M,W,F12:00-12:50(X),2015ECEBProfessorJohnDallesasse

DepartmentofElectricalandComputerEngineering2114MicroandNanotechnologyLaboratory

Tel:(217)333-8416E-mail:jdallesa@illinois.edu

OfficeHours:Wednesday13:00–14:00

Today’sDiscussion

•  DensityCalculations•  MillerIndices•  Symmetry•  Assignments•  TopicsforNextLecture

2

TentativeSchedule[1]

JAN17Courseoverview

JAN19Introtosemiconductorelectronics

JAN22Materialsandcrystalstructures

JAN24Bondingforcesandenergybandsinsolids

JAN26Metals,semiconductors,insulators,electrons,holes

JAN29Intrinsicandextrinsicmaterial

JAN31Distributionfunctionsandcarrierconcentrations

FEB2Distributionfunctionsandcarrierconcentrations

FEB5Temperaturedependence,compensation

FEB7Conductivityandmobility

FEB9Resistance,temperature,impurityconcentration

FEB12InvarianceofFermilevelatequilibrium

FEB14Opticalabsorptionandluminescence

FEB16Generationandrecombination

3 **Subject to Change**

CubicCrystalDensityCalculations

DefineaUnitCell

DeterminetheNumberof

LatticePointsPerUnitCell

CalculatetheMassofEachLatticePoint*

MultiplytheNumberof

LatticePointsperUnitCellbytheMassPerLatticePointandDividebytheUnitCellVolume

*Each lattice point may consist of multiple atoms 5

FCCLattice:HowManyLatticePointsPerUnitCell?

6

HowManyLatticePoints?

7

Example:Silicon

•  Thediamondlatticecanbethoughtofasafacecenteredcubic(fcc)structurewithanadditionalatomplacedat1/4a+1/4b+1/4cfromeachofthefccatoms

•  VolumeDensityofSilicon–  LatticeConst=aSi=5.43Å=5.43x10-8cm–  DiamondStructure

•  4latticepointsperunitcell,2atomsperlatticepoint,so8atoms/unitcell•  8atoms/(aSi)3

•  =5x1022atoms/cm3

–  Atomicweightforsilicon=28.1(gram/mole)–  Avogadro’sNumber=6.02x1023atoms/mole–  DensityofSilicon

•  =5x1022(atoms/cm3)X28.1(grams/mole)X(1mole/6x1023atoms)•  =2.33gram/cm-3

8 atomscm3 × grams

mole× moleatoms

= gramscm3

Example:AlxGa1-xAsDefine a Unit Cell AlGaAs has a zinc blende lattice The unit cell is FCC with 2 atoms per lattice point The lattice spacing is determined using Vegard's Law (linear interpolation): AlxGa1−xAs Lattice Spacing: aAlGaAs = xaAlAs + 1− x( )aGaAs Al0.25Ga0.75As Lattice Spacing: a = (0.25)(5.6605)+ (0.75)(5.6533) = 5.6551 AngstromsDetermine the Number of Lattice Points Per Unit Cell: 4Calculate the Mass of Each Lattice Point

Mass of As: mAsAtom = 74.92gmole

× mole6.02 ×1023atoms

= 1.24 ×10−22 gatom

Mass of Al0.25Ga0.75: 0.25 × 26.986.02 ×1023

⎛⎝⎜

⎞⎠⎟ + 0.75 × 69.72

6.02 ×1023⎛⎝⎜

⎞⎠⎟ = 9.93×10−23

Mass of Each Lattice Point: mLatticePoint = 1.24 ×10−22 + 9.93×10−23 = 2.23×10−22 gLattice Point

Calculate the Density

Density =4 × 2.23×10−22( )g5.6551×10−8cm( )3 = 4.9 g

cm39

OtherMaterials?

•  BinaryZincBlende?•  TernaryZincBlende?•  QuaternaryZincBlende?

–  InAlGaPversusInGaAsP•  Wurtzite?

•  Caution:UseVegard’slawtoestimatepropertiessuchaslatticeconstantonlyifaspecificreferenceisnotavailable

10

OtherDensityConcepts

•  ArealMassDensity:Thedensityofaplaneofmaterial

•  PackingFraction:Volumewithinaunitcelloccupiedbyatomsiftheatomsareassumedtobehardsphereswitharadiusofhalftheatomicspacing– Note:Itisonlyinthecaseofthesimplecubicstructurethatthelatticeconstantisthesameastheatomicspacing

11

DeterminingMillerIndices

Crystallographic Notation (hkl): Plane [hkl]: Vector Normal to Plane {hkl}: Family of Planes <hkl>: Family of Vectors

Method 1.  Determine intercept points 2.  Take reciprocal 3.  Multiply by least common multiple (smallest positive integer divisible by intercepts)

13

ClassExercise

14

DirectionVectors

Key Property: Normal to equivalent plane for cubic lattices 15

PlaneSeparation&DirectionAngles

16

Distance Between Adjacent (h k l) Planes (lattice constant "a"):

d = ah2 + k2 + l2( )1/2

Angle Between Directions [h1 k1 l1] and [h2 k2 l2 ]:

cos θ( ) = h1h2 + k1k2 + l1l2( )h1

2 + k12 + l1

2( )1/2h2

2 + k22 + l2

2( )1/2

UsefulWebsite

•  3-DImaging&RotationofCrystalStructures:–  http://www.neubert.net/Crystals/CRYStruc.htm

17

SymmetryOperations

•  Ifanoperationonthelattice(rotation,translation,inversion,etc.)producesanidenticallattice,itisasymmetryoperation

•  Planesanddirectionsareinthesamefamilyiftheyarerelatedbyasymmetryoperation

•  Simplecubicstructureshavehighsymmetryandmanyrelatedfamiliesofplanes

•  Zincblende(III-V)structureshavelowersymmetry,soplanesthatareinthesamefamilyforacubicstructuremaynotbeinthesamefamilyinazincblendestructure

19

ExamplesofFamiliesofPlanes

•  Theplanes(100),(010),and(001)areallrelatedbyasymmetryoperationforasimplecubiclattice,andarethuspartofthe{100}family

•  Forothercrystalsstructures,(100),(010),and(001)maynotbepartofthe{100}family

20

Crystallographic Notation (hkl): Plane [hkl]: Vector Normal to Plane {hkl}: Family of Planes <hkl>: Family of Vectors

SiliconPurification

Formation of Metalurgical-Grade Silicon (MGS): SiO2 + 2C → Si + 2CO (~1800 C)Purification of MGS (Removal of Al, Fe, heavy metals, etc.): Step 1: Formation of Trichlorosilane (liquid, TBoil = 32 C) Si + 3HCl → SiHCl3 + H2

Step 2: Fractional Distillation Step 3: Conversion of Trichlorosilane to Electronic-Grade Silicon 2SiHCl3 + 2H2 → 2Si + 6HCl

22

BulkGrowth

23

SiliconIngot

24

LatticeMatchedSystemsHeteroepitaxy:Grownmaterialsarelatticematchedbuthavedifferentpropertiesthanthesubstrate

26

StrainedLayers•  PseudomorphicGrowth:Epitaxialgrowthofanonlattice-matchedmaterial

27

Misfit Dislocation

OtherConcepts

•  CriticalThickness:Growththicknessabovewhichmisfitdislocationsareformed

•  StrainedLayerSuperlattice:Astructureofalternatinglayershavingtensileandcompressivestrainsuchthatnetstrainbalanceoccursandmisfitdislocationsarenotformed

28

Assignments

•  Readinfopacket–keycoursepoliciesandscheduleareoutlinedhere,includinghourlyexamdates

•  HomeworkassignedeveryFriday,duefollowingFriday•  BegintoreadChapter1ofStreetman’sbook

–  Mon1/22Sections1.1,1.2,1.3.1,1.4–  IsuggestreadingallofChapter1,butonlytheabovesectionsareassigned

–  Wed1/24:ReviewStreetmanChapter2–  Wed1/24:§'s3.1,3.1.1,3.1.2–  Fri1/26:§'s3.1.3,3.2.1(HW1Due)–  Mon1/29:§'s3.2.3,3.2.4

•  Chapter1&2inPierretcoverssimilarmaterial,andcomplementsStreetmanforanotherperspective

30

Outline,1/26/18

•  EpitaxialGrowthTechnologies•  AtomicBonding

32

InstructionalObjectives(1)BythetimeofexamNo.1(after17lectures),thestudentsshouldbeabletodothefollowing:1.Outlinetheclassificationofsolidsasmetals,semiconductors,andinsulatorsanddistinguishdirectandindirectsemiconductors.2.DeterminerelativemagnitudesoftheeffectivemassofelectronsandholesfromanE(k)diagram.3.Calculatethecarrierconcentrationinintrinsicsemiconductors.4.ApplytheFermi-Diracdistributionfunctiontodeterminetheoccupationofelectronandholestatesinasemiconductor.5.CalculatetheelectronandholeconcentrationsiftheFermilevelisgiven;determinetheFermilevelinasemiconductorifthecarrierconcentrationisgiven.6.Determinethevariationofelectronandholemobilityinasemiconductorwithtemperature,impurityconcentration,andelectricalfield.7.Applytheconceptofcompensationandspacechargeneutralitytocalculatetheelectronandholeconcentrationsincompensatedsemiconductorsamples.8.Determinethecurrentdensityandresistivityfromgivencarrierdensitiesandmobilities.9.Calculatetherecombinationcharacteristicsandexcesscarrierconcentrationsasafunctionoftimeforbothlowlevelandhighlevelinjectionconditionsinasemiconductor.10.Usequasi-Fermilevelstocalculatethenon-equilibriumconcentrationsofelectronsandholesinasemiconductorunderuniformphotoexcitation.11.Calculatethedriftanddiffusioncomponentsofelectronandholecurrents.12.CalculatethediffusioncoefficientsfromgivenvaluesofcarriermobilitythroughtheEinstein’srelationshipanddeterminethebuilt-infieldinanon-uniformlydopedsample.

https://my.ece.illinois.edu/courses/description.asp?ECE340 34

InstructionalObjectives(2)BythetimeofExamNo.2(after32lectures),thestudentsshouldbeabletodoalloftheitemslistedunderA,plusthefollowing:13.Calculatethecontactpotentialofap-njunction.14.Estimatetheactualcarrierconcentrationinthedepletionregionofap-njunctioninequilibrium.15.Calculatethemaximumelectricalfieldinap-njunctioninequilibrium.16.Distinguishbetweenthecurrentconductionmechanismsinforwardandreversebiaseddiodes.17.Calculatetheminorityandmajoritycarriercurrentsinaforwardorreversebiasedp-njunctiondiode.18.Predictthebreakdownvoltageofap+-njunctionanddistinguishwhetheritisduetoavalanchebreakdownorZenertunneling.19.Calculatethechargestoragedelaytimeinswitchingp-njunctiondiodes.20.Calculatethecapacitanceofareversebiasedp-njunctiondiode.21.Calculatethecapacitanceofaforwardbiasedp-njunctiondiode.22.Predictwhetherametal-semiconductorcontactwillbearectifyingcontactoranohmiccontactbasedonthemetalworkfunctionandthesemiconductorelectronaffinityanddoping.23.Calculatetheelectricalfieldandpotentialdropacrosstheneutralregionsofwidebase,forwardbiasedp+-njunctiondiode.24.Calculatethevoltagedropacrossthequasi-neutralbaseofaforwardbiasednarrowbasep+-njunctiondiode.25.Calculatetheexcesscarrierconcentrationsattheboundariesbetweenthespace-chargeregionandtheneutraln-andp-typeregionsofap-njunctionforeitherforwardorreversebias.

https://my.ece.illinois.edu/courses/description.asp?ECE340 35

InstructionalObjectives(3)BythetimeoftheFinalExam,after44classperiods,thestudentsshouldbeabletodoalloftheitemslistedunderAandB,plusthefollowing:26.CalculatetheterminalparametersofaBJTintermsofthematerialpropertiesanddevicestructure.27.Estimatethebasetransportfactor“B”ofaBJTandrank-ordertheinternalcurrentswhichlimitthegainofthetransistor.28.DeterminetherankorderoftheelectricalfieldsinthedifferentregionsofaBJTinforwardactivebias.29.CalculatethethresholdvoltageofanidealMOScapacitor.30.PredicttheC-VcharacteristicsofanMOScapacitor.31.CalculatetheinversionchargeinanMOScapacitorasafunctionofgateanddrainbiasvoltage.32.EstimatethedraincurrentofanMOStransistorabovethresholdforlowdrainvoltage.33.EstimatethedraincurrentofanMOStransistoratpinch-off.34.DistinguishwhetheraMOSFETwithaparticularstructurewilloperateasanenhancementordepletionmodedevice.35.Determinetheshort-circuitcurrentandopen-circuitvoltageforanilluminatedp/njunctionsolarcell.

https://my.ece.illinois.edu/courses/description.asp?ECE340 36

CoursePurpose&Objectives

•  Introducekeyconceptsinsemiconductormaterials

•  Provideabasicunderstandingofp-njunctions

•  Provideabasicunderstandingoflight-emittingdiodesandphotodetectors

•  Provideabasicunderstandingoffieldeffecttransistors

•  Provideabasicunderstandingofbipolarjunctiontransistors

n-type emitter n-type collector

p-type base

ForwardBias

ReverseBias

electron flow

hole flowleakagecurrent

injectedelectrons

injectedholes

37

TentativeSchedule[2]

FEB19Quasi-Fermilevelsandphotoconductivedevices

FEB21Carrierdiffusion

FEB23Built-infields,diffusionandrecombination

Feb26Review,discussion,problems(2/27exam)

FEB28Steadystatecarrierinjection,diffusionlength

MAR2p-njunctionsinequilibrium&contactpotential

MAR5p-njunctionFermilevelsandspacecharge

MAR7Continuep-njunctionspacecharge

MAR9NOCLASS(EOH)

MAR12p-njunctioncurrentflow

MAR14Carrierinjectionandthediodeequation

MAR16Minorityandmajoritycarriercurrents

3/19-3/23SpringBreakMAR26Reverse-biasbreakdown

MAR28Storedcharge,diffusionandjunctioncapacitance

MAR30Photodiodes,I-Vunderillumination

38 **Subject to Change**

TentativeSchedule[3]

APR2LEDsandDiodeLasers

APR4Metal-semiconductorjunctions

APR6MIS-FETs:Basicoperation,idealMOScapacitor

APR9MOScapacitors:flatband&thresholdvoltage

APR11Review,discussion,problems(4/12exam)

APR13MOScapacitors:C-Vanalysis

APR16MOSFETs:Output&transfercharacteristics

APR18MOSFETs:smallsignalanalysis,amps,inverters

APR20Narrow-basediode

APR23BJTfundamentals

APR25BJTspecifics

APR27BJTnormalmodeoperation

APR30BJTcommonemitteramplifierandcurrentgain

MAY2(LASTLECTURE)Review,discussion,problemsolving

FINALEXAM**Date&timetobeannounced**

39 **Subject to Change**

ImportantInformation

•  CourseWebsite:–  http://courses.engr.illinois.edu/ece340/

•  DownloadandReviewSyllabus/CourseInformationfromWebsite!•  CourseCoordinator:Prof.JohnDallesasse

–  jdallesa@illinois.edu–  Coordinatesschedule,policies,absenceissues,homework,quizzes,

exams,etc.•  ContactInformationandOfficeHoursforAllECE340Professors&

TAsinSyllabus•  LectureSlides:Clickon“(Sec.X)”nexttomynameininstructorlist•  DRESStudents:ContactProf.DallesasseASAP•  Textbook:

–  “SolidStateElectronicDevices,”Streetman&Banerjee,7thEdition–  Supplemental:“SemiconductorDeviceFundamentals,”Pierret–  Additionalreferencetextslistedinsyllabus

41

KeyPoints

•  AttendClass!–  3unannouncedquizzes,eachworth5%ofyourgrade–  Youmusttakethequizinyoursection–  Excusedabsencesmustbepre-arrangedwiththecoursedirector–  Absencesforillness,etc.needanotefromtheDean

•  Seepolicyonabsencesinthesyllabus•  NoLateHomework

–  Homeworkdueonthedateofanexcusedabsencemustbeturnedinaheadoftime

–  Youmustturninhomeworkinyoursection–  Noexcusedabsencesforhomeworkassignments–  Top10of11homeworkassignmentsusedincalculationofcoursegrade

•  Doallofthemtobestpreparefortheexams!•  NoCheating

–  Penaltiesaresevereandwillbeenforced•  TurnOffYourPhone

–  Novideorecording,audiorecording,orphotography

42

Homework

•  AssignedFriday,DueFollowingFriday– Duedatesshowninsyllabus

•  DueatStartofClass•  FollowGuidelinesinSyllabus•  PeerDiscussionsRelatedtoHomeworkareAcceptableandEncouraged

•  DirectlyCopyingSomeoneElse’sHomeworkisNotAcceptable– Gradershavebeeninstructedtowatchforevidenceofplagiarism

–  Bothpartieswillreceivea“0”ontheproblemorassignment

43

Absences

•  Theabsencepolicyinthesyllabuswillbestrictlyenforced•  Toreceiveanexcusedabsence(quiz),youmust:

–  Pre-arrangetheabsencewiththecoursedirector(validreasonandproofrequired)

–  CompleteanExcusedAbsenceFormattheUndergraduateCollegeOffice,Room207EngineeringHall(333-0050)

•  Theformmustbesignedbyaphysician,medicalofficial,ortheEmergencyDean(OfficeoftheDeanofStudents)

•  TheDean’sOfficehasrecentlyputastrictpolicyinplace(3documenteddaysofillness)–  Excusedquizscorewillbeproratedbaseduponaverageofcompletedscores–  Noexcusedabsencesaregivenforhomework,butonlythebest10of11are

usedtocalculateyourfinalgrade–  Excusedabsencesarenotgivenforexams,exceptinaccordancewiththe

UIUCStudentCode–  Unexcusedworkwillreceivea“0”

•  Failuretotakethefinalwillresultinan“incomplete”grade(ifexcused)ora“0”(ifunexcused)

44

Exams

•  ExamI:TuesdayFebruary27th,7:30-8:30pm•  ExamII:ThursdayApril12th,7:30-8:30pm•  FinalExam:Date/TimeToBeAnnounced

– DeterminedbyUniversityF&S

45

Grading

GradingCriterion

Homework 10%

Quizzes 15%

HourExamI 20%

HourExamII 20%

FinalExam 35%

Total 100%

HistoricalGradeTrends*

Spring2016

Fall2016

Spring2017

A’s 27% 28% 27%

B’s 37% 26% 38%

C’s 27% 25% 27%

D’s 6% 16% 4%

F’s 3% 5% 4%

*Past performance is not necessarily indicative of future results

46

MyRecommendations

•  Readthesyllabusandinformationpostedonthecoursewebsite

•  Attendclass&participate•  Attendofficehours(TAandProfessors)•  Readthebook•  Re-readthebook•  Lookatandreadselectedportionsofthesupplemental

texts•  Formstudygroupstoreviewconceptsanddiscusshigh-

levelapproachesforsolvinghomeworkproblems–  Don’tformstudygroupstocopyhomeworksolutions

•  Don’tmissanyhomework,quizzes,orexams•  It’shardtoovercomeazero

•  Askquestionsinclass!47