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M,W,F12:00-12:50(X),2015ECEBProfessorJohnDallesasse
DepartmentofElectricalandComputerEngineering2114MicroandNanotechnologyLaboratory
Tel:(217)333-8416E-mail:[email protected]
OfficeHours:Wednesday13:00–14:00
PleaseReviewe-MailSent2/2
Web Info: The symptoms of mumps usually develop 14 to 25 days after becoming infected with the mumps virus (this delay is known as the incubation period). The average incubation period is around 17 days. Swelling of the parotid glands is the most common symptom of mumps.
Today’sDiscussion
• Compensation• Mobility• Assignments• TopicsforNextLecture
3
TentativeSchedule[1]
JAN17Courseoverview
JAN19Introtosemiconductorelectronics
JAN22Materialsandcrystalstructures
JAN24Bondingforcesandenergybandsinsolids
JAN26Metals,semiconductors,insulators,electrons,holes
JAN29Intrinsicandextrinsicmaterial
JAN31Distributionfunctionsandcarrierconcentrations
FEB2Distributionfunctionsandcarrierconcentrations
FEB5Temperaturedependence,compensation
FEB7Conductivityandmobility
FEB9Resistance,temperature,impurityconcentration
FEB12InvarianceofFermilevelatequilibrium
FEB14Opticalabsorptionandluminescence
FEB16Generationandrecombination
4 **Subject to Change**
Continued
WhereDidWeGetni?
Calculate using:
ni = NcNve−Eg /2kT
or consult a reference (table, etc.)
Comment:IncompleteImpurityIonization
• Atlowdopingdensities(<1017cm-3),amodifiedversionoftheFermiDistributioncanbeusedtodeterminethefractionofionizedshallowdonorsoracceptors
• Notvalidforhighdopingdensity(impuritybandformation)• NotvalidasT->0K(insufficientionizationenergy)• ThetermsFAandFDareassociatedwithfactorssuchasbanddegeneracyandspin
states(amongothereffects)
ND+ = ND 1− ′f ED( )⎡⎣ ⎤⎦
ND+ = ND
1+ FDeΔED+ Efn−EC( )⎡⎣ ⎤⎦/kT
FD 2 for SiliconΔED is the donor ionization energyΔED ≡ EC − ED( )
NA+ = NA ′f EA( )
NA+ = NA
1+ FAeΔEA+ EV −Efp( )⎡⎣ ⎤⎦/kT
FA 4 for SiliconΔEA is the acceptor ionization energyΔEA ≡ EA − EV( )
Donor Ionization Acceptor Ionization
In this class, we will generally assume complete ionization and not do this calculation.
IntrinsicConcentrationforSi,Ge,andGaAs
no po = NcNve−(Eg )/kT = ni
2 (T )
ni (T ) = NcNve−(Eg )/2kT
ni (T ) = 22π kTh2
⎛⎝⎜
⎞⎠⎟3/2
mn*mp
*( )3/4 e−(Eg )/2kT
Intrinsic Carrier Concentration Depends Upon: • Energy Gap Eg • Temperature T • Electron Effective Mass • Hole Effective Mass
Note: Graph is neglecting T3/2 term and Eg(T)
9
CarrierConcentrationTemperatureDependence
Bound Donor Electrons
Free Donor Electrons
Thermal Generation of Carriers
500K 227°C
100K -173°C
10
ni (T ) = 22π kTh2
⎛⎝⎜
⎞⎠⎟2
mn*mp
*( )e−(Eg )/2kT
no Nd
n ∝ e−Ed /2kT
WhatHappensiftheCrystalisDopedWithBothDonorsandAcceptors?
Charge Neutrality Equation :po + Nd
+ = no + Na−
no = Nd
+ − Na−( ) + po Nd
+ − Na−
Example Revisited:Donor-Doped Silicon, 1017 cm−3
Since Nd (As) >> ni ,
no Nd = 1017cm−3
po =ni
2
no=
1.5 ×1010cm−3( )2
1017cm−3
po = 2.25 ×103cm−3 <<1017cm−3
12
WhatHappensiftheCrystalisDopedWithBothDonorsandAcceptors?
Charge Neutrality Equationpo + Nd
+ = no + Na−
13
Case 1: ND > NA and ND − NA niGiven GaAs at 300K withND = 1×1017cm−3
NA = 5 ×1016cm−3
Then:no no − po = ND
+ − NA− = 1×1017 − 5 ×1016cm−3
no 5 ×1016cm−3
po =ni
2
no
2 ×106( )2
5 ×1016 = 8 ×10−5cm−3
Case 2: NA > ND and NA − ND niGiven Si at 300K withNA = 1×1017cm−3
ND = 5 ×1016cm−3
Then:po po − no = NA
− − ND+ = 1×1017 − 5 ×1016cm−3
po 5 ×1016cm−3
no =ni
2
po
1.5 ×1010( )2
5 ×1016 = 4.5 ×103cm−3
WhatHappensClosetotheIntrinsicConcentration?
Charge Neutrality Equationpo + Nd
+ = no + Na−
14
Case 3: ND > NA and ND − NA niGiven Ge at 300K with ND = 1×1014 cm−3 and NA = 7 ×1013cm−3
Then:no − po = ND
+ − NA− = 1×1014 − 7 ×1013cm−3
no − po = 3×1013cm−3 (1)
po =ni
2
no=
2.5 ×1013( )2
no (2)
Substituting (2) into (1):
no −2.5 ×1013( )2
no= 3×1013cm−3
Multiply through by no and rearrange:
no2 − 3×1013no − 2.5 ×1013( )2
= 0
Solution to quadratic equation:
no =3×1013 ± 3×1013( )2
+ 4 2.5 ×1013( )2
2= 3×1013 ± 5.8 ×1013
2= 4.4 ×1013 ← disgard negative
po = 1.4 ×1013 ← use either expression to calculate
Close to the intrinsic concentration, we cannot neglect these carriers!
ConductivityandMobility
DriftVersusRandomMotion
16
Electron Motion
e-
vx = −µnEx
+ + +
V - -
-
Diffusion:ABriefComment• Inthecaseofauniformdistribution
ofcarriersinthesolid,therandommotionisaveragedoutandthereisnonetmovementofcarriersfromoneregiontoanother
• Ifthereisnonetmotionofcarriers,thereisnonetcurrent
• Wewillconsidercarrierdriftundertheconditionwherethedistributionofcarriersisuniformsuchthatthereisnodiffusioncontributiontothenetcurrent– Wewillcomebacktothis
assumptionlater
Net "e-" flow = 0
ei− • vi
i∑ = 0
Plane
e-
e-
e-
e-
e- e-
17
For Uniform e- Distribution
DriftinaSemiconductor
+ -
Assume uniform distribution of carriers: no diffusion
18
• Anelectroninavacuumwillcontinuetoaccelerateundertheinfluenceofanelectricfield
• Anelectrontravelingthroughthecrystalwillexperiencetheperiodicpotentialofthelatticeatoms
• Theelectronwillbescatteredasitencounters+and–regionsofspacecharge
• Thiswillimpartamomentumchangetotheelectron
• Afasterelectronwillscattermorequickly,impartingmoremomentumchangeperunittime
ElectronMotioninaCrystal
V e-
E
V e-
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
+ - -
- -
19
ElectronDriftinaConstantElectricField
ForceDuetoElectricField:• Theapplicationofaelectricfield
createsanetforceoneachelectronF=-qE,soforthedistribution:
• Thisforcecreatesanetmomentum
forthepopulationofelectronsinthedirectionofthefield
ThereMustBeanOffsettingForce:• Scatteringevents(electroncollisions)
limitthevelocityoftheelectron• Thenetrateofchangeof
momentum,includingcollisions,iszeroundersteady-stateconditions
• Ifthenetrateofchangeofmomentumwerenotzero,currentwouldnotbeconstantforagivenappliedfield.Itwouldeitherincreasewithoutboundordroptozero.
Force for "n" electrons = (−q)nEx = ma = mdvxdt field
= dpxdt field
20
Force for a single electron:F = −qEx
Force for "n" electrons:
−nqEx =dpxdt field
MeanFreeTimeandCollisionProbability
• WestartwithaninitialpopulationofN0electrons(orholes)attimet=0
• WeassumethatanygivenelectronhasafixedprobabilityintimePofhavingacollision(scattering)
• Ifwethinkofscatteringcentersasfixedpoints,anelectronwithaveragevelocity<v>travelsanaveragedistance<l>beforecolliding
• Theaveragetimebetweencollisionsisthus:
• TheprobabilityintimeΔtofhavingacollisionisthereforegivenby:
t =lv
≡ t P = Δtt
� � � � �
� � �
�
� �
�
�
�
� � �
� � N0
� � � � �
� � �
�
� �
� �
� �
� � N(t)
Some time later “t”
� Experienced Collision
Assignments
• Readinfopacket–keycoursepoliciesandscheduleareoutlinedhere,includinghourlyexamdates
• HomeworkassignedeveryFriday,duefollowingFriday
• ReadingfromStreetman’sbook:– Wed1/31:§'s3.3.1,3.3.2– Fri2/2:§'s3.3.1,3.3.2(HW2Due)– Mon2/5:§'s3.3.3,3.3.4– Wed2/7:§3.4.1
• Chapter1&2inPierretcoverssimilarmaterial
23
Assignments
• Readinfopacket–keycoursepoliciesandscheduleareoutlinedhere,includinghourlyexamdates
• HomeworkassignedeveryFriday,duefollowingFriday
• ReadingfromStreetman’sbook:– Wed2/7:§3.4.1– Fri2/9:§'s3.4.2,3.4.3(HW3Due)– Mon2/12:§3.5– Wed2/14:§'s4.1,4.3.1
• Chapters1-3inPierretcoverssimilarmaterial
24
Outline,2/9/18
• FinishMobility
26
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 28
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 29
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 30
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
31
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
32 **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**
33 **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
35
KeyPoints
• AttendClass!– 3unannouncedquizzes,eachworth5%ofyourgrade– Youmusttakethequizinyoursection– Excusedabsencesmustbepre-arrangedwiththecoursedirector– Absencesforillness,etc.needanotefromtheDean
• Seepolicyonabsencesinthesyllabus• NoLateHomework
– Homeworkdueonthedateofanexcusedabsencemustbeturnedinaheadoftime
– Youmustturninhomeworkinyoursection– Noexcusedabsencesforhomeworkassignments– Top10of11homeworkassignmentsusedincalculationofcoursegrade
• Doallofthemtobestpreparefortheexams!• NoCheating
– Penaltiesaresevereandwillbeenforced• TurnOffYourPhone
– Novideorecording,audiorecording,orphotography
36
Homework
• AssignedFriday,DueFollowingFriday– Duedatesshowninsyllabus
• DueatStartofClass• FollowGuidelinesinSyllabus• PeerDiscussionsRelatedtoHomeworkareAcceptableandEncouraged
• DirectlyCopyingSomeoneElse’sHomeworkisNotAcceptable– Gradershavebeeninstructedtowatchforevidenceofplagiarism
– Bothpartieswillreceivea“0”ontheproblemorassignment
37
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)
38
Exams
• ExamI:TuesdayFebruary27th,7:30-8:30pm• ExamII:ThursdayApril12th,7:30-8:30pm• FinalExam:Date/TimeToBeAnnounced
– DeterminedbyUniversityF&S
39
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
40
MyRecommendations
• Readthesyllabusandinformationpostedonthecoursewebsite
• Attendclass&participate• Attendofficehours(TAandProfessors)• Readthebook• Re-readthebook• Lookatandreadselectedportionsofthesupplemental
texts• Formstudygroupstoreviewconceptsanddiscusshigh-
levelapproachesforsolvinghomeworkproblems– Don’tformstudygroupstocopyhomeworksolutions
• Don’tmissanyhomework,quizzes,orexams• It’shardtoovercomeazero
• Askquestionsinclass!41