Diffusion in Semiconductor IC Technology

This lecture, presented by Dr. G.S. Virdi, Ex-Chief Scientist at CSIR–Central Electronics Engineering Research Institute, Pilani, is an important part of the IC Technology and Microelectronic Devices course. The lecture provides an in-depth explanation of diffusion, one of the key doping techniques used to introduce impurities into semiconductors to modify their electrical properties.

It covers the fundamental diffusion processes, diffusion equations (Fick’s Laws), dopant profiles, and influencing factors such as temperature, lattice structure, and defects. The comparison between diffusion and ion implantation techniques is also elaborated with practical insights and diagrams.

This lecture will be highly beneficial for engineering and science students (B.Tech, M.Tech, and M.Sc), as well as researchers interested in semiconductor device fabrication and IC processing.

1. IC Technology -Diffusion
Dr.G.S.Virdi
Ex.Chief Scientist
CSIR-Central Electronics Engineering Research Institute
Pilani—33303 1,India

2. Overview
•Introduction
•BasicDiffusionProcess
•DiffusionEquation
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3. Diffusionandionimplantationarethetwokeyprocesses
tointroduceacontrolledamountofdopants
intosemiconductorsandtoaltertheconductivitytype.
•Figurecomparesthesetwotechniquesandtheresulting
dopantprofiles.Inthediffusionprocess,thedopantatoms
areintroducedfromthegasphaseofbyusingdoped-oxide
sources.
•Thedopingconcentrationdecreasesmonotonicallyfromthe
surface,andthein-depthdistributionofthedopantis
determinedmainlybythetemperatureanddiffusiontime.
•Generallyspeaking,diffusionandionimplantation
complementeachother.Forinstance,diffusionisusedto
formadeepjunction,suchasann-tubinaCMOSdevice,
whileionimplantationisutilizedtoformashallowjunction,
likeasource/drainjunctionofaMOSFET.
IntroductiontoDiffusion
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4. Shallow
junction
Deep
junction
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5. Comparisonof(a)diffusionand(b)ionimplantationfortheselective
introductionofdopantsintoasemiconductorsubstrate.
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6. Diffusion
Anexampleofthechemicalreaction
diffusionusingaliquidsourceis
4POCl
3+3O
2 2P
2O
5+6Cl
2
forphosphorous
TheP
2O
5formsaglassonsiliconwaferandisthenreducedto
phosphorousbysilicon.
2P
2O
5+5Si 4P+5SiO
2
Thephosphorousisreleasedanddiffusesintothesiliconand
Chlorineisvented.
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7. •Boronisthemostcommonp-typeimpurityinsilicon,
whereasarsenicandphosphorusareusedextensivelyasn-
typedopants.
•Thesethreeelementsarehighlysolubleinsiliconwith
solubilitiesexceeding5x10
20atoms/cm
3inthediffusion
temperaturerange(between800
oCand1200
oC).
•Thesedopantscanbeintroducedviaseveralmeans,
includingsolidsources(BNforB,As
2O
3forAs,andP
2O
5for
P),liquidsources(BBr
3,AsCl
3,andPOCl
3),andgaseous
sources(B
2H
6,AsH
3,andPH
3).
•Usually,thegaseoussourceistransportedtothe
semiconductorsurfacebyaninertgas(e.g.N
2)andisthen
reducedatthesurface.
Diffusion
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8. Schematicdiagramofatypicalopen-tubediffusionsystem
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9. •Fordiffusioningalliumarsenide,thehighvapourpressureof
arsenicrequiresspecialmethodstopreventthelossof
arsenicbydecompositionorevaporation.
•Thesemethodsincludediffusioninsealedampuleswithan
overpressureofarsenicanddiffusioninanopentube
furnacewithadopedoxidecappinglayer(e.gSiliconnitride)
•Mostofthestudiesofp-typediffusionhavebeenconfined
touseofzincintheformsofZn-Ga-AsalloysandZnAs
2for
thesealedampuleapproachorZnO-SiO
2fortheopen-tube
approach.
•Then-typedopantsingalliumarsenideincludeseleniumand
tellurium.
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10. DiffusionEquation
•Diffusioninasemiconductorcanbevisualizedastheatomic
movementofthedopantinthecrystallatticebyvacancies
orinterstitials.
•Thereisafiniteprobabilitythatahostatomcanacquire
sufficientenergytoleavethelatticesiteandtobecomean
interstitialatomtherebycreatingavacancy.
•Whenaneighboringimpuritymigratestothevacancysite,
themechanismiscalledvacancydiffusion.
•Ifaninterstitialatommovesfromoneplacetoanother
withoutoccupyingalatticesitethemechanismisinterstitial
diffusion.
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11. (a):Diagramtoshowvacancydiffusioninasemiconductor.
(b):Diagramtoshowinterstitialdiffusioninasemiconductor.
Source:
http://web.eng.gla.ac.uk/groups/sim_centre/courses/diffusion/diff_3.html
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12. Modelsofatomicdiffusionmechanismsforatwo-dimensional lattice,witha
beingthelatticeconstant:(a)Vacancymechanism.
(b)Interstitialmechanism.
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13. DiffusionEquation
•Thebasicdiffusionprocessofimpurityatomsissimilarto
thatofchargecarriers.LetFbethefluxofdopantatoms
traversingthroughaunitareainaunittime,and
•whereDisthediffusioncoefficient,Cisthedopant
concentration,andxisthedistanceinonedimension.
•Theequationimpartsthatthemaindrivingforceofthe
diffusionprocessistheconcentrationgradient,∂C/∂x.
•Infact,thefluxisproportionaltotheconcentrationgradient,
andthedopantatomswilldiffusefromahigh-concentration
regiontowardalow-concentrationregion.
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14. DiffusionEquation
•Thebasicdiffusionprocessofimpurityatomsissimilarto
thatofchargecarriers.LetFbethefluxofdopantatoms
traversingthroughaunitareainaunittime,and
•whereDisthediffusioncoefficient,Cisthedopant
concentration,andxisthedistanceinonedimension.
•Theequationimpartsthatthemaindrivingforceofthe
diffusionprocessistheconcentrationgradient,∂C/∂x.
•Infact,thefluxisproportionaltotheconcentrationgradient,
andthedopantatomswilldiffusefromahigh-concentration
regiontowardalow-concentrationregion.
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15. DiffusionEquation
•Thenegativesignontheright-hand-sideofstatesthat
mattersflowinthedirectionofdecreasingdopant
concentration,thatis,theconcentrationgradientisnegative.
•Accordingtothelawofconservationofmatter,thechange
ofthedopantconcentrationwithtimemustbeequivalentto
thelocaldecreaseofthediffusionflux,intheabsenceofa
sourceorasink.
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16. DiffusionEquation
•Whentheconcentrationofthedopantislow,thediffusion
constantatagiventemperaturecanbeconsideredasa
constantandcanbewrittenas:
•ThisequationisreferredtoasFick'sSecondLawofDiffusion.
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17. DiffusionEquation
coefficientsforlowconcentrationsofvarious
•Figureonnextslideshowsthemeasureddiffusion
dopant
impuritiesinsiliconandgalliumarsenide.
•Thelogarithmofthediffusioncoefficientsplottedagainst
thereciprocaloftheabsolutetemperatureyieldastraight
lineinmostofthecases,implyingthatoverthetemperature
range,thediffusioncoefficientscanbeexpressedas:.
whereDodenotesthediffusioncoefficientextrapolatedto
infinitetemperatureandE
astandsfortheArrhenius
activationenergy.
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18. Diffusioncoefficient(alsocalleddiffusivity)asafunctionofthereciprocalof
temperaturefor(a)siliconand(b)galliumarsenide.
Fastmoving
species
Slowmoving
species
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19. Forinterstitialdiffusion,Eaisrelatedtotheenergyrequired
tomoveadopantatomfromoneinterstitialsitetoanother.
ThevaluesofE
aarebetween0.5to1.5eVinbothSiand
GaAs.
Forvacancydiffusion,Eaisrelatedtoboththeenergiesof
motionandformationofvacancies.
Hence,E
aforvacancydiffusionislargerthanthatfor
interstitialdiffusionandisusuallybetween3to5eV.
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20. DiffusionProfiles
•Thediffusionprofileofdopantatomsisdependentontheinitialand
boundaryconditions.
•Solutionofequationhavebeenobtainedforvarioussimpleconditions,
includingconstant-surface-concentrationdiffusionandconstant-total-
dopantdiffusion.
•Inthefirstscenario,impurityatomsaretransportedfromavapour
sourceontothesemiconductorsurfaceanddiffuseintothe
semiconductorwafer.
•Thevapoursourcemaintainsaconstantlevelofsurfaceconcentration
duringtheentirediffusionperiod.
•Inthesecondsituation,afixedamountofdopantisdepositedontothe
semiconductorsurfaceandissubsequentlydiffusedintothewafer.
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21. ConstantSurfaceDiffusion
•Theinitialconditionatt=0is
C(x,0)=0
Whichstatesthatthedopantconcentrationinthehost
semiconductorisinitiallyzero.
•Theboundaryconditionare
C(0,t)=C
sandC(∞,t)=0
•whereCsisthesurfaceconcentration(atx=0)whichis
independentoftime.
•Thesecondboundaryconditionstatesthatatlargedistances
fromthesurface,therearenoimpurityatoms.
•ThesolutionoftheFick’sdiffusionequationthatsatisfiesthe
initialandboundaryconditionsisgivenby:
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22. ErrorFunctionAlgebra
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23. Diffusionprofiles.(a)Normalizedcomplementaryerrorfunction(erfc)versusdistancefor
successivediffusiontimes.
(b)NormalizedGaussianfunctionversusdistanceforsuccessivetimes.
ConstantSurfaceDiffusion
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24. ConstantTotalDopant
•Afixed(orconstant)amountofdopantisdepositedontothe
semiconductorsurfaceinathinlayer,andthedopantis
subsequentlydiffusedintothesemiconductor.
•Theinitialconditionatt=0isagainC(x,0)=0.
Theboundaryconditionsare:
whereSisthetotalamountofdopantperunitarea.
Thesolutionofthediffusionequationsatisfyingtheabove
conditionsis:
ThisexpressionistheGaussiandistribution,andthedopant
profileisdisplayedinFigure
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25. NormalizedconcentrationversusnormalizeddistancefortheerfcandGaussian
functions.
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26. Influencingfactorsfordiffusion
•Diffusingspecies:Interstitialatomsdiffuseeasilythan
substitutionalatoms.
•Againsubstitutionalatomswithsmalldifferenceinatomic
radiuswithparentatomsdiffusewitheasethanatomswith
largerdiameter.
•Temperature:Itisthemostinfluencingfactor.Theirrelations
canbegivenbythefollowingArrheniusequation
•whereD
0isapre-exponentialconstant,Qistheactivation
energyfordiffusion,Risgasconstant(Boltzmann’sconstant)
andTisabsolutetemperature.
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27. Influencingfactorsfordiffusion
•Fromthetemperaturedependenceofdiffusivity,itis
experimentallypossibletofindthevaluesofQandD
0.
•Latticestructure:Diffusivityishighforopenlatticestructure
andinopenlatticedirections.
•Presenceofdefects:Theotherimportantinfluencingfactor
ofdiffusivityispresenceofdefects.Manyatomic/volume
diffusionprocessesareinfluencedbypointdefectslike
vacancies,interstitials.
•Apartfromthese,dislocationsandgrainboundaries,i.e.
short-circuitpathsastheyfamouslyknown,greatly
enhancesthediffusivity.
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28. Junctiondepthmeasurementbygroovingandstaining.
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29. EvaluationofDiffusedLayers(contd..)
•IncaseifR
0ismuchlargerthanaandb,then
•Thejunctiondepthisthepositionwherethedopant
concentrationequalsthesubstrateconcentrationC
Bor
C(x
j)=C
B
•Thus,ifthejunctiondepthandC
Bareknown,theC
sandthe
impuritydistributioncanbecalculated,providedthe
diffusionprofile.
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30. Thank You…
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