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

DepartmentofElectricalandComputerEngineering2114MicroandNanotechnologyLaboratory

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

OfficeHours:Wednesday13:00–14:00

Today’sDiscussion

•  p-nJunctions(Continued)•  Assignments•  TopicsforNextLecture

2

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

3 **Subject to Change**

Electron&HoleCurrents

IdealDiodeEquation CurrentComponents

I =qADp

Lp

Δpn +qADn

LnΔnp = qA

Dp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( )

Defining Io = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟, I = Io e

qV /kT −1( )

I = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( ) = Io eqV /kT −1( )

Under large reverse bias Vr kTq

⎛⎝⎜

⎞⎠⎟

, e−qVr /kT −1( ) ≈ −1 so

I = −qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟= −Io

5

MajorityCarrierCurrent:n-Side

6

Calculation of Majority Carrier Current :

Itot = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( )

= Inn + I pn = In (xn )+ I p (xn ) ⇐ majority carrier + minority carrier current

= In (xn )+ qADp

Lp

pne− xn /Lp eqV /kT −1( )

so:Inn ≡ Majority Carrier CurrentI pn ≡ Minority Carrier CurrentIn (xn ) ≡ Majority Carrier Current Referenced to Depletion Region EdgeI p (xn ) ≡ Minority Carrier Current Referenced to Depletion Region Edge

MajorityCarrierCurrent:n-Side

7

Itot = In (xn )+ qADp

Lp

pne− xn /Lp eqV /kT −1( )

so:

In (xn ) = Itot − I pn = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( )⎡

⎣⎢⎢

⎤

⎦⎥⎥− qA

Dp

Lp

pne− xn /Lp eqV /kT −1( )⎡

⎣⎢⎢

⎤

⎦⎥⎥

= qADp

Lp

1− e− xn /Lp( ) pn + Dn

Lnnp

⎡

⎣⎢⎢

⎤

⎦⎥⎥eqV /kT −1( )

where xn is the coordinate system with xn = 0 at the edge of the n-side depletion region

Relative to the "x" coordinate system with the origin at the metallurgical junction:

In (x) = qADp

Lp

1− e− x−xn( )/Lp( ) pn + Dn

Lnnp

⎡

⎣⎢⎢

⎤

⎦⎥⎥eqV /kT −1( )

where xn is the width of the depletion region on the n-side of the junction

MajorityCarrierCurrent:p-Side

8

Calculation of Majority Carrier Current :

Itot = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( )

= I pp + Inp = In (xp )+ I p (xp ) ⇐ majority carrier + minority carrier current

= I p (xp )+ qA Dn

Lnnpe

− xp /Ln eqV /kT −1( )so:I pp ≡ Majority Carrier Current

Inp ≡ Minority Carrier Current

I p (xp ) ≡ Majority Carrier Current Referenced to Depletion Region EdgeIn (xp ) ≡ Minority Carrier Current Referenced to Depletion Region Edgexp is a transformed coordinate system: xp = −x − xpwhere:The "x" coordinate system is the + going system referenced to the metallurgical junctionxp is the p-side depletion region width

MajorityCarrierCurrent:p-side

9

Itot = I p (xp )+ qA Dn

Lnnpe

− xp /Ln eqV /kT −1( )so:

I p (xp ) = Itot − Inp = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( )⎡

⎣⎢⎢

⎤

⎦⎥⎥− qA Dn

Lnnpe

− xp /Ln eqV /kT −1( )⎡

⎣⎢

⎤

⎦⎥

= qADp

Lp

1− e− xp /Lp( ) pn + Dp

Lp

pn⎡

⎣⎢⎢

⎤

⎦⎥⎥eqV /kT −1( )

where x p is the negative-going coordinate system with x p = 0 at the edge of the n-side depletion region

Referenced to Metallurgical Junction and + going System:

I p (xp ) = qADp

Lp

1− ex+xp /Lp( ) pn + Dp

Lp

pn⎡

⎣⎢⎢

⎤

⎦⎥⎥eqV /kT −1( )

Drift&DiffusioninForwardBias

Diffusion Dominant

Drift Dominant

Drift Dominant

Drift +

Diffusion

Drift +

Diffusion

Example:p-nDiodeDetermine the current at bias voltages of +0.5 and -0.5V.Silicon p-n junction with an area of 10−4 cm2 at 300K:

I = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟eqV /kT −1( ) = Io eqV /kT −1( )

Calculate equilibrium minority carrier concentrations:

pn =ni

2

nn=

1.5 ×1010( )2

1015 = 2.25 ×105cm−3

np =ni

2

pp=

1.5 ×1010( )2

1017 = 2.25 ×103cm−3

Calculate the MINORITY CARRIER diffusion coefficient and diffusion length:

Dp =kTq

µp = 0.0259 × 450 = 11.66 cm2 /s ← holes on n-side

Dn =kTq

µn = 0.0259 × 700 = 18.13 cm2 /s ← electrons on p-side

Lp = Dpτ p = 11.66 × 10 ×10−6( ) = 1.08 ×10−2 cm

Ln = Dnτ n = 18.13× 0.1×10−6( ) = 1.35 ×10−3 cm

Calculate Io :

Io = qADp

Lp

pn +Dn

Lnnp

⎛

⎝⎜⎞

⎠⎟

= 1.6 ×10−19( )× 0.0001( ) 11.660.0108

2.25 ×105( ) + 18.130.00135

2.25 ×103( )⎛⎝⎜

⎞⎠⎟

= 4.370 ×10−15 A = 4.370 fA

Current at a voltage of +0.5 V: I = Io e0.5/0.0259 −1( ) ≈1.058 ×10−6A

Current at a voltage of -0.5 V: I ≈ −Io = −4.37 ×10−15A

p-side n-side

Na=1017cm-3 Nd=1015cm-3

τn=0.1μs τp=10μs

μp=200cm2/V-s μn=1300cm2/V-s

μn=700cm2/V-s μp=450cm2/V-s

KeyPoint:•  Usethecorrectmobilityin

thecalculationofDpandDn

•  Minoritycarriermobility

12

AnotherDerivationoftheIdealDiodeEquation

ChargeControlApproximation•  Insteadystate,therateatwhich

wereplenishchargeacrossthexn=0orxp=0planemustequaltheamountofminoritycarrierchargelostthroughrecombinationinanintervaloftime

•  Therateatwhichchargeislostisequaltothetotalamountofchargedividedbythechargelifetime

Recall that: Ln ≡ Dnτ n and Lp ≡ Dpτ p

so: τ n =Ln

2

Dn

and τ p =Lp

2

Dp

Qp = qA δ0

∞

∫ p xn( )dxn = qAΔpn e− xn /Lp dxn0

∞

∫= qAΔpnLp

Qn = qA δ0

∞

∫ n xp( )dxp = qAΔnp e− xp /Ln dxp0

∞

∫= qAΔnpLn

14 Note: xp and xn coordinate systems

Summary of Models

15

ReverseBias:DriftTermDominant

po

ipo

apo

pnn

Np2

=

≅ −

noi

no

dno

nnp

Nn2

=

≅ ++dN

−aN

0 Xn -Xp

+dN

−aN

Φn (drift) >>Φn (diff ),Φ p (drift) >>Φ p (diff )

)()(

)()(

)(

0)(

np

pnp

n

npnp

Lx

noL

x

nn

ononn

onnnn

xpLD

qAxI

dxxpdqADxI

epepxp

ppppxpp

pn

pn

δ

δδ

=

−=

−=Δ=

−=−=Δ−=Δ

−−

)()(

)()(

)(

0

)(

pn

npn

p

pnpn

Lnx

opp

opopp

opppp

xnLDqAxI

dxxnd

qADxI

enxn

nnnnxnn

p

δ

δδ

−=

+=

−=

−=−=Δ

−−=Δ

−

onp

opp nn −=Δ

Δpn = pn eq −Vr( )/kT −1( )

− pon

opnp(xn ) = δ p(xn )+ pon

+dN

+dN

−aN

−aN

0 0

oppp nxnxn += )()( δMinority carriers that

“random walk” into the depletion region will be swept away (~within a

diffusion length)

Lp Ln

17

I = I p (xn = 0)+ In (xn = 0)xnaxis = I p (xn = 0)− In (xp = 0)xpaxis so:

I =qADp

Lp

Δpn +qADn

LnΔnp = qA

Dp

Lp

(− pno )+Dn

Ln(−npo )

⎛

⎝⎜⎞

⎠⎟

= −qADp

Lp

(pno )+Dn

Ln(npo )

⎛

⎝⎜⎞

⎠⎟= −I0

Combining Terms:

E!

ReverseBiasQuasiFermiLevels

Δpn = pn eq(−Vr )/kT −1( ) − pn for Vr kT / q

Similarly: Δnp −np

•  Minoritycarrierconcentrationapproacheszeroattheedgeofthedepletionregion

•  Thiseffectistermed“minoritycarrierextraction”

•  Thereversesaturationcurrentisadrift-dominatedcurrent,buttheminoritycarriersarriveatthedepletionregionbywayofdiffusion

Thermal Generation

Thermal Generation

- - -

+ + +

Reverse Bias, Edge of Depletion Region:

pn = ni2e Fn−Fp( )/kT ≈ 0 18

ReverseBiasChargeDistribution

pp

np

nn

pnpn xn0( ) = ppe

−q V0−V( )/kTnp −xp0( ) = nne−q V0−V( )/kT

nn xn0( ) nn pp −xp0( ) pp

ReverseBiasChargeDistribution

pp

np

nn

pn

nn xn0( ) nn pp −xp0( ) pp

Δp = pn xn0( )− pn ∞( )= pne

qV /kT − pn= pn e

qV /kT −1( ) − pn

np −xp0( )− np −∞( ) = Δn

npeqV /kT − np =

np eqV /kT −1( ) =

−np

np −xp0( ) = nne−qV0 /kT eqV /kT= npe

qV /kTpn xn0( ) = ppe

−qV0 /kT eqV /kT

= pneqV /kT

JunctionCurrents:Revisited

Assignments

•  HomeworkassignedeveryFriday,duefollowingFriday

•  ReadingfromStreetman’sbook:– Mon3/5:§'s5.2,5.2.1,5.2.2,5.2.3– Wed3/7:§5.2.3

•  Chapters3,4,and5inPierretcoversimilarmaterial

23

Assignments

•  HomeworkassignedeveryFriday,duefollowingFriday

•  ReadingfromStreetman’sbook:– Mon3/12:§'s5.2.3,5.3,5.3.1– Wed3/14:§5.3.2– Wed3/16:§’s5.3.2,5.3.3

•  Chapters3,4,and5inPierretcoversimilarmaterial

24

Outline,3/26/18

•  ContinuepnJunctions

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[1]

JAN17Courseoverview

JAN19Introtosemiconductorelectronics

JAN22Materialsandcrystalstructures

JAN24Bondingforcesandenergybandsinsolids

JAN26Metals,semiconductors,insulators,electrons,holes

JAN29Intrinsicandextrinsicmaterial

JAN31Distributionfunctionsandcarrierconcentrations

FEB2Distributionfunctionsandcarrierconcentrations

FEB5Temperaturedependence,compensation

FEB7Conductivityandmobility

FEB9Resistance,temperature,impurityconcentration

FEB12InvarianceofFermilevelatequilibrium

FEB14Opticalabsorptionandluminescence

FEB16Generationandrecombination

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

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 42

✔

✔ ✔ ✔

✔

✔

✔

✔

✔

✔

✔ ✔

Plus continuity equation, steady-state carrier injection, and diffusion length

Quiz1Statistics

•  Average:8.65•  StandardDeviation:1.49

ExamIStatistics

•  Average(AllSections):71.88•  StandardDeviation(AllSections):15.44

StreetmanErrata(6thEdition)

•  Equation4-30:“ΔxA”notδxA•  Equation4-33b:“τp”not“τn”

45

FinalExamSchedule