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Nanomaterials 2020, 10, x FOR PEER REVIEW 4 of 11 calculation of the intensity involves again the transfer matrix method. Both aspects are taken into account in the calculations carried out previously for different metals and dielectrics [25]. Nanomaterials 2020, 10, 830 4 of 11 3. Results and Discussion 3. Results and Discussion The minimum requirement to obtain light multireflections able to produce interference is the preseTnhce omfitnwimo puamrarleleqluinirtemrfaencetst,onoebtaatitnheliganhat lmytueltoirbeefledcettieocntesdabanledttohpe roothdeurcaetianhteirgfhelryenrecfeleicsttinhge psurersfaencecelofcatwteod patrallecleirntateinrfadciesst,aonnce,atwtheicahnaclayntebteo btuendedtectotedobatnadinthceoontshterur cativaehiogrhldyersetflruectinvge sinutrefrafcerleonccaet.ed at a certain distance, which can be tuned to obtain constructive or destructive interference. The maximum interference for visible excitation lasers is obtained for aluminum as the reffllecting layer,,becauseoffiittsshiighiimaaggininaarryyppaarrttnni((n=nr +iini)),,ccombiinedwiitthamaterialwithnoabsorption 23 iri (ni ~ 0) and the smallest nr possible [25]. According to the simulations, air is the optimum dielectric ir medium, thus we have evaluated the amplifification related to alumina membranes which are not detached from their aluminum base. Figure 1a sketches the section of a supported membrane with a single layer graphene transferred on top of it. The relevant parameters are indicated—the depth of the pore h, the diameter of the pore d, the distance between pores D and the thickness of the bottom Al2O3 barriierllayerb..Fiigurre1bshowsthecalculatedRamanampliffiication (for calculation details see 23 Ref. [2266)])fofrorggrarpaphheneneepphhoonnoonnssccoonnssidideerrininggththeessimimplelessttposssiibllessysttemwhere the dielectric layer is eitherAl2O3 ((redtrianglles))orair(greencircles).Theidealplatformwouldthusincludeadielectric layer formed by air with 120 nm thickness for 488 nm laser excitation. The supported membranes are aninttermediiatteessitiutuaatitoionnwwhhereereaiariirsipsrpesrensetnintainfracfrtiaocntiofnthoeftdhieledciterlieccltaryicerl,aaytetrh,eatptohresp.oTrhees.mTohset ImnotesrtfIenretenrcferiesnscteroisngstlryodnegplyenddepenent donenitsotnhitcsktnheicsks,nienssth, ins cthaissectahsedtheeptdhepofththoef tphoerepso,rhesin, hFiingFuirgeu1rae, s1oa,itsoisitchisacllheanlgleingitnoggteotgeentoeungohucgohnctoronltroofltohfisthpiasrpaamraetmeretienrtihnetfhaebfraicbartiicoantiopnropcreoscse. sSse.vServaelrsaeltseotsf soufpsuppoprtoerdtemdemebmrabnraensewsewreroebotbaitnaiendedwwithithpoproeredidaimametetresr,s,dd, ,ininththeerraannggee10–20nmand difffferent depths (h)—around 60,, 100aand22000nnm(S(SEEMimimaaggesesofofthtehemmemembrbarnaenewwithith ∼h 2~0200n0mnmis sishoshwonwin iFnigFuirgeu1rec )1.cT)h. eTphreespernecsenocfeAol2fOA3latOtheabtothtteomboottfotmheopfotrhees ipsodretsriims ednetarilmfoerntthael ifnotrerthfereintcerpferroecnecses 23 psorotcheissbsaorrthieirslbaayrerrieirslraeydeurciesdrebdyucaesdtebaydaysdtecardeyasdeecorfetahseaonfothdeizantiodnizcautriorennctufrorlelonwt feodllobwyeadpboyrea- pwoirdee-nwiindgentrienagtmtreantm, tehnist,ltahtiesrltartearttmreeantmt aetntetmatptetsmtpotsintcoreinacsreetahse tahirefariarcftriaocntiofntohfetmhembemrabnreantoebtoe bcleocsleorsteor thoethideeiadlesailtusiattuioantiodnetdeertmerinmeidnebdy bthyethsiemsuimlautiloatniso.ns. Figure 1. (a) Schema of the section of a supported membrane with a single layer graphene transferred Figure 1. (a) Schema of the section of a supported membrane with a single layer graphene transferred on top of it, (b) calculated Raman amplification with Al2O3 (red triangles) or air (green circles) as on top of it, (b) calculated Raman amplification with Al2O3 (red triangles) or air (green circles) as the the dielectric layer for 488 nm laser excitation, (c) scanning electron microscopy (SEM) images of an dielectric layer for 488 nm laser excitation, (c) scanning electron microscopy (SEM) images of an alumina supported membrane with h ≈ 200 nm. alumina supported membrane with h ≈ 200 nm. Figure 2a,b show in-plane and tilted SEM images of a supported alumina membrane with pore depth around 100 nm (sample named h = 100 nm) and ~18 nm pore diameter. The transference of a single layer graphene on top of the membrane strongly modifies its AFM topographic imagePDF Image | Supported Ultra-Thin Alumina Membranes with Graphene
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