m,w,f 12:00-12:50 (x), 2015 eceb 2114 micro and ......invariance of fermi level at equilibrium feb...
TRANSCRIPT
M,W,F12:00-12:50(X),2015ECEBProfessorJohnDallesasse
DepartmentofElectricalandComputerEngineering2114MicroandNanotechnologyLaboratory
Tel:(217)333-8416E-mail:[email protected]
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
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OtherDensityConcepts
• ArealMassDensity:Thedensityofaplaneofmaterial
• PackingFraction:Volumewithinaunitcelloccupiedbyatomsiftheatomsareassumedtobehardsphereswitharadiusofhalftheatomicspacing– Note:Itisonlyinthecaseofthesimplecubicstructurethatthelatticeconstantisthesameastheatomicspacing
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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
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DirectionVectors
Key Property: Normal to equivalent plane for cubic lattices 15
PlaneSeparation&DirectionAngles
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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
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SymmetryOperations
• Ifanoperationonthelattice(rotation,translation,inversion,etc.)producesanidenticallattice,itisasymmetryoperation
• Planesanddirectionsareinthesamefamilyiftheyarerelatedbyasymmetryoperation
• Simplecubicstructureshavehighsymmetryandmanyrelatedfamiliesofplanes
• Zincblende(III-V)structureshavelowersymmetry,soplanesthatareinthesamefamilyforacubicstructuremaynotbeinthesamefamilyinazincblendestructure
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ExamplesofFamiliesofPlanes
• Theplanes(100),(010),and(001)areallrelatedbyasymmetryoperationforasimplecubiclattice,andarethuspartofthe{100}family
• Forothercrystalsstructures,(100),(010),and(001)maynotbepartofthe{100}family
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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
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BulkGrowth
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SiliconIngot
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LatticeMatchedSystemsHeteroepitaxy:Grownmaterialsarelatticematchedbuthavedifferentpropertiesthanthesubstrate
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StrainedLayers• PseudomorphicGrowth:Epitaxialgrowthofanonlattice-matchedmaterial
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Misfit Dislocation
OtherConcepts
• CriticalThickness:Growththicknessabovewhichmisfitdislocationsareformed
• StrainedLayerSuperlattice:Astructureofalternatinglayershavingtensileandcompressivestrainsuchthatnetstrainbalanceoccursandmisfitdislocationsarenotformed
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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
– [email protected]– 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)
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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
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MyRecommendations
• Readthesyllabusandinformationpostedonthecoursewebsite
• Attendclass&participate• Attendofficehours(TAandProfessors)• Readthebook• Re-readthebook• Lookatandreadselectedportionsofthesupplemental
texts• Formstudygroupstoreviewconceptsanddiscusshigh-
levelapproachesforsolvinghomeworkproblems– Don’tformstudygroupstocopyhomeworksolutions
• Don’tmissanyhomework,quizzes,orexams• It’shardtoovercomeazero
• Askquestionsinclass!47