Electrical and physical topography in energy-filtered photoelectron emission microscopy of two-dimensional silicon pn junctions

(1)

HAL Id: cea-01477558

https://hal-cea.archives-ouvertes.fr/cea-01477558

Submitted on 27 Sep 2017

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Electrical and physical topography in energy-filtered

photoelectron emission microscopy of two-dimensional

silicon pn junctions

Maylis Lavayssière, Matthias Escher, Olivier Renault, Denis Mariolle,

Nicholas Barrett

To cite this version:

Maylis Lavayssière, Matthias Escher, Olivier Renault, Denis Mariolle, Nicholas Barrett. Electrical and

physical topography in energy-filtered photoelectron emission microscopy of two-dimensional silicon

pn junctions. Journal of Electron Spectroscopy and Related Phenomena, Elsevier, 2013, 186, pp.30

-38. �10.1016/j.elspec.2013.01.014�. �cea-01477558�

(2)

ContentslistsavailableatSciVerseScienceDirect

Journal

of

Electron

Spectroscopy

and

Phenomena

jou rn a l h o m e pa ge :w w w . e l s e v i e r . c o m / l o c a t e / e l s p e c

Electrical

and

physical

topography

in

energy-ﬁltered

photoelectron

emission

microscopy

of

two-dimensional

silicon

pn

junctions

Maylis

Lavayssière

a

_,

_Matthias

_Escher

b

_,

_Olivier

_Renault

a

_,

_Denis

_Mariolle

a

_,

_Nicholas

_Barrett

c,∗

a_CEA,_LETI,_MINATEC_Campus,₁₇_rue_des_Martyrs,₃₈₀₅₄_Grenoble_Cedex_9,_France b_Focus_GmbH,₆₅₅₁₀_Hünstetten,_Germany

c_CEA,_{IRAMIS/SPCSI/LENSIS,}_F-91191_{Gif-sur-Yvette,}_France

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received17May2012

Receivedinrevisedform7January2013 Accepted17January2013

Available online 12 February 2013 Keywords:

Pnjunction

Photoelectronemissionmicroscopy Surfaceimaging

Simulations

a

b

s

t

r

a

c

t

Photoelectronemissionmicroscopy(PEEM)isapowerfulnon-destructivetoolforspatiallyresolved,

spectroscopicanalysisofsurfaceswithsub-micronchemicalheterogeneities.However,inthecaseof

micronscalepatternedsemiconductors,bandline-upsatpnjunctionshaveabuilt-inlateralelectricﬁeld

whichcansigniﬁcantlyalterthePEEMimageofthestructurewithrespecttoitsphysicaldimensions.

Furthermore,realsurfacesmayalsohavephysicaltopographywhichcanreinforceorcounteractthe

electricallyinduceddistortionatapnjunction.WehavemeasuredtheexperimentalPEEMimage

dis-tortionatsuchajunctionandcarriedoutnumericalsimulationsofthePEEMimages.Thesimulations

includeenergyﬁlteringandtheuseofacontrastapertureinthebackfocalplaneinordertodescribe

thechangesinthePEEMimageofthejunctionwithrespecttoitsrealphysicaldimensions.Threshold

imagingdoesnotgiveareliablemeasurementofmicronsizedpandntypepatterns.Athighertake-off

energies,forexampleusingSi2pelectrons,thepatternwidthisclosertotherealphysicalsize.Physical

topographymustalsobequantitativelyaccountedfor.TheresultscanbegeneralizedtoPEEMimaging

ofanystructurewithabuilt-inlateralelectricﬁeld.

1. Introduction

Photoemission electron microscopy (PEEM) is a powerful

surfacesensitivetechniquesuitableforfullﬁeldimagingof

doping-inducedcontrastinsemiconductors.Intheenergyﬁlteredmodeit

combineshighspatialandenergyresolutionallowinga

compre-hensive,non-destructivespectroscopicanalysistobecarriedout

[1].Correlationofthespatialdistributionofcorelevelsandvalence

bandedgesallowsonetomapchemicalandvalencebandstates.

InPEEMa highextractor voltage,typically 12–20kV, isapplied

betweenthesampleandtheentrancelens oftheobjective.The

practicallateralresolutionisdeterminedbythecounting

statis-ticsand thesphericalandchromaticaberrationsoftheelectron

optics[2]whiletheultimateresolutionlimitisgivenbythe

diffrac-tiondiskofthelowenergyelectrons.Inthevicinityofaplanar

pnjunction(thejunctionbeingina planeperpendiculartothe

opticalaxis),alateralelectricﬁeldiscreated,whichaltersthe

sur-faceelectrical topographyandhencethePEEMimage.Thelocal

ﬁeldatapnjunctioninsiliconcaneasilybeofthesameorderof

magnitudeastheextractorﬁeld.Electronsemittedfromthe

sur-faceinthephysicalvicinityofthejunctionaredeviatedlaterally,

∗ Correspondingauthor.Tel.:+33169083272;fax:+33169088446 E-mailaddress:nick.barrett@cea.fr(N.Barrett).

perturbingthePEEMimage.Notonlywillthepositionofthe

junc-tion as measured in PEEM be different from the real physical

position,butalsotheapparentjunctionwidthmaybemodiﬁed.

Anunderstandingoftheeffectofthebuilt-involtagecould

there-forebeusedtomeasurethelocallateralelectricﬁeldatthejunction

fromthePEEMimage.Thephysicalwidthofahighqualityjunction

ismuchsmallerthanstandardthresholdPEEMresolution(typically

50nm).However,thespacechargeofthedepletionwidthcanvary

fromseveralnmuptoseveralmicronsdependingonthedoping

levels.Therefore,theseregionsshouldprovideacharacteristic

sig-nalintheimagesasshowninsomepioneeringPEEMworkonpn

junctions[3].Thedistortionsinelectronemissionmicroscopydue

tothedopingdependentspacechargeregionhavebeendiscussed

byFranketal.[4].Potentialmappinginsemiconductor

electron-icsbyelectronemissionmicroscopyhasbeenreviewedbyNepijko

etal.[5].Thebasicelectronopticsystemconsideredisacathode

immersionlensandacontrastapertureorknifeedgeinthefocal

plane.Thedeviationoftheelectronsemittedfromthesurfacewas

calculatedanalytically,modelednumericallyandfoundtoagree

withimaginginbrightanddarkﬁeldmodes.Thebuilt-inelectric

ﬁeldacrossthepnjunctiondeviatestheelectronsfromthep-type

regiontothen-typeregion.Theeffectisshownschematicallyin

Fig.1. Typical values used forthe simulationsare an extractor

ﬁeldof 6.6kVmm−1 and abuilt-inplanarjunctionvoltageof∼

0.9V,givinganeffectiveﬁeldvectorinﬂuencingthephotoelectron

(3)

Fig.1. Schematicoftheperturbationoftheextractorﬁeldbysamplesurface elec-tricaltopographyinacathodeimmersionlens.

trajectoriesstartingatthesurface.Awayfromthesamplethe

effec-tiveﬁeldvectorislessaffected.

Inrealpatternedsampleselectricaltopography cancombine

withphysicaltopographyduetothepatterningprocess.The

focus-ing/defocusingeffectof3Dstructureshasalreadybeeninvestigated

inemissionmicroscopy[6]andinmirrorelectronmicroscopy[7,8].

Dipsor wellswilltendtofocus thephoto-emitted(orreﬂected

electronsinthecaseoflowenergyelectronmicroscopy)whereas

aprotuberancewilldefocusthem.Thus,closetoapnjunctionthe

ﬁeldlineswillbedistortedduetoa combinationofthebuilt-in

ﬁeldfromthebandline-upandtheperturbationoftheextractor

ﬁeldduetophysicaltopography.Finally,thebandline-upatthe

surfacecanbeinﬂuencedbyboththesurfacecompositionandthe

photoemissionprocess.Nativeoxidecanberemovedandthe

sur-facepassivated,however,residualoxideanddefectsmaystillbe

present,givingrisetobandbendingandpinningoftheFermilevel.

Thegenerationofelectronholepairsduringthephotoemission

pro-cesscanalsoshiftthebandline-upviathesurfacephotovoltage[9].

Thusalthoughweareinterestedintheeffectofthebuilt-involtage

ofthejunction,thePEEMimagemayalsobemodiﬁedbysurface

effects.Inthispaperweinvestigatethecombinedeffectof

electri-calandphysicaltopographyatpnjunctionsonPEEMimaging.First,

theenergyﬁlteredthresholdandSi2pPEEMmeasurementsare

pre-sented.Then,thenumericalmodelincludinganimmersionlensand

contrastapertureforthesimulationsisdescribedandtested.Finally

thesimulationsofthecombinedphysicalandelectricaltopography

arecomparedwithexperimentanddiscussed.

2. Experiment

2.1. Samplepreparation

Thesampleconsistedofhighlyn-dopedpatterns(hereafterN+₎

ona p-dopedSi(100)substrate(resistivity5-10.m),hereafter

denotedP.Patterningwasdonebydeep-UVphotolithographywith

HF-lastwet cleaningat 950◦C toremove nativeoxide.Cavities

wereetchedusinggaseousHCl(180Torr,750◦C).Cavity

dimen-sions wereadjusted toaccount for theisotropic etchingbelow

thethermal oxide. Epitaxialgrowth of boronand phosphorous

dopedsiliconinthecavitieswasperformedat950◦C,20Torrusing

SiH2Cl2,B2H6andPH3gasprecursors.Epitaxialgrowthwas

pre-ferredtoionimplantationinordertoavoidcollateraldamagedue

totheionenergyandtominimizedopingproﬁlescreatingsharp

planarjunctions.PEEMimagingwasdoneona“0”-shaped,Ptype

patterninasurroundingN+_ﬁeld._Prior_to_PEEM_analysis,_the

sur-faceswere passivated using a three stepsprocess to minimize

surfacebandbending.Afterdegreasingintrichloroethylene,

rins-inginacetoneandde-ionizedwater,aﬁrstetchingwasdoneusing

abufferedoxideetchant(BOE:49%,HF:40%,NH4Fina7:1ratio).

ThesamplewasthenchemicallyoxidizedusingaPiranhasolution

(1/3H2O2,2/3H2SO4,concentrations30%and96%respectively)for

20min.Thesamplewasre-etchedinBOEfor30min,driedunder

N2andimmediatelyintroducedintothePEEMvacuumsystem.

The N+ _doping _level _was _measured _with _dual-beam

time-of ﬂight mass spectrometry using 1keV Cs+ _sputtering _to _be

1.8×1019_atoms_cm−3_,_the_as_supplied_substrate_doping_level_was

1.4_×1015_atoms_cm−3_,_creating_a_built-in_voltage_of_0.884_V_at_the

planar pn junction.The space charge regionon the N+ _side _is

estimatedat10nmandonthePdopedsubstrateat540nm.The

localizedepitaxialgrowthproducedaphysicaltopographyatthe

junctionbecauseitwasnotpossibletostoptheepitaxialgrowth

rateat exactlythesame heightasthetop ofthetrench. Fig.2

showsanAFMproﬁleoftheN+_/P_structure_and _the_height

pro-ﬁle.TheepitaxialN+_grown_in_the_trenches_is₂₀_nm_higher_than

thesurroundingsubstrate.

BasedontheAFMmeasurementsandthemeasureddoping

lev-elswecanrepresenttheP/N+_/P_and_N+_/P/N+_structures_as_shown_in

Fig.3(a).Thespace–chargeregionextendsmainlyintothePdoped

sideofthejunctionwhereasintheheavilyNdopedsideitisalmost

negligible.Fig.3(b)isaschematicoftheexpectedeffectsofthe

realelectrical andphysicaltopographies ontheelectron

trajec-tories.Boththebuilt-inﬁeldduetothespace-chargeregionand

thestepatthejunctionshouldmodifythePEEMimage,asshown

schematicallybythedark(purple)andlight(yellow)ﬁeldlines,

respectively.

2.2. PEEMresults

TheopticalmicrographinFig.4(a)showsthestructureusedfor

evaluationoftheelectricaltopography.TheN+_structure_is_7.65_␮m

wide,enclosedbythepurplearrows.Inthispaperwefocusonthe

P/N+_/P_structure._The_dimension_chosen_is_far_from_the_center_of

theimagebecausetheN+_structures_at_the_center_also_undergo_a

chargingeffectduetophotoemissionwhichmightinﬂuencethe

results.[10]Thewidthofthestructureswaschosentobemuch

largerthantheexpecteddepletionwidthtoensurethataccurate

ﬂat-bandvoltages farfromthejunctionswereavailablebothin

thePEEMmeasurementand forthenumericalsimulations.The

experimentsweredoneusingaspectroscopicXPEEMinstrument

(NanoESCA,OmicronNanotechnology)temporarilyinstalledatthe

TEMPObeamlineoftheSOLEILsynchrotron(h=128.9eV).The

doublehemisphericalanalyzerusedasenergyﬁlterprovideshigh

transmissionandthereforeallowsspectroscopicimagingwithhigh

energyresolutionwithoutdegradingtheexperimentallateral

res-olution[11].Theextractorvoltagewassetat12kVandthecontrast

aperturewascloseddownto70␮m,givingalateralresolution

bet-terthan70nm.Theoverallenergyresolutionincludingtheband

widthofthephotonbeamwas0.1eVforthethresholddata,as

mea-suredattheFermilevelofasilversinglecrystalsample.Thelatter

wasalsousedtocalibratethephotonenergy.

Thresholdimageserieswereacquiredasafunctionofthe

photo-electronenergyreferencedtotheFermilevel,E−EF.Thetake-off

orkineticenergyisthedifferencebetweenthisvalueandthework

function.Atypicalimageis showninFig.4(b). Animageseries

acquiredoverthethresholdspectrumgivesadirectmeasurement

ofthesampleworkfunctionintheﬁeldofview(FoV).Darkandﬂat

ﬁeldimagingeliminatecameranoiseanddetectorinhomogeneity,

respectively. The non-isochromaticity [12] of thePEEM images

wascorrectedbyaparabolicfunctionextractedfromauniformly

dopedsamplearea[13].Thepixelbypixelphotoemissionthreshold

spectrawereﬁttedusingacustomizedMATLABroutinebya

com-plementaryerrorfunction,providinga2Dworkfunctionmapof

theFoVwithastandarddeviationof±0.02eV.Theresultingwork

(4)

Fig.2.(a)AtomicforcemicroscopyimageoftheN+_/P_structure_and_(b)_height_proﬁle_following_the_black_line_in_(a)._The_N+_region_is₂₀_nm_higher_than_the_P_substrate.

Fig.3. (a)SchematicofrealphysicalandelectricaltopographiesoftheN+_/P/N+_(top)_and_P/N+_/P_(bottom)_structures_studied_here_and_(b)_schematic_of_the_deviation_of_the

electronpathspredictedbythephysicalandelectronictopographiesoftheP/N+_/P_structure._(For_{interpretation}_of_references_to_color_in_the_text,_the_reader_is_referred_to_the

webversionofthisarticle.)

N+ _(P)_region_is _4.44_(4.38)_eV._One_would _expect_the_N+ _region

tohavea lower workfunction,however, surfacebandbending

andphotovoltagecaneasilychangethis [14].Thereis also

con-trastbetweenopenandclosedN+ _regions_due _to_biasing_of_the

pnjunctionunderphotoemissionthathasalreadybeendiscussed

[10]. TheSi 2p imageseries wasalso acquiredusing thesame

photonenergy.Atypicalimage(E0−EF=30.50eV,corresponding

toakineticenergyof26.0eV)isshowninFig.4(c).

Fig.4.(a)OpticalmicrographofN+_/P_silicon_sample_showing_the_micron_scale_doped_pattern_used_in_this_work,_(b)_typical_energy_ﬁltered_threshold_PEEM_image_for_a_take-off

energyof0.1eV,(c)energyﬁlteredimageattheSi2pcorelevel(h=128.9eV,E−EF=26.0eV)and(d)workfunctionmapobtainedfromapixelbypixelcomplementary

(5)

7.0 6.0 5.0 position (μm) (c) 26.0 eV

Intensity (arb. units)

7.0 6.0 5.0 (b) 0.5 eV 6.0 5.0 4.0 (a) 0.1 eV 14.0 13.0 12.0 position (μm) 15.0 14.0 13.0 13.0 12.0 11.0 P/N+ N+/P

Fig.5. Intensityproﬁles(bluecircles)oftheleftandrighthandjunctionsofP/N+_/P

structureattake-offenergiesof(a)0.1eV,(b)0.5eVand(c)26.0eV.Errorfunction ﬁtstotheproﬁleareshownasredlines.Thetake-offenergyismeasuredwithrespect tothevacuumlevelE0oftheN+region.(Forinterpretationofreferencestocolorin

thisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

TomeasurethewidthoftheP/N+_/P_structure_{complementary}

errorfunctionshavebeenusedtoﬁttheintensityproﬁlesofthe

leftandrighthandjunctions.TheresultsareshowninFig.5.The

widths,asdeducedfromtheﬁtsinFig.5are(a)7.95,(b)7.82and(c)

7.65␮mfortake-offenergiesof0.1,0.5and26.0eV,respectively.

Thus,thewidthof thestructureasdeterminedfromthe

inten-sityproﬁleattheSi2pcorelevelgivesanidenticalvaluetothat

oftheopticalmicrograph,whereasthemeasurementsat

thresh-oldgivesigniﬁcantlylargervalues,inagreementwiththebehavior

shownintheschematicofFig.3(b).Thebuilt-inﬁeldsweeps

elec-tronstowardsthen-typeregions,reducingtheintensityfromthe

p-typeregionnearthejunction.Awidthmeasurementbasedonthe

intensityproﬁlewillthereforegivealargervaluethantheactual

physicalwidth.However,thisbehaviorneedstobequantiﬁed,both

intermsofelectricalandphysicaltopographyandistheaimofthe

simulationspresentedinthenextsection.

3. Simulations

3.1. Model

ThePEEMcontrastobservedatthejunctionhasbeen

numer-ically simulated using the standard industry code SIMION [15]

which traces the motion of charged particles in an electric

ﬁeld using a fourth-order Runge–Kutta integrator. We have

Fig.6.ElectronopticsmodelusedtosimulatetherealPEEMoptics:(a)PEEMoptical elements,(b)SIMIONoverviewofelectronpathsand(c)zoomonthePEEMﬁrst elementsincludedinthesimulations.Theredarrowsshowthepositionoftheplanes usedtoimagethesimulatedelectrondensities.(Forinterpretationofreferencesto colorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

approximatedthePEEMbyasample(thecathode),asingle

elec-trostaticlens,acontrastapertureinthefocalplaneandthescreen,

asshowninFig.6.Energyﬁlteringisobtainedbydeﬁningthe

take-offenergyofthephotoelectrons.Althoughtheelectronopticsare

simpliﬁed compared totheNanoESCA instrument (notablytwo

projectivelenses,atransferlensandanalyzerentranceandexitslits

shouldbeadded),theydoreproducetheessentialcharacteristicsof

anenergyﬁlteredPEEMwithacontrastapertureinthefocalplane.

Causticeffects,observedinlowenergyelectronmicroscopy,arenot

included,i.e.weassumeonlydeviationsintheplaneperpendicular

totheopticalaxis[8].Thisisreasonablesincetheenergyﬁltering

preventssimultaneousimagingofphotoelectronsinabandwidth

greaterthantheenergyresolutionofthePEEM.

Theelectronsaresimulatedbyanarrayofpointsources

dis-tributed across the sample surface; each point source has 11

differentstartinganglesfrom₋₁₀◦to+10◦in2◦steps.Thebuilt-in

potentialduetothepnjunctionissimulatedbyanarrayof

lin-earvoltagedropsacrossthedepletionwidth.ThecentralPorN+

regionwas7.65␮mwide,correspondingtotheoptically

deter-minedwidth.Theelectronintensitydistributioncanbeextracted

atanyplaneperpendiculartotheelectronopticalaxis,inparticular

justabovethesamplesurfaceandatthescreenpositionasindicated

bythethick(red)arrowsinFig.6(b).Thisallowsdeterminationof

theinﬂuenceofthecontrastapertureontheintensitydistribution

inthePEEMimage.Totestofthevalidityofourelectronoptics

wehavecalculatedthemagniﬁcationofthePEEMsimulationas

afunctionoftake-offenergy,i.e.electronkineticenergy,deﬁned

astheelectronenergyabovethreshold,measuredexperimentally.

TheresultsareplottedinFig.7andcompared,usingalinear

scal-ingfactor,tothecalculatedmagniﬁcationofthePEEMoptics(solid

line).

Theseinitialsimulationsonlytakeaccountoftheeffectofthe

built-involtageacrossthejunctionandtheelectronopticsofthe

PEEMcolumn.Theydonotsimulate,forexample,the

photoelec-tronyield.Anempiricalcorrectionforthiseffectwillbeintroduced

below.Furthermore,theworkfunctionvariesslightlybetweenN+

andPregions,thesimulationofaPEEMimagetakenataﬁxedE−EF

valuethereforerequirestheuseofdifferentphotoelectrontake-off

(6)

2.7 2.6 2.5 2.4 100/Mag 200 100 0 KE (eV)

Fig.7.Simulatedmagnification(circles)obtainedusingthesimplifiedimaging col-umncompared,usingalinearscalingfactor,withthecalculatedmagnification(solid line)ofthefullPEEMelectronopticsasafunctionofkineticenergy.

3.2. Results

Asaﬁrststepwecalculatethedeviationoftheelectronsdue

tothelateralelectricﬁeldandthephysicaltopography,without

takingintoaccounttake-offenergydifferencesorelectronyield.

InFig.8weshowthesimulatedelectronintensityoftheN+_/P/N+

andP/N+_/P_structures_in_a_plane_just_above_the_sample_and_as

mea-suredonthescreen,i.e.inthepositionsdeﬁnedbytheredarrows

inFig.6(b).Aﬁvepointnearestneighborsmoothingisdonetothe

simulatedrawdata.Asintuitivelyexpected,electronsaredeviated

fromthep-typeregionnearthejunctiontoreinforcetheintensity

onthen-typesideinbothcases.Thisgivesrisetoadarkstripeonthe

p-typesidewithanadjacentbrightstripeinthePEEMimageofthe

junctionwithoutthecontrastaperture,aspreviouslyobservedand

predictednumerically[16].Theintroductionofarealisticcontrast

aperturecenteredinthefocalplanewithrespecttotheelectron

opticalaxisactsasanangularselectorandcutsoffstrongly

devi-atedelectrons.We haveuseda70␮mcontrastaperture which

givesahighspatialresolutionasrequiredintheexperiment.The

intensitydistributionobservedonthescreenmodiﬁes

consider-ablywithrespecttothatintheabsenceofacontrastaperture,as

canbeseenfromthedarker(blueandred)curvesinFig.8.The

majoreffectofthecontrastapertureistosuppressthebrightstripe

duetohighlydeviatedelectrons;however,italsodisplacesthedark

stripefurtherintothePdopedregion.Infact,withorwithoutthe

contrastapertureitisdifﬁculttoaccuratelymeasurethejunction

position.

Thecut-off effectof thecontrastaperturehasbeenchecked

experimentally.WeshowinFig.9thresholdimagesofthesame

structurewitha70␮mcontrastapertureincenteredandoff

cen-terpositionswithrespecttotheelectronopticalaxisofthePEEM

column.Theintensesignalduetothehighlydeviated electrons

iscutbythecenteredcontrastaperturewhereasintheoffcenter

positionsthereisalmostaperfectsymmetry,withthebrightlines

observedintheNdopedregions.Theseimageswereobtainedon

aP+_/N_patterned_sample,_but_as_can_be_deduced_from_the

simu-lationsinFig.8thisdoesnotqualitativelychangethecut-offof

thehighlydeviatedelectronsbythecontrastaperture.The

simula-tionsthereforereproducequalitativelytheexperimentaldeviation

ofthephotoemittedelectronsby thebuilt-in junctionﬁeld. For

thecomparisonofthesimulationswithexperiment,wefocuson

theP/N+_/P_structure._In_order_to_evaluate_the_effect_of_the

phys-icaltopography we have repeatedthesimulations of Fig.8 for

theP/N+_/P_structure _with_and_without_the_{experimentally}

mea-sured step of 20 nm. The results are shown in Fig. 10(a) for

theelectrondensityjustabovethesampleandin Fig.10(b)for

electron intensity on the screen with the contrast aperture in

place.

FromFig.10(a)thephysicalandelectricaltopographieswork

inoppositedirections.Thebrightstripeduetothebuilt-in

elec-tricﬁeldisinsidetheN+_area,_whereas_for_only_a_physical_height

differenceof20nmatthejunctionabrightstripeiscreatedon

thePsideofthejunction.Onthescreen(Fig.10(b))thecontrast

aperturehascutoffthehighlydeviatedelectronsattheoriginof

thesestripesandweseethatthemodiﬁcationofthePEEMimage

isdue,inthiscase,principallytothebuilt-inelectricﬁeld,although

thevariation intheintensityproﬁleacrossthejunctionis

par-tiallycompensatedbythephysicaltopography.Inthefollowing

wewillthereforeconsideronlytheeffectofthebuilt-inelectric

ﬁeldalthoughitshouldbeborne inmindthatlargerheight

dif-ferencesatajunctionwouldsigniﬁcantlyaffectthemeasurement

ofthestructurewidth.AscanbeseenfromFig.8inthepresence

ofacontrastaperture,thebrightdeviatedintensityissuppressed

andthereisadipintheintensityonthescreeninside(outside)

thecentralP(N+₎_structure._The_physical_junction_position_is_close

totheouter(inner)edgeofthisdiprespectively.Thus,depending

onthecriterionusedexperimentallytopositionthejunction,the

measuredwidthwillbedifferent.Forexample,iftheoutsideedge

Fig.8.Simulatedphotoelectrondensityemittedfromthesamplesurface(lightblueandredlines)andonthePEEMscreenafterpassingthroughthecontrastaperture(dark lines)forthe(a)N+_/P/N+_and_(b)_P/N+_/P_structures._The_pattern_dimensions_on_the_screen_are_given_with_respect_to_the_sample_surface_using_the_PEEM_objective_{magniﬁcation.}

Thecontrastaperturesuppressesthebrightstripeduetohighlydeviatedelectronsanddisplacesthelowone.(Forinterpretationofreferencestocolorinthisﬁgurelegend, thereaderisreferredtothewebversionofthisarticle.)

(7)

Fig.9. BrightanddarkﬁeldPEEMimagesofaP+_/N_sample_obtained_by_varying_the_position_of_the_contrast_aperture._When_the_contrast_aperture_is_off-center_with_respect

totheopticalaxis,thebrightstripeduetothedeviatedelectronsbecomesclearlyvisible.

ofthedipisusedthenthestructurewidthwillappearlargerthan

therealphysicalwidth.Thesimulationsusedtocomparewiththe

experimentalresultstakeintoaccounttheintensitydifferencesby

empiricallyincludingagradientofthenumberofphotoelectrons

acrossthedepletionregionforeachtake-offenergy.Theintensity

fromthePregionisalwaysgreaterthanthatfromtheN+_region

intheimagesusedforcomparisonwiththesimulations.Wehave

thereforearbitrarilysetthehigher,Pintensityattwicethe

num-berofparticles(108every10nm)intherangeof−10◦_/+10◦_as_the

lowerN+_intensity_emission₍₅₄_particles_every₁₀_nm_in_the_range

of₋₁₀◦/+10◦).Notethatweassumethatthelateralelectricﬁeld

duetothebuilt-injunctionvoltageisdeterminedbytherelative

dopinglevelswhereasthetake-offenergyismeasuredwithrespect

totheexperimentallydeterminedthresholdenergy.

Thesimulatedproﬁles,takinginto accountthebuilt-inﬁeld,

physicaltopographyandthedifferentlevelsofintensityintheP

Electron density (arb. units)

-8

-6

-4

-2

0

2

4

6

8 Position (

μm)

(b)

_screen

Electron density (arb. units)

-8

-6

-4

-2

0

2

4

6

8 (a)

sample

Fig.10.Simulatedphotoelectronintensityemittedfrom(a)thesamplesurface and(b)onthePEEMscreenafterpassingthroughthecontrastapertureforthe P/N+_/P_structure_with_physical_(blue),_electrical_(orange)_and_physical_and

elec-tricaltopographies(red)topography.Atake-offenergyof0.1eVwasused.The contrastaperturesuppressesthebrightstripesduetohighlydeviatedelectrons. Thesimulatedprofilenearthesamplesurface(a)showsthatphysicalandelectrical topographiesworkinoppositedirectionswhereasthescreenprofileshowsthatin thiscase,theelectricaltopographydominatesthedistortionofthePEEMimage.(For interpretationofreferencestocolorinthisfigurelegend,thereaderisreferredto thewebversionofthisarticle.)

Intensity (arb. units)

-4.4

-4.0

Position (

μm)

4.4

4.0 (b)

_{0.1 eV}

0.5 eV

26.0 eV

Intensity (arb. units)

-4

-2

0

2

4 Position (

μm)

(a)

_{0.1 eV}

0.5 eV

26.0 eV

Fig.11.(a)Simulatedintensityproﬁlesattake-offenergiesof(fromtoptobottom) 0.1,0.5and26.0eVoftheP/N+_/P_structure._The_vertical_dotted_lines_represent_the

realjunctionpositionasdeterminedfromopticalmicroscopy.Simulationsinclude variationinthetake-offenergyacrossthejunction,20nmphysicaltopographyand varyingelectronyielddeﬁnedbythemeasuredthresholdshiftand(b)close-upsof thesimulatedintensityproﬁlesacrosstheleft(P/N+₎_and_right_(N+_/P)_hand_junctions

in(a).

andN+_regions _via_a _gradient_of_emitted_particles_are_shown_in

Fig.11(a)for0.1,0.5and26.0eV.Theverticaldottedlinesindicate

thejunctionpositionasmeasuredbyopticalmicroscopy.Thelower

panelshowsclose-upsofthesimulatedintensityproﬁleacrossthe

leftandrighthandjunctions.Asthetake-offenergyincreases,the

effectivewidthoftheN+_central_structure_as_measured_from_the

intensityproﬁledecreases,in agreementwiththeexperimental

data.Thesemoresophisticatedsimulationsatthresholdconﬁrm

thepositionoftheintensitydipwithrespecttothephysical

junc-tionpositionseeninFig.8.Theapparentwidthofthestructure,as

determinedfromaﬁttothefastestchangingpartoftheintensity

proﬁle,shrinksby0.35␮mbetweenatake-offenergyof0.1eVand

26.0eV.Thechangeintheapparentwidthisofthesameorderas

thedepletionregiononthePsideandtwoordersofmagnitude

greaterthanthedepletionregionontheN+ _side_of_the_junction.

FortheSi2pproﬁle(take-offenergy26eV)theedgesofthe

inten-sityproﬁleofthecentralN+_region_coincide_with_the_real_junction

(8)

12

10

8

6

4 Position (

μm)

Intensity (arb. units)

(a)

(b)

(c)

7.65 μm

7.82 μm

7.95 μm

Fig.12.Fullexperimentalintensityproﬁlesattake-offenergiesof(a)0.1,(b)0.5 and(c)26.0eVoftheP/N+_/P_structure_used_to_obtain_the_proﬁles_in_Fig.₅_._The_width

oftheN+_region_as_found_from_the_error_function_ﬁts_in_Fig.₅_is_indicated_in_each

case.

4. Discussion

Fig.12showsthewholeexperimentalintensityproﬁlesusedto

fortheﬁtsinFig.5.Theexperimentalproﬁleacrossthejunction

ismuchbroaderthaninthesimulation.Thismaybeduetothe

factthattheexperimentalenergyresolution,0.1eV,isthesameas

thelowesttake-offenergyconsidered.Lowtake-offenergy

elec-tronsareexpectedtobethemostsensitivetolateralﬁeldsacross

thejunction[6].Theﬁnitebandpassmeansthat inthe

experi-mentelectronswithtake-offenergiesvaryingoverapproximately

0.1eVarerecordedinthesameimage.Therewillthereforebea

spreadinthedeviationoftheelectronsbythebuilt-inﬁeld,

broad-eningtheintensityproﬁlemeasuredacrossthejunction.Theeffect

oftheexperimentalresolutioncanbeseeninFig.13.Weshow

twoimagesfromthethresholdseries,Fig.13(a)isrecordedatthe

valueoftheN+_work_function_(4.44_eV)_whereas_Fig.₁₃_(b)_is_the

imageobtainedat4.24eV.Thedopedregionsaredarkbutthere

arestillbrightstripesfromnearthejunctions.E0−EF=4.24eVis

morethantwicetheenergyresolutionbelowtheworkfunctionso

thattheimageshouldbeuniformlydark.However,photoelectrons

deviatedbythebuilt-inﬁeldatthejunctionwillhaveaneffective

take-offenergylowerthanelectronsemittedfarfromthejunction.

TheywillthereforebeimagedatlowerE−EF,whichiswhatwe

observe.Theworkfunctionmapalsoshowselectronemissionat

lowerE−EF.Notethatthiscannotbeduetoﬁeld-enhanced

emis-sionduetothe20nmstepbetweenthePandtheN+_regions_since_it

isnotpresentatthejunctionbetweentheinnerN+_region_and_the_P

region.Verylowenergyelectronsarethereforedoublyunsuitable

fordirectmeasurementsofdopedpatterndimensions.Ontheone

handtheyarethemoststronglyaffectedbythebuilt-inﬁeld,and

ontheotherhand,iftheenergyresolutionissimilartothetake-off

energy,therewillbeanadditionalspreadoftheelectronpaths.

Thewidthofthecentralstructureapproachestherealphysical

valueof7.65␮mfor26.0eV.However,unfortunately,thesignal

tonoiseratiooftheintensityproﬁleat26.0eVisalsomuchlower.

ThisistobeexpectedforPEEMimagingofacorelevelwithrespect

tothresholdelectrons.A moreaccuratemeasurementtherefore

requiresnotonlyhightake-offenergybutalsomuchlonger

count-ingtimeinordertoobtainareliablevalue.Itshouldbeemphasized

thatthedifferencesobservedinthemeasurementofthejunction

positionareabsolutevalues.Theydonotdependonthewidthof

thestructureitselfbutonthevalueofthebuilt-inﬁeldacrossthe

junction,inotherwords,ontherelativedopinglevelsoneitherside

ofthejunction.Atthreshold,thedifferenceis0.3–0.4␮m.Thus,if

muchsmallerstructuresaretobeimaged,thedifferencecanbeas

bigorevenbiggerthanthedimensionsofinterest.

Asanillustrationofthis, wehaveimagedadifferentsample

withamuchnarrowerstructureconsistingoftwo100nmwideN+

stripes100nmapartonaPtypesubstrate(Fig.14(a)).Fig.14(b–f)

shows threshold imagesof the structure. Contrast inversion is

observedbetweentheoutlyingp-typesubstrateandthecentral

regioncontainingthen-typestripes.Moreimportantly,however,

apartfromtheimageacquiredforE−EF=4.95eV,thePtypeband

separatingthetwoN+_stripes_is_invisible_in_the_PEEM_image._This

isconﬁrmedbythelocalthresholdspectrainFig.14(g)extracted

fromtheregionsofinterestacrossthestructure.Whereasthe

pho-toemissionthresholdtypicalofthePtypesubstrateisclearlyvisible

farfromthestructure,atthecenteradoublethresholdisobserved

correspondingtoelectronsemittedfrombothPandN+_patterns.

It isthereforeimpossibletoresolve thecentralPbandbecause

ofthebuilt-inﬁeld.Thisisindependentofthelateralresolution

ofthePEEMwhichisbetterthan70nm.Inthiscase,theN+_and

Pdopinglevelsare1020_and₁₀15_atom_cm−3_,_{respectively,}

corre-spondingtoabuilt-involtageof0.914Vandaspacechargeregion

1.10␮mwide.Infact,thecentralPstructureisfullydepletedand

thestructureactsasa300nmN+_stripe_for_imaging._Most_patterns

willfallbetweenthetwoextremesillustratedhere.Whenusing

thresholdelectronsgreatcaremustbetakeninordertodeduce

Fig.13. ThresholdPEEMimagesrecordedat(a)E− EF=4.44eV(theworkfunctionvalue)and(b)E0−EF=4.24eVshowingthattheintensityatE−EFbelowtheworkfunction

(9)

Fig.14. (a)Structurecomposedof100nmN+_and_P_stripes,_(b–f)_samples_of_the_threshold_image_series_showing_that_the_structure_reacts_as_a₃₀₀_nm_N+_stripe_in_imaging

modeand(g)thresholdspectraextractedfromimageseries.Thedoublethresholdforthelocalspectraofthestripestructureshowsthecontributionofelectronsfromboth PandN+_regions.

dimensionsinthepresenceofstructureswithanbuilt-inlateral

ﬁeld.Thiswillbethecaseforalmostallpatternedsemiconducting

samples.Moregenerally,anypotentialasymmetrywillgiveriseto

alateralﬁeld.Forexample,atferroelectricdomainwallstherecan

beastronglateralﬁeldinducedbysurfacechargeofoppositesign,

proportionaltothepolarizationdifferencebetweentwodomains.

Fromthesimulationsitisapparentthattake-offenergiesofmore

thanafeweV(here26.0eV)aresufﬁcienttominimizetheeffect

ofbuilt-inﬁelds.Onemethodcouldbetosystematicallyimagethe

samestructureasafunctionoftake-offenergytodeterminethe

valueatwhichtheapparentsizenolongerchanges.Deviationof

theelectronpathsbyanbuilt-inlateralﬁeldcouldalsobeusedto

measuretheﬁeldstrength.Thiswouldrequireacompleteelectron

opticsimulationofthePEEMinstrument.Inthepresentsimulations

wehaveusedrealisticsample-to-objectivedistance,objectivelens,

contrastapertureandPEEMmagniﬁcation.Theseappearsufﬁcient

toreproducetheessentialbehaviorofthelowenergyelectrons.A

morequantitativeapproachwouldrequiresimulationofthefull

PEEMoptics,includingtheeffectoftheanalyzerentranceslitand

passenergy,inotherwords,thephasespacelossbetweenthePEEM

columnandtheenergyanalyzer.Themethodcouldthenbeapplied

tomeasuresurfacedopinglevelsandhencethedepletionwidthof

apnjunction,asdiscussedrecentlyusingthesecondaryelectron

signalfromascanningelectronmicroscope[17].

5. Conclusions

Wehavecarriedoutaquantitativestudyoftheeffectof

elec-tricaland physical topography on thewidth of N+ _and _P _type

regionsinaP/N+_/P_structure_as_measured_by_PEEM._At_threshold

theexperimentallydeterminedwidthsaresigniﬁcantlylargerthan

therealphysicalwidth.Asthetake-offenergyincreases,the

mea-suredwidthdecreases.At26.0eVanintensityproﬁleofthePEEM

imagegivesanaccuratemeasurementofthestructure.Wehave

simulatedthePEEMcathodelens,andincludedtheexperimentally

determinedbuilt-involtagesandphysicaltopographyofthe

sam-ple.Dependingonthesignofthelatter,thetwocontributionscan

actinthesameorinoppositedirectionsonthePEEMmeasured

dimensions.TheN+ _region_is₂₀_nm_higher_than_the_P_substrate

givingatopographywhichactsintheoppositesensetothe

built-inﬁeldatthejunctionbutdoesnotqualitativelychangethetrendin

structurewidthasmeasuredbyPEEM.Knowledgeofthephysical

topographyandoneofthedopinglevelscouldbeusedtodetermine

thesurfacedopinglevelontheothersideofthejunction.These

conclusionscouldbeextended tothemore generalcaseof any

electricalasymmetryimagedbyPEEM,forexample,aSchottky

bar-rierorferroelectricdomainwall.Moredetailedsimulationscould

includeboththeintensityandtheshapeofthethresholdspectra,for

exampleusingHenkesmodelforthesecondaryelectrontail[18].At

lowtake-offenergies,highspectroscopicresolutionismandatory.

ForafullyquantitativemodelofPEEMimagingofstructureswith

lateralelectricﬁelds,electronopticssimulationsshouldincludethe

fullPEEMcolumnandtheenergyﬁlter.

Acknowledgments

WethankFOCUSGmbHforcompanydataonthePEEMoptics.

M.L.beneﬁtedfromaCEAPh.D.grant.Theworkwassupportedby

theFrenchNationalResearchAgency(ANR)throughtheRecherche

TechnologiquedeBase(RTB)program,andwaspartlyperformed

intheMinatecNanocharacterizationCentre.WethankSOLEILfor

provisionofSRfacilitiesandtheTEMPOstafffortheirhelp.

References

[1]R.J. Phaneuf, H.-C. Kan, M. Marsi, L. Gregoratti, S. Günther, M. Kiski-nova, J. Appl. Phys. 88 (2) (2000) 863, http://dx.doi.org/10.1063/1. 373748,http://link.aip.org/link/JAPIAU/v88/i2/p863/s1&Agg=doi

[2]A.Bailly,O. Renault,N.Barrett, T.Desrues, D. Mariolle,L.F.Zagonel, M. Escher, J. Phys. Conden. Matter: Inst. Phys. J. 21 (31) (2009) 314002, http://www.ncbi.nlm.nih.gov/pubmed/21828563

[3]M.Giesen,J.Phaneuf,E.D.Williams,T.L.Einstein,Surf.Sci.396(100)(1998) 411–421.

[4]L. Frank, I. Müllerová, D.A. Valdaitsev, A. Gloskovskii, S.A. Nepijko, H.-J. Elmers, G. Schönhense, J. Appl. Phys. 100 (9) (2006) 093712, http://link.aip.org/link/JAPIAU/v100/i9/p093712/s1&Agg=doi

[5]S.A.Nepijko,N.N.Sedov,G.Schönhense,M.Escher,J.Microsc.206(Pt2)(2002) 132–138,http://www.ncbi.nlm.nih.gov/pubmed/12000552

[6]S.Nepijko,N.N. Sedov,O. Schmidt, G. Schönhense,X.Bao, W.Huang, J. Microsc.202(Pt3)(2001)480–487,http://www.ncbi.nlm.nih.gov/pubmed/ 11422670

[7]H.-C. Kan, R.J. Phaneuf, J. Vacuum Sci. Technol. B: Microelectron. Nanometer Struct. 19 (4) (2001) 1158, http://link.aip.org/link/JVTBD9/ v19/i4/p1158/s1&Agg=doi

[8]S.M.Kennedy,C.X.Zheng,W.X.Tang,D.M.Paganin,D.E.Jesson,Ultramicroscopy 111(5)(2011)356–363,http://www.ncbi.nlm.nih.gov/pubmed/21334287 [9]M.H.Hecht,Phys.Rev.B41(11)(1990)7918–7922.

[10]M. Lavayssière, O. Renault, D. Mariolle, M. Veillerot, J.P. Barnes, J.M. Hartmann, J. Leroy,N. Barrett, Appl.Phys. Lett. 99(20)(2011) 202107, http://link.aip.org/link/APPLAB/v99/i20/p202107/s1&Agg=doi

[11]M.Escher,N.Weber,M.Merkel,C.Ziethen,P.Bernhard,G.Schönhense,S. Schmidt,F.Forster,F.Reinert,B.Krömker,D.Funnemann,J.Phys.:Conden. Matter17(16)(2005)S1329–S1338,doi:10.1088/0953-8984/17/16/004. [12] M.Escher,K.Winkler,O.Renault,N.Barrett,J.ElectronSpectrosc.Relat.

(10)

[13]F.delaPena,N.Barrett,L.F.Zagonel,M.Walls,O.Renault,Surf.Sci.604(19-20) (2010)1628–1636,doi:10.1016/j.susc.2010.06.006.

[14]N. Barrett, L.F. Zagonel, O. Renault, a. Bailly, J. Phys. Conden. Matter: Inst.Phys.J.21(31)(2009)314015,http://www.ncbi.nlm.nih.gov/pubmed/ 21828576

[15]S.I.S.Inc.SIMION3d.http://simion.com/

[16]S.A.Nepijko,A.Gloskovskii,N.N.Sedov,G.Schönhense,J.Microsc.211(2003 April)89–94.

[17]J.T.Heath,C.-S.Jiang,M.M.Al-Jassim,J.Appl.Phys.111(4)(2012)046103, http://link.aip.org/link/JAPIAU/v111/i4/p046103/s1&Agg=doi

[18]B.L. Henke, J.A. Smith, D.T. Attwood, J. Appl. Phys. (1977) 1852, http://link.aip.org/link/JAPIAU/v48/i5/p1852/s1&Agg=doi.