence,doubleheterostructure,andquantum
welllasersarediscussed.Thestraineffectofthequantumwelllaserisdescribedin
detail because it is well known that the effect is very important to understand the
modes (TE and TM modes) of quantum well laser oscillations.
IwouldliketoexpressmyspecialthankstoProfessorNobuyaMoriforhelping
me to clarify the subject and providing me his calculated results used in Chap. 9,
and also to my colleagues at Sharp Corporation with whom I have had many
stimulateddiscussionsonthebasicphysicsofsemiconductorlasers.Itwasverysad
thatProfessorTatsuyaEzakiofHiroshimaUniversitydiedveryrecently,whomade
the detailed analysis of quantum dot physics for his Ph.D thesis (see Sect. 8.8).
Finally, I want to thank Dr. Claus E. Ascheron and the staff of the Springer
Verlagfortheirhelpandforthevaluablesuggestionsforclarificationofthisbook.
Osaka Chihiro Hamaguchi
September 2009