STEM–EELS analysis reveals stable high-density He in nanopores of amorphous silicon coatings deposited by magnetron sputtering
Abstract
A broad interest has been showed recently on the study of nanostructuring of thin films and surfaces obtained by low‐energy He plasma treatments and He incorporation via magnetron sputtering. In this paper spatially resolved electron energy‐loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) is used to locate and characterize the He state in nanoporous amorphous silicon coatings deposited by magnetron sputtering. A dedicated MATLAB program was developed to quantify the helium density inside individual pores based on the energy position shift or peak intensity of the He K‐edge. A good agreement was observed between the high density (~35‐60 at/nm3) and pressure (0.3‐1.0 GPa) values obtained in nanoscale analysis and the values derived from macroscopic measurements (the composition obtained by proton backscattering spectroscopy coupled to the macroscopic porosity estimated from ellipsometry). This work provides new insights into these novel porous coatings, providing evidence of highdensity He located inside the pores and validating the methodology applied here to characterize the formation of pores filled with the helium process gas during deposition. A similar stabilization of condensed He bubbles has been previously demonstrated by high‐energy He ion implantation in metals and is newly demonstrated here using a widely employed methodology, magnetron sputtering, for achieving coatings with a high density of homogeneously distributed pores and He storage capacities as high as 21 at%.
Full text
STEM‐EELSanalysis e ealss ablehigh‐densi yHeinnanopo eso amo phous
siliconcoa ingsdeposi edbymagne onspu e ing
RolandSchie holza,b,*,Be andLac oixa,VandaGodinhoa,JaimeCaballe o‐He nándeza,Ma ial
DuchampcandAsunciónFe nándeza,*
aIns i u odeCienciadeMa e ialesdeSe illa,CSIC‐Uni .Se illa,A da.Amé icoVespucio49,41092
Se illa,Spain
bIns i u ü Ene gie‐undKlima o schung,G undlagende Elek ochemie(IEK9),
Fo schungszen umJülichGmbH,52425Jülich,Ge many
cE ns Ruska‐Cen e o Mic oscopyandSpec oscopywi hElec ons,Fo schungszen umJülich
GmbH,52425Jülich,Ge many
* [email p o ec ed],[email protected]
Abs ac
Ab oadin e es hasbeenshowed ecen lyon hes udyo nanos uc u ingo hin ilms
andsu acesob ainedbylow‐ene gyHeplasma ea men sandHeinco po a ion iamagne on
spu e ing.In hispape spa ially esol edelec onene gy‐lossspec oscopy(EELS)inascanning
ansmissionelec onmic oscope(STEM)isused oloca eandcha ac e ize heHes a ein
nanopo ousamo phoussiliconcoa ingsdeposi edbymagne onspu e ing.Adedica edMATLAB
p og amwasde eloped oquan i y heheliumdensi yinsideindi idualpo esbasedon heene gy
posi ionshi o peakin ensi yo heHeK‐edge.Agoodag eemen wasobse edbe ween he
highdensi y(~35‐60a /nm3)andp essu e(0.3‐1.0GPa) aluesob ainedinnanoscaleanalysisand
he aluesde i ed ommac oscopicmeasu emen s( hecomposi ionob ainedbyp o on
backsca e ingspec oscopycoupled o hemac oscopicpo osi yes ima ed omellipsome y).
Thiswo kp o idesnewinsigh sin o heseno elpo ouscoa ings,p o idinge idenceo high‐
densi yHeloca edinside hepo esand alida ing heme hodologyappliedhe e ocha ac e ize
he o ma iono po es illedwi h heheliump ocessgasdu ingdeposi ion.Asimila s abiliza ion
o condensedHebubbleshasbeenp e iouslydemons a edbyhigh‐ene gyHeionimplan a ionin
me alsandisnewlydemons a edhe eusingawidelyemployedme hodology,magne on
spu e ing, o achie ingcoa ingswi hahighdensi yo homogeneouslydis ibu edpo esandHe
s o agecapaci iesashighas21a %.
Keywo ds:spa ially esol edEELS,spec umimaging,magne onspu e ing,amo phouspo ous
siliconcoa ings,closednanopo es,condensedHebubbles, educed e ac i eindex
1. In oduc ion
Thein oduc iono po osi yinnanoma e ialshasbeena opico inc easingin e es o e
helas decade,and esea che o sha ebeen ocusedon hesyn hesisandcha ac e iza iono
newlydesignedpo ousandnanos uc u edma e ials.A undamen alunde s andingo he
nanos uc u epe mi s hecon olanddesigno po ousma e ialswi h ailo ed unc ionali ies.
Amongmanyo he s,po oussiliconcu en ly emainsoneo hemos ac i ely esea ched
ma e ials o di e seapplica ionssuchassenso s,pho onicde ices,mic oelec onicsandsola
ene gycon e sion[1‐6].Being ullycompa iblewi h hees ablishedmic oelec onics echnology,
hemos a ac ing ea u eo po oussiliconis hewide angeo e ac i eindexes ha canbe
achie edby a ying hepe cen ageo po osi y.Ina ecen wo k,wep oposedanewbo om‐up
app oach op epa epo oussiliconcoa ingsbymagne onspu e ingasanal e na i e ou e o he
adi ionalelec ochemical‐basedp ocesses[7].In ha wo k,wedemons a ed hepossibili yo
p oducingpo oussiliconcoa ingswi h ailo ed e ac i eindices( om3.75 o4.75a 500nm)
usingmagne onspu e ingwi hHeo A as hep ocessgas[7,8].Inaddi ion o head an ageso
hewell‐knownindus ialscale‐upo hemagne onspu e ingp ocess,ou p ocedu ep o ides
manypossibili ies o hedesignandp oduc iono a iousde icesal e na ing o exampledense
andpo ouslaye s,in insico dopedsilicon,e c.[7].Thelow‐ e ac i e‐indexcoa ingsp oduced
exhibi amic os uc u eo closedpo es ha canbeo ien ed o hecoa ing’sg owingdi ec ion.In
hisp e iouswo k[7], heinco po a iono ahighHeamoun (up o30a %)inside hecoa ings
wasde ec edbyp o onbacksca e edspec oscopy,andi wasp oposed ha Hewasmos likely
appedinside heclosedpo esdu ingdeposi ion[7,8].In ac ,inano he p e iouspape ,weused
spa ially esol edelec onene gy‐lossspec oscopy(EELS)inascanning ansmissionelec on
mic oscope(STEM) odemons a e ha amo phouspo ousSiNxOycoa ingscanbep epa edby
magne onspu e ing, e ealingclosedpo escon ainingmolecula N2inside[9].
A hispoin o he esea ch, hechallengein hep esen wo kis oin es iga e heloca ion
o heHein hepo ousSicoa ingsaswellas oquan i y heheliumwi hnano‐scale esolu ion
using heSTEM/EELSme hodologya ailablein heTEM acili ieso ou labo a o y.The
inco po a iono Heinme alshasbeenwellin es iga eddue oi simpo anceinnuclea
echnology.Ionimplan a ionhasbeenused o e‐c ea e hecondi ionso he eac o smainly o
in es iga edamagecausedinma e ials.In hesewo ks, heex emelylowsolubili yo Hein
me alshasbeen epo ed obe hecauseo he o ma iono Hebubblesdu ingionimplan a ion
[10‐12].Inmos o hesewo ks,heliumimplan edinc ys allinema e ialsleads o he o ma iona
ace aindep ho alaye o la gelydispe sedbubbleswi hdiame e s anging om2 o25nm.
EELSwasused o hee alua iono heliumdensi yinside hesebubbles.The i s app oachwas o
use heblueshi o heHe1s→2p ansionasa unc iono Hedensi y[10,13].La e ,spa ially
esol edEELSwas epo ed obeable o eco dspec ao singlebubblesbyse e alau ho s
[12,14‐16].Thead an agehe eis ha heheliumdensi ycanbe e ie eda henanoscaleusing
wodi e en me hods.Oneme hoduses hein eg a edin ensi yunde heHeK‐edge,and he
o he uses heal eadymen ionedene gyshi o he1s→2p ansion.Adesc ip iono bo h
me hodsisgi enin e e ence12(and he e e ences he ein).The i s aimo hewo kp esen ed
he ewas oapplyasimila STEM/EELSme hodology ocon i m ha heHeinco po a edin he
amo phoussiliconcoa ingsp epa edbymagne onspu e ing emainsinside heclosedpo es
and,i so, ocha ac e ize hephysicalpa ame e s(densi y,p essu e)o He.Bo hgoalswe e
accomplished,asdesc ibedin hispape ,andanadhocMATLAB ou inewasalsode eloped.
Addi ionally,wecompa e he alues o heHedensi yob ainedinside hemic oscope o he
alueses ima ed ommac oscopicmeasu emen s.No e ha ou esul sp esen edin hispape
e ealsimila s abiliza iono condensedHein henanopo es(Hedensi ieso ~30‐50a /nm3)as
ha p e iouslydemons a edinbubbles o medbyhigh‐ene gyHeionimplan a ioninme als
[12,14‐16].Ahighamoun o Hecan he e o ebes o edands abilizeda oom empe a u einside
heclosedpo es.Tos o easimila densi yinamac oscopic anka oom empe a u e,p essu es
o app oxima ely1kba wouldbe equi ed[17].
To e‐c ea e hecondi ionso hecoldplasmaincon ac wi h henuclea eac o walls,
some esea che sha ea i iciallyin oducedHeindi e en me alsusingalsomagne on
spu e inginHe/A mix u es[18‐20].Mo e ecen ly heexposu e oHeplasmasandHe
inco po a ion iamagne onspu e ingha ealsobeenp esen edasa ou e o nanos uc u ing
me als[21‐23].Inall hesea icles,al hough hep esenceo Heandnanopo eswas epo edby
TEMimages,noquan i ica iono heHecondenseds a ewasp o ided.A hispoin ,i is
impo an oemphasize he ele anceo hep esen wo k ha newlydemons a es ha coa ings
canbep epa edbymagne onspu e ingcon ainingahighdensi yo homogeneouslydis ibu ed
po es illedwi hheliuminacondenseds a e.
2. Expe imen al
2.1 Deposi ionde ails
Inou p e iouswo k[7]weshowed hedependenceo hepo esizeanddis ibu ionon
se e aldeposi ionpa ame e so hemagne onspu e ingdeposi ion.Basedon hisin o ma ion,
adeposi ionpowe o 300Win adio equency(RF)wasselec edin hispape oob ain a he
la geandsepa a edpo es o acili a e heindi idualpo eanalysisbySTEM/EELS(see he
mic og aphshownin igu e1).Themagne onheadwasplaceda a30°angle o heno malo he
subs a ea adis anceo 5cm(see heinse in igu e1le ).Fo compa isonpu posesadense
coa ingwasalsodeposi edusing150WinRF‐modeandasubs a ebiaso 100V.Bo h, hedense
andpo ousamo phoussiliconcoa ings,we edeposi ed omapu eSi a ge (Ku JLeske
99.999%pu e).Be o edeposi ion hebasep essu ewas10‐4Pa.Thepo ouscoa ingwasdeposi ed
a p(He)=4.8Pa,while hedensecoa ingwasdeposi eda p(A )=1.3Pa.Silicon(100)andqua z
we eusedassubs a es.Table1summa izes hedeposi ioncondi ionsandlabels o hes udied
samples.
2.2Cha ac e iza iono hecoa ings
The hicknesso hecoa ingswasexaminedusingscanningelec onmic oscopy(HITACHIS‐
4800SEM‐FEG)wo kinga 2kVon ac u edsampleswi hou anyconduc i ecoa ing.
Themic os uc u eo hecoa ingswasin es iga edby ansmissionelec onmic oscopy
(TEM)usingaFEITecnaiF30mic oscopeope a eda 300kVequippedwi haGa anGIFQuan um
963ene gy il e a heLabo a o yo NanoscopiesandSpec oscopies(LANE‐ICMSE,Se illa,
Spain).C oss‐sec ionalTEMspecimenso hecoa ingsdeposi edonSisubs a eswe ep epa ed
using hecon en ionalapp oachbymechanicalpolishinganddimpleg inding ollowedbyA +ion
millingun ilelec on anspa encywasa ained.Thequan i a i eSTEM/EELSanalysiso indi idual
nano‐po eso highlypo ouscoa ings equi es hep epa a iono hinlamellao less han100nm
hickness,whichshouldincludeclosed illedpo es.Howe e ,o e lapo po esshouldbea oided,
and e ysmallpo eswillmake heSTEM/EELSanalysiso indi idualpo esmo edi icul .In his
sense hepo oussampledeposi eda 300Wis e yadequa easshowninFig.1.
Thecomposi ionso he hin ilmswe ee alua edusingp o onbacksca e ing
spec ome y(p‐BS)a heNa ionalCen e o Accele a o s(CNA,Se illa,Spain)usinga3‐MV
andemaccele a o .Thespec awe eob ainedusing wodi e en ene gies,1.0and2.3MeV, o
hep o onbeamandasu aceba ie de ec o se a 165°.Toob ain he hicknessand
composi iono he ilms,bo hspec awe esimul aneouslysimula ed o e e ysampleusing he
SIMNRAcode[24](seemo ede ailsin e .7)
Theop icalcha ac e iza ionwaspe o medoncoa ingsonqua zsubs a esinaUVISEL
spec oscopicellipsome e omHORIBAJobinY onwi hanincidenceangleo 60°anda
wa eleng h angeo 563‐1550nm.Theda awe eanalyzedusing heDel apsi2so wa e
de elopedbyHORIBAJobinY on.
2.3STEM‐EELSspec umimagingda aanalysis
Annula da k ieldscanning ansmissionelec onmic og aphs(ADF‐STEM)andspa ially
esol edelec onene gyloss‐spec a(EELS)we e eco dedsimul aneouslyin heTecnaiF30on
singlepo eso a iousdiame e s.Thespec umimageswe eacqui edin helow‐loss egionwi h
apixelsizeo 1nmusingsubpixelscanning(16*16).A eachposi ion,anEELSspec umo 2048
pixelso leng hwi hene gydispe siono 0.05eV/channelwas eco dedusinganin eg a ion ime
be ween0.05and0.07s.
TheHeK‐edgepeakco esponding o he1s o2p ansi ionwasplaceda app oxima ely
22eVon hehighene gy ailo heSiplasmona app oxima ely17eV[25].Top ocess heEELS
spec umimageda ase andex ac heHesignal,aMATLABp og amwasde elopedbasedon he
me hoddesc ibedin e e ence12.A e siono hisp og amisp o idedin hesuppo ing
in o ma ionsec ion.Fi s , he awda awe ealignedwi h heze olosspeak(ZLP)andsubjec ed o
mul i a ia es a is icalanalysis(MSA)[26] o emo e hes a is icalnoise.Theplu alsca e ing
dis ibu ionwas hen emo ed om hespec ausingFou ie ‐logmul iplesca e ing
decon olu ion(P og amFLOG[27]).Thespecimen hicknessmapwascalcula edusing helog‐
a iome hod[27]using hemean eepa hcalcula edusing heIMFP ou ine[27].Usingou
expe imen alcondi ions,amean eepa ho λ=145nmwasob ainedusing heMalisequa ion
[28].Thecon ibu iono heSiplasmonwas i edwi h he unc iongi enineq.1 om e e ence
29:=/((2−2)2+(∆)2)(equa ion1)
He e,Ep ep esen s heplasmonene gy,∆Epco esponds o hepeakwid h,anda ep esen s he
ampli ude.Toimp o e heHesignalex ac ion,asecondpeakwas equi eda ene gieshighe
han23eV.Thiscon ibu ionmaybedue osu aceoxideSiO2o ca boncon amina ion(bo ha
app oxima ely24eV).These woplasmoncon ibu ionswe e i edsimul aneously o heda ain
wo anges( om16 o20.5eVand om23.5 o40eV)onbo hsideso heHe‐Kedge.Du ing he
i , heEp alueo hesecondplasmonwas ixedbe ween23and25eV.Thesumo hese wo
con ibu ions(SiandSiO2plasmon)is e e ed oas hebackg oundsignal o heHe‐Kedge.A e
sub ac iono hebackg oundsignal, he esidualsignalwas i edin heHeK‐edge ange om
20.5 o23.5eV.Fo heHe1s→2p ansion,asimpleGaussian unc ionwasused o i ingas
his unc ionwas epo ed oyieldgood esul s[12].Anexampleo he i ingp ocedu ewillbe
shownbelowin he“Resul sandDiscussion”sec ion(Fig.3c).
Toquan i y hea omicdensi yo Hea eachposi iono hespec umimage, wome hods
we eused.InMe hod1[12], heHedensi ynHeisgi enby
nHe=IHe
IZLP
1
dσHe
(equa ion2)
whe eIZLPandIHea e hein eg a edin ensi ieso heze olosspeak(ZLP)and heHeK‐edge,
espec i ely.σHeis hec oss‐sec iono heHe1s→2p ansion,whichwascalcula edusing he
p og amSigmak3[27].Fo ou expe imen alcondi ions(accele a ion ol ageo 300kV,
con e gencesemi‐angleα=12.4m ad,collec ionsemi‐angleβ=9.6m ad,andin eg a ion ange
o 3eV),weob ainedσHe=6.410‐24m².dis hepo e hicknessa hepixelposi ion.Thisla e
aluewase alua edas hecomplemen o hespecimen hicknessa eachpa icula pixel
compa edwi h he aluea a e e encepixelou side hepo es.Thisme hodwassugges edin
e e ences14and15andwasc oss‐checkedusing heSTEM‐ADFimagecon as assuminga
uni o mellipsoidal olumeo hepo espe pendicula o heg owingdi ec ion.The esul so IHe
andIZLPwe es o edin2Dmaps,and hemapo Hedensi ywascalcula edusing hesepa ame e s.
Tocon i m hesemeasu emen s,ano he me hod(Me hod2)wasused o compa ison.
Thisme hod elieson helinea ela ionshipbe ween heblueene gyshi (ΔEHe)o heHeK‐edge
compa edwi hi sposi ion o he eea om(21.218eV, e .30)and heheliumdensi y(nHe):
∆E=C×nHe (equa ion3)
whe eCandδa econs an s.Theene gyshi isa ibu ed o hesho ‐ angePauli epulsion
be weenelec onso heneighbo inga oms[13].In hiswo k,weassume ha heHedensi y
inside hepo eswill ollowasimila linea law.In heli e a u e,somedisc epanciesinCandδ
aluescanbeobse ed[10,12,14,15],andweused woex eme alueso C.Me hod2(a)usesE=
0.015nHe+0.45[15],andMe hod2(b)usesE=0.044nHe+0.07eV[14].Finally, heHep essu epHe
inside hepo escanbees ima ed om henHe aluesp o idedby he wome hodsusinga
sui ableequa iono s a e(EOS)[11,12]dependingon heHedensi y ange.
3. Resul sanddiscussion
3.1Po oussiliconcoa ingwi h educed e ac i eindex
Figu e1shows hemic os uc u eo hein es iga edpo ouscoa ing(a‐pSi(300),which
consis so ahighlypo ouss uc u eo closedpo eso ien edin hemagne ondi ec ion(Fig.1a).
Thehigh‐ esolu ionTEMimage(Fig.1b)shows heshapeo hepo esinde ailand e eals he
amo phouss uc u eo heSi‐ma ix.Wi haRFpowe o 300Wsupplied o hemagne on,an
inc easeinpo esizeisobse edcompa edwi h hecoa ings epo edin hep e iouswo k[7].
Po eswi hdiame e s anging om2 o60nmcanbeobse ed o hea‐pSi(300)coa ing.The
po esexhibi simila mino diame e sas heonesinp e ioussamples[7](a e agesizeo 9±2
nm),while hemajo diame e sa ela ge .Thepo esa eeasie oseeon heADF‐STEMimage
whichp esen sahighe con as (Fig.1c).Thisimagepoin sou ha o ou EELSanalysis(sec ion
3.2),weneed ochoosea hin egiono hespecimen o indisola edpo es(close o hebo de )
bu no oo hinso ha hepo es emainclosed.
Thep o onbacksca e ing(p‐BS)spec umo hissampleiscompa edwi h ha o he
densesampleinFigu e2.As ongsignalco esponding oHeinside hecoa ingisobse edin he
po oussample,co esponding oaHeamoun o 21a %(seeTable2).Inaddi ion oSi, hedense
sample,a‐Si(150)(bias),whichwasdeposi edunde A a mosphe ewi ha ol ageapplied o he
subs a e,showsasmallsignalco esponding o heinco po a iono A .Theinco po a iono A in
samplesdeposi edbymagne onspu e ingwi hanappliedsubs a ebiashasbeen epo ed
p e iouslybyo he au ho s[31];ne e heless, hisinco po a iondoesno esul in he
in oduc iono po osi y(de ailsconce ning hemic os uc u eo hisdensecoa inga ep o ided
in e e ence7).
Thein oduc iono po osi yleads oadec easeo bo h he e ac i eindexandex inc ion
coe icien .Table3summa izes he alueso he e ac i eindicesanddampingcons an so bo h
coa ingsa 605nm.Using hee ec i emediumapp oxima ions[32],onecanexp ess he ela i e
elec icalpe mi i i yo hepo ouscoa ing,ahe e ogeneousmedia( ,e ),asa unc iono he
dielec iccons an so hecon inuousma ix( ,c)anddispe sedphase( ,d)and he olume
ac ion()occupiedby hepo es(eq.4, e .32):
ε ,eff=ε ,c 1‐3ϕε ,c‐ε ,d
2ε ,c+ε ,d+ϕε ,c‐ε ,d(equa ion4)
Wecalcula ed hedielec iccons an ,ε=n²–k²,using he alueso nandkmeasu edby
ellipsome ya 605nm,aslis edinTable3andde i edapo osi yo 22% o hepo ouscoa inga‐
pSi(300)assuming ha hedielec iccons an o hema ixissimila o ha o a‐Si(150)(bias)and
se ing ,d o hepo es o1[33].
3.2Ex ac iono heHeEELSsignalande alua iono physicalpa ame e s(densi y,p essu e)
InFigu e1,i ispossible oobse esomeisola edpo esinwhich hespa ially esol edEELS
analysiscouldbepe o med.Figu e3ap esen s heADF‐STEMsignalacqui edinpa allelwi h he
spec umimage,whichenclosesanisola edpo e.The e o e,anEELSspec umco esponds o
eachoneo he1x1nm2pixelsin heimage.In heADFsignal, hema ixwi hhighe a omic
numbe andsca e ingc osssec ionappea sb igh ,and hepo esappea da k.InFigu e3b, h ee
EELSspec aco esponding o h eeselec edpixelsa hecen e , hebo de andou sideo he
po ea ep esen edwi ha e icalshi o compa isonpu poses.
Fo heselec edpixel(16,10),whichco esponds oazoneou side hepo e, helowloss
spec umcon ainsapeakco esponding o heSiplasmona 17eV[25].Mo ing owa d hepo e,
pixel(5,10)a hebo de ,asmallpeaka app oxima ely22eVbegins oappea ha becomes
s onge a hecen e o hepo e,pixel(6,13).Thissupe imposedpeakco esponds o heHeK
edge[25],con i ming hep esenceo Heinside hepo es.
Tocha ac e ize hephysicalpa ame e so Hein hecoa ing, hesignalo heHeK‐edgea
eachposi ionwasex ac ed om heEELSspec a ollowing hep ocedu edesc ibedinde ailin
sec ion2.3(seealso heMATLABp og amin hesuppo ingin o ma ion).Toillus a e heme hod,
i so hebackg oundsignal o hema ixposi ionou side(16,10)andinside(6,13) hepo ea e
p esen edinFigu es3cand3d.Thisbackg oundsignalincludes hepeako heSiplasmonaswell
asano he peak o hesu aceSiO2componen .The igu esalsoshow he esidualsignalob ained
bysub ac iono hebackg oundandexpe imen alspec a.No e ha heHesignala
app oxima ely22eVisclea ly isiblein he esidualsignalinside hepo e(Fig.3d),whilea la line
isobse edabo e16eV o heposi ionou side hepo e(Fig.3c).These esul sclea ly alida e
ou i ingp ocedu e o heex ac iono heHesignal.The woaddi ional ea u esin he esidual
signala ene gieso app oxima ely5 o10eV(Fig.3c)and10 o15eV(Fig.3d)canbea ibu ed
o heSi/SiO2in e aceplasmon[16,34]and heca i yplasmons[16], espec i ely.
Figu e4illus a es heme hodsused oe alua e heHedensi yinside hepo es.Usingou
MATLAB ou ine(seesuppo ingin o ma ion)and ollowing hep ocedu esdesc ibedabo e, he
ex ac edheliumsignalwas i wi haGaussian unc ion(Figu e3d),and heco esponding
in eg also heHein ensi y(IHe)andene gyshi (ΔEHe) ela i e o heHe eea om aluewe e
s o edin2Dmaps(seeFigu es4aand4e).Asdemons a edon heelemen alin ensi ymap
(Figu e4a),heliumisloca edinside henanopo e olume.Thelocalspecimen hicknessa each
pixelposi ionisindica edinFigu e4b.Thepo e hicknessmap(Figu e4c)wasp epa edby
selec ing hepixel(17,9)asa e e ence o hespecimen hickness( e =38.8nm).In hiscase,a
maximum alueo 6.5nmwasobse ed o hepo e hickness,whichiscompa able o hemino
axiso heellipsoidalpo e(7nm)measu edon heADF‐imageinFigu e3a.Using he esul so he
Hein ensi yandpo e hickness,i waspossible op epa e heheliumdensi ymapasdesc ibedin
Me hod1(seeeq.2)andp esen edinFigu e4(d).Byconside ingonly hepixelsclose o hepo e
cen e ( oa oidsu acee ec s)[14], hedensi yinside hepo e anges om25 o54a /nm3,and
ameandensi yo 36a /nm3wasmeasu ed.Thedec easingo nHe om he op o hebo omo
hepo ecanbeexplainedbyHedeso p ionunde elec oni adia ion,as epo edbyDa ide al.
[15,16]du ingSTEM eco dingo hespec umimagingda a.
FollowingMe hod2(desc ibedinsec ion2.3),Figu e4eshows helocalene gyshi ΔEo
heHeK‐edge om he alueo he eea oms[30].Figu es4 and4gp esen heco esponding
He‐densi ymapscalcula edacco ding oeq.3usingMe hods2(a)[15]and2(b)[14].Bycompa ing
Figu es4d,4 and4g,agoodag eemen be ween heHedensi yob ainedusingMe hods1and
2(a)isobse ed.
Table4summa izes henHe aluesob ainedin wodi e en po esusing heabo e
men ionedme hods o hecha ac e iza iono heHes a einpo ousa‐Sicoa ingsdeposi edby
magne onspu e ing.Fo he wopo es,agoodag eemen isobse ed o heHedensi yusing
Me hods1and2a,whichp o idesagoodindica iono he eliabili yo ou p ocedu e.E eni
di e en au ho sag eeon helinea cha ac e o ΔEandnHedependence, he aluesgi en o C
a ysigni ican ly[10,12,14,15].Fo ou densi y ange(app oxima ely20‐70a /nm3),webelie e
ha hesys emisbe e desc ibedusingMe hod2abecause helawgi enbyDa ide al.[15]was
es ablished o asigni ican numbe o eco dedda ain he20‐100a /nm3 ange.Thelawgi enby
Ta e nae al.[14](Me hod2b)wasde e minedusingsmalle Hedensi ies,10‐40a /nm3,and hus
doesno comple elydesc ibeou sys em.Thisideaissuppo edbyLucasandco‐wo ke s[13],who
obse ed ha heC alueisalsodependen on empe a u eanddensi y.
Knowing hedensi yo Heinside hepo es, hein e nalp essu ebecomesa ele an
pa ame e obede e mined.A highe a omicdensi ies, heidealgaslawisinaccu a e.Walsh[12]
discusseddi e en semi‐empi icalequa ionso s a es(EOSs) ocalcula e heHep essu einside
hepo es om hemeasu ednHe.Fo ou densi y ange, heT inkausEOS[11]is hemos sui able.
Themaximum,minimumandmeanHedensi y aluesdesc ibedbe o ewe eused ocalcula e he
Hep essu e,and he esul sa ep esen edinTable4.UsingMe hod1and2(a) o he i s po e
(Po e#1,p esen edinFigs.3and4),ameanp essu eo 0.3GPawasde e mined,and hep essu e
locally eachesup o0.8GPa.In hesecondpo ein es iga ed(Po e#2),highe meanp essu e
alueso 0.5and1GPawe eobse ed,and hep essu elocally eachesup o2GPa.These
di e encesin he wopo esa eno necessa ilysigni ican conside ing hela geunce ain ieso
heHedensi ymeasu emen s ha mainlyo igina e om hedi icul yo accu a elymeasu ing he
localpo e hicknessand omHedeso p iondu ing hemeasu emen s.Ne e heless, heselocal
measu emen sp o ideagoodindica ion ha heHep essu einside hepo eisin heGPa ange,
whichisse e alo de so magni udehighe han hep essu ein hedeposi ionchambe ,pHe=4.8
Fig.3
Fig.4