Application of a two-temperature model for the investigation of the periodic structure formation on Si surface in femtosecond laser interactions

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1 JOURNAL OF OPOLRONS AND ADVAND MARALS Vol. No. Marh p Applao of a wo-mpraur modl for h vsgao of h prod sruur formao o S surfa fmosod lasr raos. JY. DRRN a*. SARN a M. SNS a.. NA ab a Laboraor Lasrs Plasmas Proédés Phooqus UMR NRS 68/Uvrsé d la Médrraé 6 avu d Lumy 88 Marsll Fra b Laboraor Hubr ur UMR NRS 556/Uvrsé d Lyo 8 ru oî Lauras a. F 4 Sa- Fra W osdr h as of surfa rradao by a small umbr of fmosod lasr shos ladg o h formao of surfa rppls. o pla hs ff w propos a umral modl ha aous for h followg prosss: rfr of h lasr rradao wh a lromag surfa wav propagag o a slo sampl; fr arrr formao ad lasr rgy absorpo; rgy rlaao ad lro-phoo ouplg. W prform umral alulaos ag o aou h rfr of a surfa wav wh lasr; ad prs h obad smulao rsuls ordr o pla formao mhasms of h prmally obsrvd pars. Rvd Ju 9; apd Novmbr 9 Kywords: LPSS Fmosod lasr Rppl la slo. roduo Ulrashor puls lasr raos hav may applaos dffr aras suh as lasr mromahg maral aalyss ao-parl formao. parular fmosod lasrs a b usd o form surfa prod sruurs LPSS. hs sruurs a fd a applao h dvlopm of phoovola lls du o had absorpo : bla slo []. parular prvous prms dmosrad ha wh small lasr flu ad small umbr of lasr shos ar wavlgh spad prod sruurs alld rppls appar o h surfa of lasr-rradad maral. Wh largr umbr of shos s appld logad sruurs wr show o grow provdg good absorpo proprs of lgh ulravol ad vsbl wavlghs []. hs sruur formao was obsrvd for dffr arg marals mals [4] smoduors ad dlrs [56]. Dsgg h bs shap for rasg absorpo o smoduors phoovola lls phoossors rqurs a br udrsadg of h growh of sps ad rppls fmosod lasr raos [7]. Prvously umrous vsgaos boh prmal ad horal osdrd LPSS [8-]. For sa h modl of Sp osdrs lrodyam raos of lasr wav wh dfs of marals modfyg lromag flds polarao ad rgy absorpo of h arg []. h LPSS formao pross was furhrmor dsrbd by Kuramoo-Svashsy quao [4]. A y da of hs modl s h formao of slf-orgad sruurs [7]. addo o pla fmosod lasr rao ladg o h appara of h so-alld Hgh Spaal Frquy LPSS or HSFL a modl basd o h sod harmo grao was proposd [5]. Furhrmor ohr plaaos volvd h surfa wavs o mals surfas surfa plasmos [6] or surfa sabls [7]. Howvr fusd dlr marals hav a ras mall bhavour [8] afr fr arrr grao by o or mulphoo oao. hs papr w propos a wo-dmsoal modl ha aous for h rfr of lasr wav wh aohr lro-mag wav surfa wav. h modl provds som sghs o h dsy profl of h lasr grad fr-arrrs ad mpraurs.. Modl ad alulao dals o sudy h mhasms of fmosod lasr rao wh slo w us a wo mpraur modl M dsrbg lro ad la hrmal bhavor [9]. our quao sysm h surfa s a ; ad s h dph. Sold o lqud phas raso s osdrd by usg h halpy H whl la mpraur quals fuso mpraur of slo. W solv h followg s of quaos for h lros ad h la for bul Slo κ. κ. S

2 Applao of a wo-mpraur modl for h vsgao of h prod sruur formao o S surfa... 6 whr ad ar lro ad la mpraur; s h spf ha apay of lros; µ κ s h ha oduvy for lros []; s h olma osa; mobly; lro; µ s h lro s h fr arrr dsy; s h harg of ad κ ar a from []. τ s dsrbs h lro-la ouplg; τ s h lro-phoo ollso m []. quao s solvd wo dmsos arsa dph ad surfa by usg a mpl shm ad Forward lmao award Subsuo algorhm. al odo s K ad boudary odos ar Numa s odos. W osdr h oao prosss slo by usg h fr arrr bala quao ha aous o ad wo phoo oao Augr rombao ad mpa oao [] A A δ h h lasr whr [ m ] lasr Augr s h fr arrr dsy lroshols A s h absorpvy of lasr wav o R slo surfa [ m ] ra [ mw. ] [ s ] ra ad [ m ] 6. s s h o-phoo-oao s h wo-phoo-oao ra δ s h mpa oao lro avalah s h Augr rombao ra Augr of fr arrrs. Numral soluo s obad by usg a pl Rug- Kua 4 h ordr shm. h rflvy R ad h rgy absorpo off α abs ar ddud from dlr fuo basd o h Drud s modl []. r R g Γ lasr. lasr r Γ lasr m g Γ whr r s h ral dsy dd for opal m lasr bradow slo r ; s h val bad dsy g s h ompl dlr osa of ud maral []. h al odo for h fr arrr lros or hols dsy s m 5 m h m g hr g s h slo bad ; h s h Pla osa []. Fg.. Shmas of h wo-wav rao h arsa fram. o alula h rgy sour osdrg h rfr ff w us h pla wav prssos wh h followg lr flds whr s h lasr wav; s h surfa wav h org of h surfa wav s plad h so; ad govr lr fld polarao;

3 6. JY. Drr. Sar M. Ss.. a λ ad λ ar lasr ad surfa wav pulsaos whr λ s lasr wavlgh ad λ s surfa wav wavlgh; r. ad r. ar wav phass whr s y r. W also df s s s as show o Fg.. h oal sy Poyg vor o arg s [... ] s.... W assum ha h bam s Gaussa spo s spo Full Wdh a Half Mamum FWHM. W also hos a Gaussa dsrbuo for h mporal profl τ a FWHM. abs α τ ; l spo l τ τ o alula h lasr sy w a h avrag valu ovr h lasr prod λ. f λ λ ; Alhough f λ λ avrag o lasr prod s s s s s s 4 4 s 8 ; o obsrv h prssy of a smpl rfr par fr arrr dsy ad mpraurs w osdr h rfr bw h d ad h rfld wav o surfa by ag m 8 λ λ. h lasr flu f absorbd by h slo arg s gv by h dr rbad absorpo o phoo oao Augr rombao ad mpa oao []. hrfor h sour rm for h M D quao s: A A S Augr lasr lasr abs... δ α h h 4 h alulao paramrs usd h M modl ad h fr arrr bala quao ar dsrbd abl.

4 Applao of a wo-mpraur modl for h vsgao of h prod sruur formao o S surfa... 6 abl. Paramrs usd o solv h M quao fr arrr quao ad ompu h dlr fuo. Paramr Valu U Rfr J. m. K [] κ µ W. m. K [] µ.5m. V. s J. m. K [] κ 585. W. m. K []. m. K τ s τ 5.. W 5 δ.6 4 Augr.8 W [] m [] m [] s [] m 6. s []. V [] [] g 8 5 Γ 5.5 m [] m. s []. Rsuls ad dsusso h dvlopd modl dsrbg boh maral oao ad h lro-phoo ouplg s usd o sudy fmosod raos wh a slo arg moo-rysall sampl. A srs of alulaos s prformd o am h dsy of fr arrrs ad lro mpraur o surfa udr rfrd lasr rradao. [K] [µm] [ 7 m - ] Fg.. alulad dsrbuo of lro mpraur ad of fr arrr dsy a h lasr-rradad surfa whou surfa wav. h prsd profls ar obad a a m dlay ps afr h mamum of h Gaussa lasr puls for puls wdh of fs a 8 m for sgl lasr puls. Spo damr FWMH s µm; ad lasr flu s J.m -. Sampl s 4 µm larg ad µm dph. Fg. shows h ff of h lasr puls o lro mpraur ad fr arrr dsy dsrbuos o surfa a ps afr h mamum of h fmosod lasr puls. Lasr flu s J.m -. W obsrv ha h mpraur dsrbuo follows h lasr sy profl. h radal dsrbuo of fr arrr dsy shows ha a saurao rgm has b rahd. h obad shap of h dsrbuo a b plad by h saurao lasr lgh absorpo ha ours as soo as h dsy of fr arrrs rahs h ral plasma dsy [] sy 7 W.m [µm] Fg.. Radal sy dsrbuo obad a h lasr rradad surfa wh h rfr bw h lasr puls ad h surfa wav. alulao rsuls ar obad a ps µm wh λ λ 8 m.

5 64. JY. Drr. Sar M. Ss.. a Fg. w plod h radal sy dsrbuo produd a ps o h lasr-rradad surfa for wo wavs. h ff of rfr dsrbd so s a o aou. Hr h mamum sy s. 7 W.m - orrspods o J.m - of oal flu. h shap of h lasr profl s Gaussa ad h spo damr FWMH s µm. h spag bw osllaos s Λ 8 m. Hr w s λ λ 8 m o smplfy h alulaos of h avrag of h Poyg s vor ovr h osllao prod. W hoos lr fld ampluds ad o provd a good oras for obsrvg osllaos. Mamum rfr amplud s ormald o h flu of J.m -. [K] [µm] Fg. 4. alulad radal dsrbuo of h lro mpraur a ps m dlay from mamum lasr puls osllao. µm. Fg. 4 shows h radal dsrbuo of h lro mpraur a h surfa a ps afr lasr mamum sy. A hs m lro rgy s rasfrrd o h la ad dffuss alog boh h ad h as. h obsrvd shap of h lro mpraur profl s affd by boh h rfr ad h hrmal dffuso prosss. 7 [m - ] [µm] Fg. 5. Radal dsrbuo of fr arrr dsy a ps afr h mamum sy of lasr puls. Hr h rfr wh h surfa wav s osdrd. h lasr spo damr FWMH s µm oal flu s J.m - wavlghs of lasr ad surfa wavs ar 8 m. Fg. 5 shows h radal profl of fr arrr dsy obad a h surfa h alulaos wh h ff of h rfr dsrbd abov. h rsul dmosras ha h rfr par s osrvd h fr arrr dsy surfa profl a a dlay of ps afr mamum rrada of h lasr puls. our smulaos h rfr par s o rasd by hrmal dffuso. A smao of hrmal dffuso m for fr arrr o raspor o 8 m ofrms ha hs par a s for svral pods. Dffuso lgh a ps afr h mamum of sy s Ldff 9 m whh s o suff o ma rfrs dsappar a hs m. A 5 ps afr mamum sy hrmal dffuso lgh s smad o 75 m. hs ordrs of magud show ha h rfr par of h fr arrr dsy a las svral pods ad s possbl o obsrv h sam par h la mpraur dsrbuo by lrophoo ouplg dsrbd by h ouplg rm h quao. Our rsuls dmosra ha h rfr of lasr wav wh a surfa wav produs osllaos sy o h surfa of h slo sampl. hs osllaos ar also obsrvd h lro mpraur dsrbuo ad h fr arrr dsy dsrbuo o surfa wh a 8 m prody. W also obsrvd a saurao rgm fr arrr dsy whh dmosras ha fr arrr grao s lmd. h hrshold flu for obsrvg saurao s. J.m -. y modulag h spaal shap of sy w dmosra ha s possbl o ma rfrs h fr arrr dsy whh a b obsrvd for svral pods. W prs ha svral prosss a b volvd h formao of h sod wav: - h raos of lasr wav wh surfa dfs a lad o h dffrao ad h rfr ha rsul h surfa wav formao. hs plaao was proposd Sp al. papr []; - h obsrvd fr arrr dsy shows grads whh a lad o lro plasma wavs ul flag of hss grads or rombao of fr arrrs wh h la. hs pross may lad o h formao of h surfa plasmo wav. 4. olusos hs papr w hav dvlopd a modl o vsga h lasr rao wh a slo surfa ag o aou h rfrs bw h lasr lr fld ad a surfa wav. W hav obad h radal dsrbuo of fr arrr dsy ad h radal lro mpraur dsrbuo. arrr dsy profls show h followg: - f lasr wav rfrs wh a surfa wav h rsuld sy osllaos appar h fr arrr dsy profl; - h prod of h osllaos orrspods o h dffrao prod;

6 Applao of a wo-mpraur modl for h vsgao of h prod sruur formao o S surfa hrmal dffuso dos o ras h fr arrr dsy osllaos afr a ps dlay ; - A saurao rgm s obsrvd h fr arrr dsy for a flu grar ha. J.m -. - lro mpraur osllaos a b rasmd o h la mpraur by h pross of lro-phoo dffuso. Mor alulaos wll provd som rsuls o h possbly o pr h subsysm hrmal par o h la mpraur dsrbuo wh h lro-phoo dffuso pross. hs rsuls da ha h rfrs wh h surfa wav a b osdrd h plaao of fmosod LPSS growh pross. Suh a ff a pla why osllaos ar p mmory of h maral udr aourg fmosod lasr rradao Aowldgms hs wor s fudd by Frh Msry of Rsarh udr Prory op Ph.D. suppor. W also ha o hmr Adrï Kabash Jürg Rf Mahu Gullrm ad Rava Soa for fruful dsussos. Rfrs [] A. Srpgül A. Kur. aç J.. ary. Maur Joural Of Naophoos []. Sar M. Halbwa R. orrs P. Dlapor M. Ss S. Maru V. Vrvsh F. orrgrosa H. L. Rou S. asd Prodgs SP []. Wu. H. rouh L. Zhao J.. ary R. You J. A. Lvso. Maur R. M. Farrll P. Gohosar A. Kargr Appld Physs Lrs 78. [4] A. Y. Vorobyv. Guo Joural of Appld Physs [5] O. Varlamova F. osah J. Rf M. shor Appld Surfa S [6] R. ll L. ou A. Mollo P. Mosar D. Av Appld Physs A [7] J. Rf F. osah M. Hy S.V. Padlov Appld Surfa S [8] M. rbaum Joural of Appld Physs [9] J. os S. audah J. Krügr W. Kau M. Lr Appld Physs A [] M. s Zs. or Appld Surfa S [] H. M. Va Drl J.. Sp J. F. Youg Physal Rvw Lrs [] V. Zorba N. ouos. Zrgo. Foas Appld Ops 47 No. Aprl 8. [] J.. Sp J. F. Youg J. S. Prso H. M. Va Drl Physal Rvw [4] N. S. Murhy R. D. Prabhu J. J. Mar L. Zhou R. L. Hadr Joural of Appld Physs [5] J. os M. Mu H. Surm Joural of Appld Physs [6] R. aylor. Haovsy. Smova Lasr ad Phoo Rvw [7] S.. Asmov V. A. Khohlov sabls Lasr-Mar rao R Prss oa Rao FL 995. [8] P. P. Rajv M. Grsvolf. Haovsy. Smova R. S. aylor P.. orum D. M. Rayr V. R. hardwaj Joural of Physs : Aom Molular ad Opal Physs 4 S7 7. [9] S.. Asmov.S. Lu'yahu Physs Usph [] N. M. ulgaova R. Soa A. Rosfld. V. Hrl W. Mar... ampbll Appld Physs A [] H. M. Va Drl Physal Rvw [] R.. Smpso roduory lros for Sss ad grs d do. Ally ad ao 987. [].. a M. Mamaulov M. Ss Opal grg * orrspodg auhor: hbaul.drr@lp.uv-mrs.fr