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

DepartmentofElectricalandComputerEngineering2114MicroandNanotechnologyLaboratory

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

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

–  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

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