The Independence of Isotropic Stress Evolution and Anisotropic Pattern Formation During Ion Bombardment of Silicon
Senior Thesis | 2026
The Independence of Isotropic Stress Evolution and Anisotropic
Pattern Formation During Ion Bombardment of Silicon
ArmaanMehta
Abstract:
Ar⁺ ionbombardmentcanleadtotheformationof self-organizednano-ripplepatternsonSisurfaceundercertainion irradiationconditions.Therearesomeexistingtheoreticalmodels thatattributethepatternformationtothedevelopmentofsurface stress.Inthisexperiment,weobservedthestressevolutionofSi (100)wafersunderlowenergy(250and500eV)Ar⁺ ion bombardmentwitha60°incidentangleatroomtemperature.This waswithintheregimeofself-organizednanopatterning,andwas investigatedusingtherealtimeMulti-beamOpticalStressSensor (MOSS)method.Ourstressdevelopmentismotivatedbythe recentresultsshowingtheindependenceofstressandthe nano-rippleformation.However,theseresultsshowedatrace amountofimpuritiesfromthestainlesssteel(Fe,CrandNi)were co-depositedonthesamplesurfaceduringtheionbombardment. Inourexperiment,sampleswerekeptcleanfromanymetal
contaminationduringtheionbombardment.Thesurface compositionsoftwotypesofsamplesweremeasuredbyX-ray PhotoelectronSpectroscopy(XPS).
Undercleanbombardmentconditions,stresswasfoundto evolveisotropicallyinboththex-andy-directions,while post-bombardmentAtomicForceMicroscopy(AFM)revealed strictlyanisotropicripplepatternsorientedparalleltotheionbeam projectiondirection.Thisdirectionalmismatchbetweenstress evolutionandsurfacepatterningconfirmstheirindependence,and demonstratesthatthisindependenceisanintrinsicpropertyofthe ionbombardmentprocessratherthananartifactofmetal contamination.Thesefindingssuggestthatstress-driven mechanismsaloneareinsufficienttoexplainnano-ripple formation,motivatingfurtherinvestigationintoalternative mechanismssuchascurvature-dependenterosionandion-induced massredistribution.
Introduction:
Siliconisthefoundationofmoderndayelectronicsand computers,usedthroughoutthesemiconductorindustryandeven infiberopticsandsolarenergy.1 Essentialtoconductingresearch onSiandmanipulatingSiforitsindustryusesareionsources, whichareusedinawidearrayofprocessesfrometchingand dopingtothinfilmgrowth.However,arecentlyobserved phenomenonoftheseionsourcesisaself-organizedsurface patterningonthematerialssurface.Inparticular,this self-organizedpatternhasmainlybeeninvestigatedintheion bombardmentofSibecauseofitsabundance,astableoxidelayer andbalancedelectricalproperties(nottooconductiveandnottoo insulating)2.Thispatterningisdependentontheconditionsthatthe materialisbeingsubjectedtoduringbombardment,inparticular angleofincidence.IthasbeennotedthatwhenAr+ionsbombard
1HitachiHigh-TechCorporation,“3.TheSemiconductorMaterial Silicon,”HitachiHigh-TechCorporation,n.d., https://www.hitachi-hightech.com/global/en/knowledge/semicondu ctor/room/about/silicon.html.
2 HitachiHigh-TechCorporation,“3.TheSemiconductorMaterial Silicon,”HitachiHigh-TechCorporation,n.d., https://www.hitachi-hightech.com/global/en/knowledge/semicondu ctor/room/about/silicon.html.
Siinthelow-energyregime,whereenergyrangesfrom200eV to1000eV,atanincidentangleθ≈45-48°,thesurfaceis smoothened.3 However,forθ≥θc,ripplepatternsformparallel totheionbeamprojectiondirection,andforθ≥80°,the patternsformperpendiculartothebeamdirection.
Althoughcurrentresearchunderstandshowtheseincident angleschangethenano-patterns,theunderlyingmechanismbehind thenano-patternformationisnotunderstood.Byunderstanding thisunderlyingmechanismandhencebeingabletomoreprecisely controlthesepatterns,manufacturerscanfitmoretransistorsona chip,makingitfasterandmoreenergy-efficient.4 Furthermore, controllingthesenano-ripplepatternscanhelpwithcreatingmore detailedanti-reflectivecoatings,opticalfilters,sensors,oreven makingbettercameralensesanddisplays.Inaddition,techniques
3 R.CuernoandJ.-SKim,“APerspectiveonNanoscalePattern FormationatSurfacesbyIon-BeamIrradiation,” Journal of Applied Physics 128,no.18(November9,2020), https://doi.org/10.1063/5.0021308.
4 RoyalSocietyofChemistry,“Silicon-ElementInformation, PropertiesandUses|PeriodicTable,”Rsc.org,2017, https://periodic-table.rsc.org/element/14/silicon.
likephotolithography,EUVlithography,andatomiclayer depositionrelyonunderstandingnanopatternstoetchandbuild structuresaccurately.
Onetheorythatattemptstoexplainthebehaviourofthis nano-patterninginionbombardmentistheBradley-Harpertheory.
TheBradley-Harpertheorystatesthattheerosioncausedbythe bombardmentdependsonthelocalsurfacecurvature,whichmeans thattheconcaveregionserodefasterthanconvexregionswhenthe ionbeamisnear-normalincidence.5 Thisdifferenceinerosion causessurfacerougheningandeventualpatternformation.
However,theBradley-Harpertheorycannotaloneexplainthese nanopatterns.WhiletheBradley-Harpertheorysuccessfully predictspatternformationatcertainangles,itsfailuretoaccount fortheobservedsmoothingbehavioratnear-normalincidenceand itsinabilitytoexplainangle-dependentpatternorientationsuggests thatadditionalphysicalmechanisms,particularlystress-related processes,mustplayacriticalroleindeterminingsurface
5 R.MarkBradleyandJamesKHarper,“TheoryofRipple TopographyInducedbyIonBombardment”6,no.4(July1,1988): 2390–95,https://doi.org/10.1116/1.575561.
evolutionduringionbombardment.Competingapproachesto understandingtheobservedbehaviorhaveattributedsmoothening andpatternformationtostressdevelopment,solookingatother modelsdependingonstressisessential.
Figure1:Stressregimesinthinfilmsystems.Compressivestress (left)causesupwardcurvatureasthesubstratecompressesandfilm stretches.Tensilestress(right)causesdownwardcurvatureasthe substratestretchesandthefilmcompresses.
DuringtheionbombardmentofSi,itisknownthatthe impactoftheionsonthesurfacegeneratesinternalforces,and theseforcesarewhatresultsinstress.Stressisdefinedasforceper unitareaasitdescribestheintensityofinternalforcesatanypoint
inthematerial.Stressisdividedintotworegimes:the Compressiveregime,andtheTensileregime(Figure1).Inthe Compressiveregime,thesubstrateisbeingcompressedandasa resultthethinfilmisbeingstretched,whereasintheTensile regime,thesubstrateisbeingstretchedandthethinfilmisbeing compressed.Themechanismthatresultsin compressivestressis thatwhenionshitthesurface,thematerialbecomesamorphous andtheionsareimplanted,causingthematerialtoexpand isotropically(uniformlyineverydirection).6 Ontheotherhand,it isbelievedthatfor tensilestress,incomingionsessentially hammeratomsintothesurface,creatingcompressiononthethin filmasatomsgetpackedtogetherinthebombardmentdirection whilethematerialexpandssideways.7
6 TeamXometry,“CompressiveStress:Definition,Unit,Formula, andExample,”www.xometry.com,April6,2023, https://www.xometry.com/resources/3d-printing/what-is-compressi ve-stress/.
7 MiaojunSunetal.,“ExperimentalStudyonAxialStressand HammerImpactingEnergyofOffshoreStandardPenetrationTest,” Applied Sciences 13,no.17(August22,2023):9487–87, https://doi.org/10.3390/app13179487.
Investigatingstressasoneofthekeymotivatorsbehindthe nano-ripplepatternsisarecentidea.Asaresult,thereisnotyeta fullunderstandingofhowstressaffectsthesepatterns.The researchthathasbeenconductedusesaMulti-beamOpticalStress Sensor(MOSS)method,whichisdetailedinmoredepthinthe methodssection.ApreviousstudybyHaojinLi,Ludwig,etal. showedusingaMOSSsystemandAtomicForceMicroscopy (AFM)thatthenano-patternformationwasindependentofstress. However,post-factoX-rayPhotoelectronSpectroscopy(XPS) revealedthatcertainimpurities,inparticularIron,Chromiumand Nickel,possiblyfromtheionsourceorchamberwalls,had accumulatedontothesamplesurface.Inthisexperiment,weaimto understandwhetherthisindependencestillholdsinconditions withoutimpurities.
Methods:
Samplesusedintheexperimentswereboron-dopedSi (100)waferswithathicknessof100μmandresistivityof5-10
Ω·cm.Theywerebombardedat65°by500eV ionswitha ����+ fluxof8.52E12[ ].Duringthebombardment, ������������ 2 �� 1
thermalcontactsilverpaste(MeiVacTP-832)wasappliedtothe entirebackofthesamplestopreventchargefromaccumulating duringionbombardmentandtocontrolthesampletemperature duringthebombardment.Thesesampleslayinavacuumchamber flatonagroundedcopperplate.Tominimizetheeffectintroduced bythesilverpasteonthestressbehavior,thepastewasappliedinto averythinanduniformlayerbetweenthesampleandthecopper plateusingathinwoodentool.Thesilverpasteremainsfluid throughouttheentireionbombardmentprocess,andsoitcanbe assumedthatthesampleswereallowedtodeformfreely throughoutthebombardmentandthatthesilverpastedidnotincur significantmorphologicalchangesduringbombardment.Results frombombardmentswithoutsilverpastedidnotsignificantlydiffer fromtheresultswiththesilverpaste,thussupportingour assumptionthatthesilverpastedoesnothinderthedeformationof thesampleduringbombardment.Althoughthissamplepreparation
didnotdifferfrompreviousresearchinthegroup,weuseda smallerchamberwithadifferentgeometrythatprevented impuritiesfromreachingthesample,whichwastestedforusing post-factoXPS.Inaddition,thebombardmenthappenedundera highvacuum (co-authoredandadaptedwith (10 7������������������) permission,HaojinandBenli.)
Figure2:Multi-beamOpticalStressSensor(MOSS)experimental setupandmeasurementprinciple.(Left)Alaserbeampasses throughanetalontocreateanarrayoflaserbeamsthatreflectsoff theSiwaferontoaCCD(chargedcoupleddevice)camera.The samplesitsonthegroundedcopperplate.(Right)Laserspotarray
patternsontheCCDcamera.Topshowsthereferencearray, whereastheothersshowthedistancechangebetweenthelaserdot andhowitcorrespondstothestressvalues.
Tomeasurethestress,weusetheMulti-beamOptical StressSensor(MOSS)technique,whichisan in situ optical methodthatenablesreal-timemeasurementofstressevolution duringionbombardment(Figure2).Itmonitorsthesurfaceby directingalaserbeamthroughanetalonthatusesreflectiontosplit thelaserintoanarray.Thisarrayconsistsoftwodotsinthe y-directionand4dotsinthex-direction.Asstressdevelopsonthe surface,thesampleundergoesslightbendingorcurvaturechanges. Thesecurvaturechangeswillinturnchangethereflectionangles ofthelaserbeams,andcausethereflectedspotpositionstochange onaposition-sensitivedetectororCCDcamera.
Tointerpretandanalyzethereal-timemoviefromtheCCD Cameraduringthebombardment,weutilizedaclusteringmodel calledK-means.K-meansiterativelyplotsanassignednumberof centroidpositionsandgroupsallpointsintodifferentclusters,each
timeminimizingthedistanceofeachpointtotheircentroid.We firstturnthemovieintoaNumpy-arrayandthenplotthese centroidpositionsontoeveryframe.Usingthesecentroid positions,wethendeterminetheDS(differentialspacing)by calculating where isthespacingbetweenthecentroid
positionswhenthesamplewasflat,beforebombardment,and is�� thecurrentspacingsbetweenthecentroidposition.Using geometricrelationshipsandStoney’sequations,wearriveatthe followingwaystocalculateforstressfromthedifferential spacings:
MOSSoffersseveraladvantagesforstudyingion bombardmentstressbecauseitprovidesnon-contact,real-time measurementswithoutinterferinginthebombardmentprocess.
Themulti-beamsetupallowssimultaneousmeasurementof curvatureinmultipledirections,andallowsdetectionof anisotropicstressdevelopmentinthex-andy-directions,whichis essentialtocomparestresstotheisotropicbehaviourofthe nanopatterns.
However,MOSShasitslimitations.Thetechniquerequires areflectivesurfaceandmeasuresonlythestress-thicknessproduct, notstressindependently.Additionally,thesmallcurvaturechanges inducedbythinion-modifiedlayersapproachthedetectionlimits ofthemethod,requiringcarefulcalibrationandsignalprocessing toextractreliablemeasurements.
Followingtheionbombardment,AtomicForceMicroscopy (AFM)wasusedtoobtainahigh-resolutionimageofthesurface. TheAFMrunsasharpprobetipacrossthesamplesurfacewhile maintainingcloseproximity.Theprobeisacantileverwithan atomicallysharptipattheend.Whenscanning,thecantileverisset intooscillationatornearitsresonantfrequency,causingthetipto vibrateverticallyasitscanslaterallyacrossthesurface.Alaser
beamisreflectedoffthecantileverandontoadetector,oscillating backandforth.Astheoscillatingtipapproachesthesample surface,itexperiencesinter-atomicforces,likevanderWaals forcesandotherelectrostaticforces,thatvarywiththedistance betweenthetipandsurfaceatoms.8 Asaresult,theoscillations changeandsotheAFMisabletodeterminethenanometerscale featuresonthesamplesurface.ThiscapabilitymakesAFM particularlywell-suitedfordetectingandquantifyingtheripple patternsformedduringionbombardment.Itallowstheprecise measurementofripplewavelength,amplitude,andorientation, whichallowsustocomparetheorganizationoftheserippleswith thestress.Inthisexperiment,AFMimagingwasperformed post-bombardmenttocharacterizethesurfacenanostructuresand correlatepatternmorphologywiththestressevolutionmeasuredin real-timeduringbombardment.
Results:
8 ParkSystems,“Non-ContactMode|HowAFMWorks-Principle ofAtomicForceMicroscopy,”YouTube,September22,2023, https://www.youtube.com/watch?v=K9FgPWK3Co4.
Inthefirstthreeexperiments,boron-dopedSi(100)wafers withathicknessof100μmwerebombardedat65°for60minutes andmonitoredusingtheMOSSsystemdescribedinMethods. Afterbombardingfor60minutes,thesamplewasleftinthe vacuumchamberforanother30minuteswhilestresswasstill beingmeasured.Beforebombardmentbegan(whenthesamplewas flat),ourprogramdeterminedthereferencedistancesbetweeneach laserdotinthearray.Thiscalculationtracksthedistancesforthe first300secondsandthenaveragesthosedistancesateveryframe. Thisisthe usedtocalculatethedifferentialspacing,whichis �� 0 correlatedtostressusingStoney’sequationandothergeometric relationships.9
Afteradurationof1000-2000secondsfromthestartof bombardment,aclearcompressivepeakformedinboththe x-directionandthey-direction.Thisinitialcompressivepeakwas consistentwithpreviousobservationsandcanbeattributedto
9 “Conversionofbeamdeflectionmeasurementstocurvature:angle ofincidencecorrectionfordifferentarraygeometries”-Eric Chason(discussedinclassbutcannotseemtofindcitationor journaloranything.)
amorphization-inducedvolumetricexpansionandionimplantation intothecrystallineSisubstrate.10 Incontrasttotheisotropicnature ofthestressdevelopmentinthesample,post-factoAFMstudies revealedanisotropicpatternsonthesurfaceofthesampleasthe ripplepatternsformedonlyparalleltothex-direction.Ultimately, theprogressionofcompressivestressinboththex-directionand y-directionsignalsthattheanisotropicnano-ripplepatternformed isindependentofthestressinduced.
Figure3:X-directionstressevolutionduring60-minuteion bombardmentat65°incidenceangle.Thestressfirstincreasesinto
10 HaojinLietal.,“TheIndependenceofNanopatternFormation andStressEvolutionduringLow-EnergyAr+Bombardmentof Si,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 571(November 30,2025):165958,https://doi.org/10.1016/j.nimb.2025.165958.
thecompressiveregime,thenincreasesatanacceleratedrate peakingatapproximately1.5GPabeforerelaxingafterthe bombardmentends.
Figure4:Y-directionstressevolutionduring60-minuteion bombardmentat65°incidenceangle.Thestressshowsinitial slightcompression,thenstabilizesbetween0.2-0.4GPathroughout themajorityofbombardment.Anotabledecreasetowardzero occursaround4000s.Thegraphitselfismuchnoisierthanthe x-direction.
Figure5:Thisshowsboththex-directionandy-directionstressin thesame60-minuteionbombardmentat65°incidenceangle.This showsthesamefeaturesbutrelativetoeachother,showingthatthe x-directionstresshashighermagnitudethanthey-directionstress.
Figure6:Thisshowsadifferentbombardmentinslightlydifferent conditions.Itisa60-minuteionbombardmentat65°incidence angle,butofathickersiliconsample.Itshowsduring bombardmentbothxandystressareverysimilar,andthatstress actsisotropically.
Toevaluatewhatphysicalrolestressplaysonthesample duringbombardment,thedifferentstagesofthestresscurvesinall fourfigureswereinvestigatedtodeterminetheconnectionbetween stressandthenano-patternsformedonthesurfacebycomparing theisotropicnatureofstresswiththeanisotropicnatureofthe nanopatterns.
Thestagesofastresscurveareclear:asteadyincrease,an acceleratedincrease,apeak,thenfinallyarelaxation(Figure3).It isimportanttonotethatthex-directionstressbeginswithaninitial dipinstressduringthereferenceperiod(thefirst300frames). Althoughstabilitytestsshowedthatdriftingoccurredat insignificantlevels,thisinitialdipbeforebombardmentcould meanexternalstimuliareslightlyaffectingthelaserbeam arrangementandhenceourcalculatedstressvalues.Regardless, thefeaturesofthegraphsoutweighthesmalldrift.Whenthe bombardmentstarts,thex-directionstressincreasessteadilyinto thecompressiveregimereachingroughly0.25GPaatthe2000 seconds(Figure3).Then,thestresscontinuestoincreaselinearly butataquickerrate,peakingatapproximately1.5GPaatthe4000 seconds,beforebeginningtodecreaseasthesamplerelaxes.
Thisrelaxationbehavioursuggeststhatthestressthatis firstintroducedisnotapermanentchangeinthematerialandcan bereversed.Thefactthatstressdoesnotrelaxcompletelytozero indicatespermanentstructuralmodificationstothesilicon substrate,likelyfromthestableamorphouslayerandimplanted
argonionsthatremainafterbombardmentstops.Previousstudies notedthatstresstypicallybecomesmorepositiveuponbeam termination,astrangecompressionthatissomewhatexemplified inthey-directionstressofthisexperiment;howeverthisshouldbe investigatedmore.Theconvergenceofx-andy-directionstressto similarfinalvaluesreinforcestheisotropicnatureoftheresidual stressstate,contrastingwiththedisjointedstressdevelopment observedduringactivebombardment.
Theinitialcompressivedevelopmentwhenbombardment startsisconsistentwithpreviousobservationsandcanbeattributed toamorphization-inducedvolumetricexpansionandion implantationintothecrystallineSisubstrate.However,amajor differencecomparedtopriorwork,whichusedahigherfluxand shortbombardmenttime,isthatthepeakoccurredlaterandfora largerduration(Figure5).Castroetal.demonstratedthat ion-beam-inducedstressdrivesviscousflowinthethinsurface layerofsilicon,amechanismthatoperatesthroughout
bombardment.11 Thesustainedcompressivestressdevelopment talkedaboutearliermayshowcontinuedviscousflowandion accumulationinthisstress-affectedlayer,processesthatwould intensifyoverlongertimedurations.
Althoughthey-directionstressissmallerinmagnitude, stressalsooccurs inthey-direction(Figure6).Unlikethe x-direction,Fig.6showsasmallincreasewhenthebombardment firstbegins,andthenstabilizesbetween0.2-0.4GPa.Whilethis representsonlyapproximately20-30%ofthemaximum x-directionstress,itisnonethelessameasurableandnotablestress development.Thepresenceofnon-zeroy-directionstressis significantbecauseitdemonstratesthatstressgeneration mechanismsoperateinbothdirections(isotropic),althoughwith differentmagnitudes.Despitetheirdifferentpeakmagnitudes,their finalstressvaluesconverge(Figure6).Oncethebombardmenthas
11 Castro,M.,R.Cuerno,L.Vázquez,andR.Gago. "Stress-InducedSolidFlowDrivesSurfaceNanopatterningof SiliconbyIon-BeamIrradiation."PhysicalReviewB86,no.21 (2012):214107.
endedandthematerialhashadtimetorelax,anisotropicresidual stressseemstooccurof0.4-0.5GPa.
Figure7:AFManalysisintheGwyddionsoftware12,showingthat alltheripplesareorganizedinthesamedirectionastheionbeam, andthattherippleheightsare4nm.
AFManalysisthroughGwyddionsoftwareshowstheAFM topographyimageofthesiliconsurfacefollowingtheion bombardmentoftheSi(100)wafer(Fig.7).Therippleheightis
12 Nečas, D., & Klapetek, P. (2012). Gwyddion: an open-source software for SPM data analysis Central European Journal of Physics, 10(1), 181-188
below4nmandtheripplesareorientedparalleltotheionbeam projectiondirection,consistentwiththeoreticalpredictionsfor bombardmentatthisincidentangle.Previoustheoreticalworkby BradleyandHarperpredictedthatrippleorientationdependson incidentangle,withpatternsformingparalleltothebeamdirection atanglesnear60°.13 Consideringthisbombardmentwasat65°,it followsthattherippleorientationwouldbeparalleltotheion beamdirection.However,asanalyzedearlier,stressbehaves isotropically(Fig.6).Comparedtotheanisotropicbehaviourofthe nano-ripples,thedifferenceinbehavioursuggeststhatthe nano-ripplesareindependent.
13 R.MarkBradleyandJamesKHarper,“TheoryofRipple TopographyInducedbyIonBombardment”6,no.4(July1,1988): 2390–95,https://doi.org/10.1116/1.575561.
Figure8:Differentialspacing(DS)evolutionforx-directionlaser beampositionduringionbombardment.Leftandrightpanelsshow DSversustimefortwodifferenthorizontalspacingpairsinthe laserarray.Bothpositionsexhibitidenticalbehavior:aninitial slightdecreasecorrespondingtotheearlycompressivestress develops,reachingmaximumDSvaluesofapproximately 0.030-0.032.
Figure9:Y-directiondifferentialspacingevolutionforthree verticallaserbeamspacingpairs.MaximumDSvaluesof ~0.005-0.008aresignificantlysmallerthanx-directionvalues (Figure8),consistentwithreducedy-stressmagnitude.Generally uniformbehavioracrossallframes.
Toinvestigatethespatialuniformityofstressacrossthe sample,welookedatthedifferentialspacing(DS)acrosseach spacingofthelaserdotarray.TheDSversustimeshowsthe multiplelaserbeampositionsoverthemovie,whereeachpointon
thegraphcorrespondstothecalculatedDSforaframefromthe CCDcameraduringbombardment(Fig,8).Figure8.showsthe y-directionspacingswhereasFigure9.showsthex-direction spacings.Thex-directionDSdatashowsconsistentbehavior acrossallthegraphs.Allshowthesamestages:aninitialslight decreasethatmatcheswiththeearlycompressivedip,followedby anincreasethroughoutbombardmentascompressivestress develops.TheDSvaluesreachmaximumchangesof approximately0.030-0.032.Thisconsistencyindicatesthat x-directionstressdevelopsuniformlyacrosstheentiresample surface,withnosignificantspatialgradientsorlocalizedstress concentrations.
Similarly,they-directionspacingsexhibitasimilar consistencyacrossallspacings,however,theDSvaluesare significantlysmaller.Anotherinterestingfeatureisthatthefirst spacinghasalowersecondpeakat0.001whereasthesecond spacingreachesthetensileregime.Thisslightdifferencecould indicateanon-uniformchange,wheremoreionsareimplantedina certainpartofthesurface.Anotherinterestingcomparisonbetween
thex-spacingsandthey-spacingsisthatthespacingdifference betweeneachconsequentframeismuchlessinthex-spacings, hencetheDSdotsaremoreconcentratedthancomparedtothe y-spacings.Thiscouldmeanthereissomeinstabilityinthe y-direction,perhapscouldbeattributedtohigherlevelsofion implantationandamorphization,meaningthesurfacelayerismore pronetochanges.
Akeydifferenceinourstudyisthatourpost-factoXPS resultsyieldednoimpurities.Theconfirmationthatstressand patternformationremainindependentevenwhenthereareno impuritiesrepresentsasignificantfindingforunderstanding ion-beamnanopatterningmechanisms.PreviousworkbyHaojinLi etal.observedthisindependencebutcouldnotruleoutthe possibilitythatsurfacecontaminationwithiron,chromium,and nickelinfluencedthestress-patternrelationship.14 Usingadifferent chamberandionsource,similarresultswereobtainedunderclean
14 HaojinLietal.,“TheIndependenceofNanopatternFormation andStressEvolutionduringLow-EnergyAr+Bombardmentof Si,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 571(November 30,2025):165958,https://doi.org/10.1016/j.nimb.2025.165958.
bombardmentconditions.Theseresultsdemonstratethatthe isotropicstressdevelopmentandanisotropicpatternformationcan beattributedtotheionbombardmentprocessitselfratherthanany impurities.Asaresult,thisfindingthatstress-drivenmechanisms, althoughisexistentandmaycontributetoothermorphological patterns,doesnotsolelycreatethenano-patternsonthesample surface.Thisworksuggeststhatwemustreturntootherpossible theoreticalmodelsthatincorporateadditionaldirectionalprocesses beyondstressalone.
Itisimportanttonotethatalthoughtheseresultssupport previoushypothesesfromotherresearchandproducereasonable results,theseresultshavenotbeencompletelyreproducible.We arecurrentlyinvestigatingfurtherandareattainingmore reproducibledatawhichreaffirmstheseresults,butarestillwaiting toachievecompleteconsistency.
Discussion:
Thisstudyinvestigatedtherelationshipbetweenstressand thenano-ripplepatternsformedbytheionbombardmentof boron-dopedSi(100)inclean,impurityfreeconditions.Our
resultsgeneralizedtheindependencebetweenstressandthese nanopatterns.ThroughusingaMOSSsystem,itwasdetermined thatthestressinducedbytheionbombardmentwasisotropic, meaninginboththex-directionandthey-direction.Incontrast, post-factostudyofthesurfaceusinganAFMrevealedthatthe nano-ripplepatternswereexclusivelyparalleltothedirectionof theionsource,assupportedbyearlierresearch.15 Thisobservation, thatisotropicstressdevelopmentcannotformanisotropicpatterns, suggeststhatstress-drivenmechanismsalonecannotfullyexplain thedirectionalsurfaceevolutionobservedduringion bombardment.
Theisotropicbehaviourofstressisclearinseveralkey findings.First,bothx-andy-directionsexhibitcompressivestress thatdevelopsthroughoutbombardment,withy-stressmaintaining valuesof0.2-0.4GPawhilex-stressreachespeakvaluesof approximately1.5GPa.Althoughthesemagnitudesdiffer
15 HaojinLietal.,“TheIndependenceofNanopatternFormation andStressEvolutionduringLow-EnergyAr+Bombardmentof Si,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 571(November 30,2025):165958,https://doi.org/10.1016/j.nimb.2025.165958.
significantlyduringactivebombardment,bothdirections ultimatelyrelaxtosimilarresidualstressvaluesof0.4-0.5GPa afterbombardmentstops.Thisconvergenceindicatesthatthe fundamentalstress-generationmechanisms,amorphization-induced volumetricexpansionandionimplantation,operateinboth directions.16 Thedifferentialspacinganalysisfurtherconfirmsthe uniformityofthestressontheSisample,astherewereno significantchangesinthedifferentialspacinggraphsforwhen comparingthedistancespair-wise.Theresidualstressthatpersists afterthebombardmentsuggeststherearepermanentstructural modifications,consistentwithpreviousobservationsof self-equilibratinginternalstressesinion-modifiedmaterials.17
Incontrast,theAFMimagesrevealstrictlyanisotropic surfacemorphology.Ripplepatternsformexclusivelyparallelto thex-direction,inthesamedirectionoftheionsource,withno correspondingfeaturesinthey-direction.Therefore,thisconflictin
16 G.Abadias,L.ElBelghitti,F.He,etal.“ReviewArticle:Stress inThinFilmsandCoatings:CurrentStatus&Challenges.” Journal of Vacuum Science & Technology A 36,no.2.
17 X.Li,Y.Chen,W.Xie,etal.“ResearchProgressofResidual StressMeasurementMethods.” Measurement: Sensors (2024).
directionalbehaviourbetweenstressandnanopatternformation leadsustobelievethesephenomenaareindependent.Thisfinding isimportantinthescienceworld’sjourneytodeterminethe underlyingmechanismbehindtheripplepatternandlimitsthe stressframeworkthatwasamodelpresentedbymany.18
Ourresultsaredirectlysupportedbypreviouswork,which usedthesamemethodologyandsimilarconditions.19 Ourproject expandsontheirresultsbycreatingamodifiedchambergeometry andanewionsourcethatpreventsanyimpuritiesfromenteringon thesampleduringbombardment.Inthispriorwork,although resultsshowedtheisotropicbehaviourofstressmoreclearly,as indicatedinFigure5,post-factoXPSindicatediron,chromium, andnickelimpuritiesonthesurface.Figure10detailsthestress evolutionforthesamplewithimpurities-followingasimilar
18 R.CuernoandJ.-SKim,“APerspectiveonNanoscalePattern FormationatSurfacesbyIon-BeamIrradiation,” Journal of Applied Physics 128,no.18(November9,2020), https://doi.org/10.1063/5.0021308.
19 HaojinLietal.,“TheIndependenceofNanopatternFormation andStressEvolutionduringLow-EnergyAr+Bombardmentof Si,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 571(November 30,2025):165958,https://doi.org/10.1016/j.nimb.2025.165958.
isotropicshapelikepreviousgraphs.Ourresultsshowsimilar isotropicbehaviourbutinapurifiedchamber,asconfirmedby post-factoXPS.Previousresearchdemonstratedthatmetal impuritiescanaffecterosionratesandpatternformation mechanisms,makingitcrucialtoverifythatourobserved stress-patternindependenceisnotinfluencedbycontamination.20 Ultimately,thisfindingeliminatesamajoralternativeexplanation andstrengthenstheconclusionthatstress-drivenmechanisms, whileperhapscontributingtoothersurfacefeatures,donot determinepatternorientationandmorphology.
20 Vayalil,S.Koyiloth,A.Gupta,S.V.Roth,andV.Ganesan. "InvestigationoftheMechanismofImpurityAssistedNanoripple FormationonSiInducedbyLowEnergyIonBeamErosion." JournalofAppliedPhysics117,no.2(2015):024309.
Fig.10:Thisgraphshowsthex-directionandy-directionstressin thesame60-minuteionbombardmentat65°incidenceangle.It hasacompressivepeakduringthebeginningofbombardment,and showsisotropicbehaviourforthexandystress.Thisisthe bombardmentintheimpurechamber.
Thefollowingquestionthenarises:ifstressdoesnot determinepatternformation,thenwhatisthemechanism responsibleforit?Severalpossibilitiescometomind.Firstisthe Bradley-Harpermodel,whichpredictspatternformationbasedon curvature-dependenterosion,witherosioninstabilitybalanced
againstsurfacediffusion.21 Thismodelsuccessfullypredictsthat patternsformparalleltothebeamdirectionatincidentanglesnear 60-65°,andourAFMresultsat65°bombardmentareconsistent withthesepredictions.However,thisbaseframeworkmustbe expandedupontoaccountfortheobservedsmoothingbehaviorat near-normalincidencethatitcurrentlyfailstoexplain.22
Anotherpossiblebehaviorthatcouldberesponsibleforthe nano-patternsision-inducedmassredistributionNorrisandAziz emphasizethatsputteringerosion,massredistribution,andsurface diffusionareallmechanismsthatcandrivepatternformation independentlyofstress-inducedviscousrelaxation.23 These mechanismscouldbedirectionalasthemassdistributionisadirect causeoftheionshittingthesurface,andthuscouldbedependent
21 R.MarkBradleyandJamesKHarper,“TheoryofRipple TopographyInducedbyIonBombardment”6,no.4(July1,1988): 2390–95,https://doi.org/10.1116/1.575561.
22 R.CuernoandJ.-SKim,“APerspectiveonNanoscalePattern FormationatSurfacesbyIon-BeamIrradiation,” Journal of Applied Physics 128,no.18(November9,2020), https://doi.org/10.1063/5.0021308.
23 Norris,ScottA.,andMichaelJ.Aziz."Ion-Induced NanopatterningofSilicon:TowardaPredictiveModel."Applied PhysicsReviews6,no.1(2019):011311.
onthedirection,unlikestresswhichwasdependentontheforce exerted.Ourobservationthatbothstressandpatternsdevelop simultaneouslysuggeststhesemechanismsoperateinparallel ratherthanstressbeingtheprimarypattern-formingdriver.The challenge,asemphasizedinrecentreviews,isindeveloping predictivemodelsthatproperlyaccountfortherelativeimportance ofeachmechanismunderdifferentbombardmentconditions.
Therelaxationbehaviourobservedafterthebombardment isovershowsthepermanenteffectsofstress.Theincomplete relaxationindicatesapossiblestructuralmodificationfromthe stableamorphouslayerandimplantedions.24 However,the relaxationthatoccursafterthepeakalsoshowsthattheeffectsare somewhatelastic.
Severallimitationsshouldbeacknowledgedforthisstudy. First,measurementswereconductedatasinglebombardment angleof65°,limitingourabilitytoassesshowstressvarieswith differentincidenceangles.Second,alimitationintheMOSS
24 G.Abadias,L.ElBelghitti,F.He,etal.“ReviewArticle:Stress inThinFilmsandCoatings:CurrentStatus&Challenges.” Journal of Vacuum Science & Technology A 36,no.2
techniqueisthatMOSSmeasuresstress-thicknessproductsrather thanstressindependently,introducinguncertaintyinabsolutestress values.Finally,althoughAFMandotherstudiesshowthatthe nano-patternsareanisotropic,thesemorphologicalinspectionsare post-bombardment,andsowemissreal-timemorphology evolutiondatathatcouldrevealwhetherpatternsdevelop progressivelyoremergesuddenlyatcriticalbombardment thresholds,andhowstressimpactsthedevelopment.
Despitetheselimitations,ourresultsclearlydemonstrate thatisotropicstressdevelopmentandanisotropicpatternformation areindependentduringionbombardment,indicatingthatcurrent theoreticalmodelsshouldlooktoothermechanismsbeyond stress-drivenevolution.Futureworkshouldinvestigatemultiple bombardmentangles,varydurationsystematicallytounderstand time-dependentmechanisms,andalsolookattheotherbehaviours outlinedearlier.
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