KARAKTERIZACIJA STRUKTURA NANO- METARSKIH DIMENZIJA PRIMENOM SPEKTROSKOPSKE ELIPSOMETRIJE*

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1 MILKA M. MIRIĆ MARKO B. RADOVIĆ RADOŠ B. GAJIĆ ZORANA D. DOHČEVIĆ-MITROVIĆ ZORAN V. POPOVIĆ Centar za fiziku čvrstog stana i nove materiale, Institut za fiziku, Beograd, Srbia NAUČNI RAD KARAKTERIZACIJA STRUKTURA NANO- METARSKIH DIMENZIJA PRIMENOM SPEKTROSKOPSKE ELIPSOMETRIJE* U ovom radu smo metodom spektroskopske elipsometrie analizirali optičke osobine tankih filmova, nanoprahova i ugleničnih nanotuba u UV-VIS-NIR oblasti. U zavisnosti od broa tankih filmova Si 3 N 4 i SiO, koristili smo dvofazni, trofazni i višefazni modeli, a za opisivane neravnina Bruggeman-ovu aproksimaciu efektivne sredine. Elektronski prelazi kod nanoprahova CeO opisali smo pomoću Tauc-Lorentz modela i utvrdili smo energetski procep materiala. Analizirali smo spektar ugleničnih nanotuba na supstratu od siliciuma. UDK 543.4:539.3:535.3:661.8'065 DOI: 10.98/HEMIND09037M Oslanaući se na posebne osobine materiala nanometarskih dimenzia, razvio se čitav niz nihovih novih primena u elektronici i optici, nanobiloškim sistemima i u medicini. Jedan od kritičnih izazova sa koima se susreću istraživači na polu nanotehnologie e kako posmatrati, meriti i manipulisati materialima nanometarskih dimenzia [1]. Veličina koa karakteriše optičke osobine materiala e nihova dielektrična funkcia. Na dielektričnu funkciu nanostrukturnih materiala poseban utica imau veličina i orientacia čestica, udeo čestica različitog materiala, neravnine na površini uzorka kao i bro i deblina filmova u višeslonim strukturama []. Dielektrična funkcia poluprovodničkih materiala povezana e sa strukturom energetskih zona 3. Prelazi koi se odviau unutar ovih zona, uklučuući i ekscitonske efekte, utiču na oblik dielektrične funkcie. Ova oblik se mena pri promeni mikrostrukture materiala, er one unose promenu u nihovu zonsku strukturu. Upravo ovi faktori otežavau interpretaciu podataka celokupnog, složenog sistema koe nosi dielektrična funkcia = r i i, gde su r i i nen realni, odnosno imaginarni deo, pa e potreban opšti parametarski opis. Spektroskopska elipsometria (SE) e optička tehnika koa meri količnik kompleksnih koeficienata s- i p- komponenti polarizacie svetlosti pri refleksii od uzorka. Prednosti SE u odnosu na druge metode su višestruke. Ova tehnika e beskontaktna i nedestruktivna. Izuzetno e precizna pri određivanu debline filmova tako da se pomoću ne može postići rezolucia mana od desetog dela 1 nm. Ona e takođe apsolutna, što znači da ne zahteva referentno merene, a realni i imaginarni deo dielektrične funkcie se mogu odrediti bez korišćena kompleksne Kramers-Kroning analize. *Rad saopšten na skupu Sedmi seminar mladih istraživača, Beograd, 4. decembar 008. Autor za prepisku: M. Mirić, Institut za fiziku, Pregrevica 118, Beograd, Srbia. E-pošta: mmiric@phy.bg.ac.rs Rad primlen:. decembar 008. Rad prihvaćen: 15. februar 009. Cil ovog rada e proučavane optičkih svostva kao i debline filmova različitih materiala nanometarskih dimenzia u UV-VIS-NIR oblasti. EKSPERIMENTALNI DEO Elipsometriski spektri analizirani u ovom radu dobieni su pomoću SOPRA GES-5 elipsometra sa mogućnošću promene upadnog ugla. On radi u osnovno konfiguracii sa rotiraućim polarizatorom. Izvor svetlosti e ksenonska lampa, a za detekciu se u UV-VIS oblasti koristi fotomultiplikator, dok se za NIR oblast koristi poluprovodnički InGaAs detektor. Za uzorke sa transparentnim supstratom korišćena e «mikrospot» opcia, da bi se izbegla neželena refleksia sa negove zadne strane. U slučau tankog filma SiO na supstratu od Si, sniman e spektar na opsegu 1,5 5,1 ev, sa korakom od 0,05 ev i upadnim uglom 75, dok su spektri uzoraka sa više filmova snimani na opsegu 1,5 4,3 ev, sa korakom 0,05 ev i upadnim uglom 70. Spektri nanopraha CeO i ugleničnih nanotuba snimani su na opsegu 1,5 6,1 ev, sa korakom takođe od 0,05 ev i upadnim uglom 70. Fitovane modela na eksperimentalnu krivu vršeno e pomoću Levenberg-Marquardt algoritma, pri čemu se analitički parametri koi se istovremeno određuu iterativnim postupkom menau sve dok funkcia greške (1) ne bude namana moguća [4,5]: N m 1 i1 N 1 eksp ( ) izr ( ) (1) ( ) U prethodnom izrazu, N predstavla ukupan bro snimlenih tačaka, m bro analitičkih parametara, ρ eksp (λ ) eksperimentalne vrednosti, ρ eksp (λ ) vrednosti izračunate na osnovu modela, λ talasna dužina svetlosti, a pomoću parametra σ se uračunava greška eksperimenta. Svi proračuni su obavleni pomoću programskog paketa Winelli_II Version

2 M.M. MIRIĆ i sar.: KARAKTERIZACIJA STRUKTURA NANOMETARSKIH DIMENZIJA... Hem. ind. 63 (3) 7 31 (009) REZULTATI I DISKUSIJA Na slici 1a prikazani su izmereni spektri elipsometriskih parametara tg(ψ) i cos(), za uzorak koi čini slo SiO na supstratu od Si. Eksperimentalni rezultati prikazani su kvadratima dok puna linia predstavla numerički modelovanu krivu. Fitovane eksperimentalnih podataka izvršeno e pomoću trofaznog modela 6, supstrat-film-ambient (slika 1b) i određena e deblina oksida. Model za uzorak koi se sastoi od stakla kao supstrata i tankog filma Si 3 N 4 prikazan e na slici b. Izmereni (kvadrati) i numerički modelovani spektri elipsometriskih parametara (puna linia), tg(ψ) i cos(), dati su na slici a. Kod ovog uzorka se pomoću SE može utvrditi postoane međusloa koi e mešavina stakla i Si 3 N 4. On e posledica činenice da površina stakla nie idealno ravna. Optičke osobine ovog međusloa određene su pomoću Bruggeman-ove aproksimacie 7. Debline sloeva su prikazane su na slici b. Naznačen e i međuslo i određen udeo svakog od dva materiala koi ulaze u negov sastav. Druga interesantna poava, otkrivena pomoću SE e da postoi tanak slo SiO koi nie unapred predviđen i koi se spontano stvorio na filmu Si 3 N 4. Slika 1. Tanki film SiO na supstratu od Si; a) rezultati merena i naboli fit; b) izgled strukture. Figure 1. Thin film of SiO on a Si substrate; a) experimental and calculated spectra; b) sketched structure. Slika. Niz sloeva na supstratu od stakla; a) rezultati merena i naboli fit; b) izgled strukture. Figure Multilayer system on glass substrate; a) experimental and calculated spectra ;b) sketched structure. Na slici 3 prikazan e model za uzorak kod koga se na supstratu od stakla nalazi čak 1 filmova, naizmenično poređanih Si 3 N 4 /SiO. Numerički modelovana kriva (puna linia), što se može videti sa slike 3a, sasvim dobro prati eksperimentalnu krivu (kvadrati). Podaci o deblinama poedinih sloeva dati su na slici 3b. 8

3 M.M. MIRIĆ i sar.: KARAKTERIZACIJA STRUKTURA NANOMETARSKIH DIMENZIJA... Hem. ind. 63 (3) 7 31 (009) Slika 3. Niz naizmeničnih sloeva Si 3 N 4 /SiO na supstratu od stakla; a) rezultati merena i naboli fit; b) izgled structure. Figure 3. Multilayer structure consisting of alternating Si 3 N 4 /SiO on a glass substrate; a) experimental and calculated spectra; b) sketched structure. Nanoprah CeO Spektri imaginarnog i realnog dela dielektrične funkcie nanopraha CeO dati su na slici 4. Eksperimentalni rezultati su fitovani pomoću Tauc-Lorentz modela 8,9 sa dva Lorentz-ova oscilatora. Opšti oblik za imaginarni deo dielektrične funkcie u ovom modelu u slučau ednog oscilatora opisan e relaciom: AE C( E Eg ) 0 1, E E g itl( E) ( E E ) C E E () 0 0, E Eg gde e E g energetski procep, E 0 energia prelaza, A intenzitet, a C širina pika. Realni deo dielektrične funkcie se izračunava pomoću Kramers-Kronig analize kao: Slika 3. Niz naizmeničnih sloeva Si 3 N 4 /SiO na supstratu od stakla; a) rezultati merena i naboli fit; b) izgled structure. Figure 3. Multilayer structure consisting of alternating Si 3 N 4 /SiO on a glass substrate; a) experimental and calculated spectra; b) sketched structure. 9

4 M.M. MIRIĆ i sar.: KARAKTERIZACIJA STRUKTURA NANOMETARSKIH DIMENZIJA... Hem. ind. 63 (3) 7 31 (009) rtl i ( ) ( E) P d (3) E E g gde e dielektrična funkcia na višim učestanostima. Prvi oscilator opisue prelaz sa nominalne Op trake na Ce4f stana [10]. Položa negovog pika dobien e na osnovu fitovana eksperimentalnih rezultata i iznosi 3,8 ev. Drugi oscilator e korišćen da bi opisao niskoenergetske repove prelaza višeg reda (Op Ce5d) i on varira u opsegu 6,9 10 ev. Imaginarni deo dielektrične funkcie odgovara gustini elektronskih stana materiala. U slučau kada važi parabolična aproksimacia, položa direktnog procepa se može odrediti na osnovu formalizma Tauc, Grigrovici i Vancu [11]. Naime, vrednost direktnog procepa se može izračunati na osnovu relacie (slika 5): Uglenične nanotube Na slici 6 prikazani su realni i imaginarni deo pseudodielektrične funkcie ugleničnih nanotuba na supstratu od siliciuma. Poam «pseudodielektrična» znači da se uzorak posmatra kao masivan iako ga čine supstrat od siliciuma i slo koi čine nanotube. Dok se ne odredi deblina sloa, ne može se mnogo znati o nanotubama, er u spektru učestvuu i optičke osobine supstrata. Kako oš uvek ne postoi odgovaraući model koi bi opisao dielektričnu funkciu ugleničnih nanotuba, ne mogu se preciznie odrediti parametri koi bi e interpretirali. Ono što se ipak može primetiti e da u delu spektra na nižim energiama, kristal siliciuma e gotovo transparentan, što znači da se apsorpcia u tom delu spektra može pripisati samo nanotubama. Uočen e pik absorpcie na energii 1,9 ev i označen e na slici 7. E) C ( E ) (4) ( 1 E g gde e koeficient apsorpcie materiala, a C 1 nagib linearne oblasti. Korišćenem izraza (4) dobiena e vrednost E g = 3,3 ev. Slika 6. Realni i imaginarni deo pseudodielektrične funkcie ugleničnih nanotuba na supstratu od siliciuma. Figure 6. Real and imaginary part of pseudodielectric function of carbon nanotubes on Si substrate. Slika 5. Određivane direktnog energetskog procepa na osnovu Tauc-ovog formalizma. Figure 5. Direct band gap calculation using Tauc formalism. Slika 7. Koeficient apsorpcie za ceo uzorak ugleničnih nanotuba na supstratu od sliciuma i za supstrat. Figure 7. Absorption coefficient for the entire sample of carbon nanotubes on Si substrate and for substrate only. ZAKLJUČAK U ovom radu e pokazano da se pomoću spektroskopske elipsometrie mogu proučavati optičke osobine materiala nanometarskih dimenzia. Činenica da e ova tehnika osetliva na postoane vrlo tankih filmova omogućila e ne samo da se izmere nihove debline, već i da 30

5 M.M. MIRIĆ i sar.: KARAKTERIZACIJA STRUKTURA NANOMETARSKIH DIMENZIJA... Hem. ind. 63 (3) 7 31 (009) se uoče neravnine u strukturi kao i tanak slo oksida koi se spontano stvorio na površini uzorka. Za karakterizaciu nanoprahova CeO bilo e neophodno parametrizovati nihovu optičku funkciu pomoću Tauc-Lorentz modela. Spektri realnog i imaginarnog dela pseudodielektrične funkcie ugleničnih nanotuba na supstratu od siliciuma takođe nose bitne informacie o energetskim prelazima unutar strukture, ali za nihovu interpretaciu potrebna e složenia analiza. Mogućnost korišćena spektroskopske elipsometrie u izučavanu optičkih osobina nanomateriala otvara put novim otkrićima u ovo oblasti. Zahvalnost Ova rad e finansiran od strane Ministarstva za nauku i tehnološki razvo Republike Srbie, proekat br : Fizika niskodimenzionih i nanometarskih struktura i materiala i evropskog FP7 proekta: Nanocharm. LITERATURA [1] G. Cao, Nanostructures and Nanomaterials, Imperial College Press, London, [] M. Losurdo, Thin Solid Films (004) [3] H.G. Tompkins, E.A. Irene, Handbook of Ellipsometry, William Andrew, New York, USA, 1996, p [4] G.E. Jellison, Jr., Appl. Opt. 30 (1991) [5] G.E. Jellison, Jr., Thin Solid Films 34 (1993) [6] R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, North-Holland Physics Publishing, Amsterdam, 1987, p. 83. [7] D.E. Aspnes, Thin Solid Films 89 (198) [8] G.E. Jellison, Jr., F.A. Modine, Appl. Phys. Lett. 69 (1996) 371. [9] G.E. Jellison, Jr., F.A. Modine, Appl. Phys. Lett. 69 (1996) 137. [10] P. Patsalas, S. Logothetidis, L. Sygellou, S. Kennou, Phys. Rev. B 68 (003) [11] J. Tauc, R. Grigorovici, A. Vancu, Phys. Stat. Sol. 15 (1966) SUMMARY CHARACTERISATION OF NANODIMENSIONAL STRUCTURES USING SPECTROSCOPIC ELLIPSOMETRY Milka M. Mirić, Marko B. Radović, Radoš B. Gaić, Zorana D. Dohčević-Mitrović, Zoran V. Popović Center for Solid State Physics and New Materials, Institute of Physics, Pregrevica 118, Belgrade, Serbia (Scientific paper) In this paper, using spectroscopic ellipsometry we studied the optical properties of thin films, nanocrystals and carbon nanotubes in UV-VIS-NIR range. With a three-phase model, we calculated the thickness of the SiO film on a silicon substrate. Using the model for multilayer structure together with the Bruggeman effective medium approximation we determined the existence of roughness on a glass substrate and we calculated the thickness of that layer. We also determined the thicknesses of 1 layers, Si 3 N 4 i SiO deposited alternately on a glass substrate. The dielectric function of CeO nanocrystal was modeled using the Tauc-Lorentz model and we calculated the value of the energy gap for this material. By analyzing the ellipsometry spectra for the carbon nanotube layer on the silicon substrate, we measured the real and imaginary part of its dielectric function. Klučne reči: Nanomateriali Optičke osobine Spektroskopska elipsometria Key words: Nanomaterials Optical properties Spectroscopic ellipsometry 31

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