Table Of ContentQUANTUM PHYSICS OF SEMICONDUCTOR MATERIALS
AND DEVICES
Quantum Physics of Semiconductor Materials
and Devices
D. Jena
CornellUniversity
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”IamoneofthosewhothinklikeNobel,thathumanitywilldrawmoregood
thanevilfromnewdiscoveries.”–MarieCurie
”Noproblemcanbesolvedfromthesamelevelofconsciousnessthatcreated
it. Wemustlearntoviewtheworldanew.”–AlbertEinstein
”Oneshouldntworkonsemiconductors,thatisafilthymess;whoknows
whetheranysemiconductorsexist”–WolfgangPauli
”Iamthinkingofsomethingmuchmoreimportantthanbombs. Iam
thinkingaboutcomputers”–JohnvonNeumann
”Itisfrequentlysaidthathavingamore-or-lessspecificpracticalgoalin
mindwilldegradethequalityofresearch. Idonotbelievethatthisis
necessarilythecaseandtomakemypointinthislectureIhavechosenmy
examplesofthenewphysicsofsemiconductorsfromresearchprojectswhich
wereverydefinitelymotivatedbypracticalconsiderations...”–William
Shockley,NobelLecture(1956)
”Somepeoplecandoonethingmagnificently,likeMichelangelo. Others
makethingslikesemiconductors,orbuild747airplanes-thattypeofwork
requireslegionsofpeople. Inordertodothingswell,thatcan’tbedoneby
oneperson,youmustfindextraordinarypeople”–SteveJobs
Preface
Semiconductorelectronicsrequiresforitsfoundationprimarilywavemechan-
icsandstatistics. However,crystallography,thermodynamics,andchemistry
also have a share in it and, quite generally, “it is incredible what miserable
quantities of thought and mathematics are needed to provide even the sim-
plest tools for daily use in semiconductor physics”.–Eberhard Spenke and
WalterSchottky
Several excellent books and monographs have been written about
the physics of semiconductors and nanostructures. I could not resist
reproducingtheaboveparagraphfromanearlyclassic,Spenke’sElec-
tronic Semiconductors written in 1958. Till today, each author of books
on this subject struggles with the same pedagogical challenge that pi-
oneers such as Spenke and Shockley faced in writing the first books
onthistopicinthe1950s,whenthefieldwasinitsinfancy.
Consider the simplest physical processes that occur in semiconduc-
tors: electronorholetransportinbandsandoverbarriers, collisionof
electrons with the atoms in the crystal, or when electrons and holes
annihilate each other to produce a photon. The correct explanation of
these processes require a quantum mechanical treatment. Any short-
cuts lead to misconceptions that can take years to dispel, and some-
timesbecomeroadblockstowardsadeeperunderstandingandappre-
ciation of the richness of the subject. A typical introductory course
on semiconductor physics would then require prerequisites of quan-
tummechanics,statisticalphysicsandthermodynamics,materialssci-
ence,andelectromagnetism. Rarelywouldastudenthaveallthisback-
groundwhen(s)hetakesacourseofthisnatureinmostuniversities.
Whathaschangedsince1950s? Semiconductordeviceshavebecome
indispensable, and integral in our daily lives. The shift towards a
semiconductor electronics and photonics-powered information econ-
omy occurred near the turn of the century. This was not the case
when the early books on semiconductor physics were written. The
connectionofthephysicstotoday’sinformationsystemssuchastran-
sistors for logic, memory, and signal amplification, and light-emitting
diodes and lasers for lighting and communications makes the subject
far more tangible and alive than an abstract one. Practitioners of the
science, technology, and art of semiconductor physics and devices are
the ”quantum mechanics” of our age in the true sense of the word.
They reside in several leading industries, research laboratories, and
universities, and are changing the world, one bit (or photon!) at a
time.
viii Preface
The quantum physics of semiconductors is not abstract, but mea-
suredroutinelyascurrentsandvoltagesindiodesandtransistors,and
seen as optical spectra of semiconductor lasers. The glow of semi-
conductor quantum well light emitting diodes in our rooms and cell
phone screens puts the power and utility of understanding the quan-
tumphysicsofsemiconductorsandnanostructuresondisplayrightin
front of our very eyes. Asher Peres captured this philosophy beauti-
fullyinhisquote:
”Quantum Phenomena do not occur in a Hilbert space. They occur in a
laboratory.”–AsherPeres
This philosophy accurately reflects the approach I have taken in
writing this book. Semiconductor physics is a laboratory to learn and
discover the concepts of quantum mechanics and thermodynamics,
condensed matter physics, and materials science, and the payoffs are
almostimmediateintheformofusefulsemiconductordevices. Ihave
had the opportunity to work on both sides of the fence – on the fun-
damental materials science and quantum physics of semiconductors,
andintheirapplicationsinsemiconductorelectronicandphotonicde-
vices. Drawingfromthisexperience,Ihavemadeaneffortinthisbook
tomakeeachtopicastangibleaspossible. Theconceptsaredeveloped
from their experimental roots, with historical trails, personalities, and
stories where possible, to reflect the subject as a human adventure.
Themathematicalstructureisthendevelopedtoexplainexperimental
observations,andthenpredictnewphenomenaanddevices. Ibelieve
this is a unique approach towards a book on this subject, one that
distinguishesitfromothersinthefield.
Thebookisaimedatthirdandfourthyearundergraduatestudents,
and graduate students in Electrical Engineering, Materials Sciences
andEngineering,AppliedPhysics,Physics,andMechanicalandChem-
icalEngineeringdepartmentsthatoffersemiconductorrelatedcourses.
It will be of interest to scientists and engineers in the industry, and in
variousresearchlaboratories. Thebookisdividedintofourmodules.
Module I, in seven chapters, presents the fundamentals rigorously,
coveringthecoreprinciplesofquantummechanics,statisticalthermo-
dynamics, and the physics of free electrons. The last two chapters of
Module I develop perturbation theory techniques without which one
isoftendisadvantagedinunderstandingsemiconductorphysics.
ModuleII,inninechaptersintroducestheconceptsofbands,gaps,
effectivemasses,andBlochtheory,developsafewmethodstocalculate
andunderstandsemiconductorbandstructures,anddevelopsmethods
tohandlearangeofsemiconductorquantumheterostructures.
Module III starts with the quantum physics of diodes and transis-
tors in the ballistic limit. It then covers several electronic phenomena
on transport and scattering using the Boltzmann transport equation,
andFermiGoldenrulefortransitions. High-fieldtransport,tunneling,
and quantummagnetotransport phenomenaround offthis moduleof
ninechapters.
ix
Module IV focuses on semiconductor photonics, by starting from a
descriptionoftheMaxwellequationsandlight,trackingtheinteraction
ofphotonswithsemiconductors,andculminatinginthedescriptionof
semiconductorheterostructurephotonicdevices.
The chapter-end exercises have been tried and tested as homework
assignments in classes. They considerably amplify the material dis-
cussed in the chapters, and are designed to encourage deep thinking,
purposeful enquiry, and thoughtful discussions. Some problems take
the reader beyond the topics of the respective chapters, into current
areas of research. Some problems connect to other fields such as biol-
ogy, astronomy, high-energy physics, and other fields in which semi-
conductors play an increasingly important role. There is no better
practice to hone one’s skills to achieve mastery over the subject than
tosolveasmanyexercisesastimepermits.
Instructors must plan the usage of the book to fit their goals. The
book has far more material than can (or should) be covered in a 1-
semester course. A typical 1-semester course at Cornell offered for
senior undergraduates and beginning graduate students covers all of
Module I, most chapters of Module II, (Chapters 12 and 13 are as-
signedasprojects),Chapters20-24inModuleIII,andChapters27and
29 of Module IV. To cater to the varying backgrounds of enrolled stu-
dents, more time is spent on Modules I and II. Once the students are
comfortable with the concepts of bands and carrier statistics in semi-
conductorsofModulesIandII,theprogressthroughModulesIIIand
IV can be rapid. I have provided a table and guidance for instructors
andstudentslaterinthisprefaceforpotentialusageofthebook.
No claim to originality is made for most of the presented mate-
rial. Nevertheless, the process of writing for pedagogical purposes
allows for fresh perspectives. Readers may encounter a few uncon-
ventional derivations, or connections made that were not apparent.
Becausemuchofsemiconductorphysicsoriginatedfromatomicquan-
tumtheory,suchexamplesabound,buthavebeen”lostintranslation”
over the past few decades. I have brought them back, as semicon-
ductors are going back to their atomic roots in the new generation of
nanostructured devices. The field is alive and kicking, new semicon-
ductors and phenomena are being discovered, synthesized, and are
being used for applications today. The presentation of the materials
in the book take these advances into fold. If the book gives ideas, or
makes connections for readers that enable them to make new discov-
eries or inventions that outdate the topics discussed here, it will have
exceededitsintendedpedagogicalpurpose.
Colleagues and students I have talked to around the world agree
that there is a place for a stand-alone book to introduce solid state
physicstoelectricalengineers,appliedphysicists,andmaterialsscien-
tistswhoworkonsemiconductors,byusingsemiconductordevicesin
thebackdrop. Itismysincerehopethatthisbookfillsthatvoid.
DebdeepJena
Ithaca,NewYork,March2022.
