Thermal excitation of d band electrons in Au: implications for laser-induced phase transformations

Transcription

1 Invitd Papr Thrmal xcitation of d band lctrons in Au: implications for lasr-inducd phas transformations Zhibin Lin and Lonid V. Zhigili * Dpartmnt of Matrials Scinc and Enginring, Univrsity of Virginia 116 Enginr's Way, Charlottsvill, VA ABSTRACT Th tmpratur dpndncs of th lctron hat capacity and th lctron-phonon coupling factor ar invstigatd for Au basd on th lctron dnsity of stats obtaind from ab initio lctronic structur calculations. Thrmal xcitation of d band lctrons lads to a significant (up to an ordr of magnitud) incras in th lctronphonon coupling factor and maks a considrabl contribution to th lctron hat capacity in th rang of lctron tmpraturs typically ralizd in fmtoscond lasr matrial procssing applications. Simulations prformd with a combind atomistic-continuum mthod dmonstrat that th incras in th strngth of th lctron-phonon coupling at high lctron tmpraturs lads to a fastr lattic hating, gnration of strongr thrmolastic strsss, and a significant dcras in th tim of th onst of th mlting procss. Th timscal of th mlting procss prdictd in th simulation accounting for th thrmal xcitation of d band lctrons is in xcllnt agrmnt with th rsults of rcnt tim-rsolvd lctron diffraction xprimnts. A simulation prformd with commonly usd approximations of a constant lctron-phonon coupling factor and a linar tmpratur dpndnc of th lctron hat capacity, on th othr hand, significantly ovrprdicts th tim of th bginning of th mlting procss, supporting th importanc of th lctron dnsity of stats ffcts and thrmal xcitation of lowr band lctrons for ralistic modling of fmtoscond puls lasr procssing. Kywords: Elctron-phonon coupling, lctron dnsity of stats, molcular dynamics, lasr mlting 1. INTRODUCTION Irradiation of a solid targt with an intns ultrashort (fmtoscond) lasr puls has th ability to bring matrial to a stat of strong lctron-lattic nonquilibrium and triggr a cascad of coupld transint procsss that includ lctron-phonon thrmalization, nonquilibrium nrgy transport, as wll as structural/phas transformations occurring undr xtrm and dynamic prssur-tmpratur conditions. Th transint and highly nonquilibrium charactr of lasr-inducd procsss maks th quantitativ thortical/computational dscription of th lasr-matrials intractions challnging. or mtals, computational modling of ultrashort-puls lasr intractions is commonly basd on th twotmpratur modl (TTM) [1], which dscribs th tim volution of th lattic and lctron tmpraturs, T l and T, by two coupld non-linar diffrntial quations: T r C ( T ) = [ K( T, Tl ) T ] G( T )( T Tl ) + S(, t) (1) t Tl Cl ( Tl ) = G( T )( T Tl ) () t whr C and K ar th hat capacitis and thrmal conductivitis of th lctrons and th lattic as dnotd by subscripts and l, G(T ) is th lctron-phonon coupling factor rlatd to th rat of th nrgy xchang btwn th lctrons and th lattic, and S ( r, t) is a sourc trm dscribing th local nrgy dposition by th lasr puls. Th modl accounts for th lasr xcitation of th conduction band lctrons, nrgy transfr to th atomic vibrations du to th lctron phonon coupling, and th lctronic hat diffusion from th irradiatd surfac to th bulk of th targt. * lzn@virginia.du; Phon: (434) ; ax: (434) ; High-Powr Lasr Ablation VI, ditd by Claud R. Phipps, Proc. of SPIE Vol. 661, 6610U, (006) X/06/$15 doi: / Proc. of SPIE Vol U-1

2 Dspit numrous succssful applications of TTM, th inhrnt limitation of th modl is its inability to adquatly dscrib th kintics of phas transformations and changs in th microstructur occurring undr highly nonquilibrium conditions inducd in th targt matrial by short puls lasr irradiation. In ordr to ovrcom this limitation w hav rcntly dvlopd a combind atomistic-continuum modl that incorporats th classical molcular dynamics (MD) mthod into th gnral framwork of th TTM modl []. In th combind TTM-MD modl, MD substituts th TTM quation for th lattic tmpratur in th rgion of irradiatd targt affctd by lasr-inducd structural transformations. Th diffusion quation for th lctron tmpratur is solvd simultanously with MD intgration of th quations of motion of atoms and an additional coupling trm is addd to th convntional MD quations of motion in ordr to account for th nrgy xchang btwn th lctrons and th lattic []. irst applications of th combind TTM-MD modl hav providd insights into th microscopic mchanisms of lasr mlting and photomchanical damag in mtal films and bulk targts [3,4,5,6]. Morovr, th important rol of non-thrmal channls of lasr nrgy rdistribution (nrgy transfr to th nrgy of collctiv atomic motions associatd with th rlaxation of lasr-inducd strsss and th nrgy of quasi-static anisotropic strsss), not accountd for in th convntional TTM modl, has bn rvald in TTM-MD modling [7]. An important aspct in th application of th TTM or TTM-MD modls for quantitativ dscriptions of th matrial rspons to th ultrashort puls lasr irradiation is th choic of adquat tmpratur dpndnt thrmophysical proprtis of th targt matrial. Du to th small hat capacity of th lctrons, lasr xcitation can transintly bring th lctron tmpratur to vry high valus, comparabl to th rmi tmpratur. At such high lctron tmpraturs, th tmpratur dpndnt thrmophysical proprtis of th systm can b dirctly affctd by th thrmal xcitation of th lowr band lctrons in nobl and transition mtals [8,9]. A dtaild analysis of th connctions btwn th lctron dnsity of stats (DOS) in th targt matrial and th tmpratur dpndnc of th lctron-phonon coupling, lctron hat capacity and thrmal conductivity ar ndd for a ralistic dscription of lasrmatrial intractions. In this papr, th ffcts of th lctron DOS on thrmophysical matrial proprtis ar illustratd for fmtoscond lasr intractions with Au films. In th nxt sction, th tmpratur dpndncs of th lctron hat capacity and th lctron-phonon coupling factor ar analyzd basd on th lctronic structur calculations prformd within th dnsity functional thory. Th rsults of th analysis of th thrmophysical proprtis of Au at high lctron tmpraturs ar incorporatd into TTM-MD modl and applid for simulations of lasr mlting of thin Au films. Th rsults of th simulations ar prsntd and rlatd to th xprimntal data obtaind for a similar systm in rcnt timrsolvd lctron diffraction xprimnts in Sction 3. A brif summary of th rsults is givn in Sction 4.. THE EECT O DOS AND THERMAL EXCITATION O ELECTRONS ON THERMOPHYSICAL PROPERTIES Th ffct of th thrmal xcitation of 5d band lctrons in Au on th thrmophysical proprtis of th matrial irradiatd by an intns lasr puls is discussd in this sction. In particular, th tmpratur dpndncs of th lctron hat capacity C (T ) and th lctron-phonon coupling factor G(T ) ar analyzd in a broad rang of th lctron tmpraturs basd on th lctron DOS obtaind from ab initio lctronic structur calculations. Th rsults of th calculations ar compard with th prdictions of th fr lctron gas modl..1 Elctron DOS, chmical potntial, and lctron hat capacity Th lctron hat capacity can b calculatd by taking th drivativ of th total lctronic nrgy dnsity with rspct to th lctron tmpratur [10]: u f ( ε, µ, T ) C ( T ) = ( ε ε ) g( ε ) dε T = (3) T V whr µ is th chmical potntial at T, ε is th rmi nrgy, g(ε) is th lctron DOS at th nrgy lvl ε, and -1 f ( ε, µ, T ) is th rmi distribution function dfind as f ( ε, µ, T ) = {xp[( ε - µ )/ kbt ] + 1}. Whn th lctron tmpratur is much smallr than th rmi tmpratur (T = K for Au [10]), only lctrons at around th rmi surfac ar xcitd and th lctron hat capacity is known to b a linar function of th lctron tmpratur, C T = γt, whr γ is th lctron hat capacity constant dfind, within th fr lctron gas modl, by th fr ( ) Proc. of SPIE Vol U-

3 lctron dnsity n and th rmi nrgy ε, γ = π nk B / ε. In particular, using th valus of th fr lctron dnsity and th rmi nrgy from Rf. [10], th lctron hat capacity constant for Au can b calculatd to b γ = 6.7 Jm -3 K -. At high lctron tmpraturs, howvr, lowr band lctrons could b xcitd to th conduction band, rsulting in dviations from th linar tmpratur dpndnc of th lctron hat capacity. Both thortical calculations [11,1,13] and X-ray photomission spctroscopy xprimnts [14] hav shown that th d band in Au, locatd rlativly clos to th rmi lvl, has a rathr complicatd structur. In th analysis of th tmpratur dpndnc of th thrmophysical proprtis of Au prformd in [9], a squar function cntrd at 4.8 V blow th rmi nrgy with a width of 5. V was usd as an approximation of th d band. In ordr to undrstand to what dgr th fin structur of th lctron DOS would affct th tmpratur dpndnt thrmophysical proprtis in Au, w prform th lctronic structur calculation using th Vinna Ab-initio Simulation Packag (VASP) [15] and obtain th lctron DOS for Au at T =0 K, shown in ig. 1. Th calculation is don for th quilibrium lattic paramtr, Å, using th Vandrbilt ultrasoft psudopotntial (US) [16] whr th xchang corrlation trm is tratd within th gnralizd gradint approximation (GGA). It can b sn from ig. 1 that, although th squar function dscribs th prsnc of high dnsity of stats associatd with d band lctrons, accounting for th dtaild structur of th d band, spcially on th high nrgy sid clos to th rmi lvl, can introduc significant corrctions to th calculatd numbr of thrmally xcitd lctrons. rom xamination of th lctron DOS togthr with th rmi distribution functions at various lctron tmpraturs, it is clar that for lctron tmpraturs lss than 0.1 V (~10 3 K) only lctrons around th rmi lvl ar xcitd, whil at T ~ 1 V (~10 4 K) or highr, th numbr of xcitd d band lctrons can b significant and should b takn into account. In ordr to calculat th lctron hat capacity from Eq. (3), it is ncssary to valuat th xprssion for f / T, which rquirs th dtrmination of th chmical potntial µ(t ). rom th consrvation of th total numbr of lctrons, on can obtain th chmical potntial by stting th rsult of th intgration of th product of DOS and th rmi distribution function at T ovr all nrgy lvls to b qual to th total numbr of lctrons N [10], N ) = f ( ε, µ ( T ), T ) g( ε dε (4) Th chmical potntial obtaind from Eq. (4) as a function of th lctron tmpratur using thr diffrnt approximations of DOS for Au is shown in ig.. It is asy Dnsity of Stats (DOS), stats/v/atom.0-03 > 6.5 a = 1) 0- E 0) = jiwith - swith swith DOS Elctron Tmpratur T, 104K -I-I--I II II II igur 1. Elctron DOS obtaind in lctron structur calculations prformd with VASP (solid lin) and a squar function approximation for th 5d band in Au usd in Rf. [9] (dashd lin). Th rmi distribution functions ar also shown for thr diffrnt valus of th lctron tmpratur. igur. Chmical potntial of Au as a function of th lctron tmpratur calculatd using thr diffrnt approximations of DOS for Au: DOS obtaind with VASP (solid lin), squar function approximation for th 5d band (dash-dottd lin), and nglcting th contribution of th d lctrons (dashd lin). Proc. of SPIE Vol U-3

4 to vrify that with only s lctrons takn into account, th chmical potntial obys th xprssion drivd from th Sommrfld xpansion in th fr lctron gas modl [10], π k BT µ ( T ) = 1 ε (5) 1 ε It is clar from ig. that in both calculations accounting for th prsnc of d band lctrons, th chmical potntials agr wll with th fr lctron gas modl, Eq. (5), for T lss than ~3000 K. Howvr, as discussd abov for ig. 1, as T is incrasing, th numbr of xcitd d band lctrons bcoms significant and th chmical potntial starts to dviat from Eq. (5). In th cas of th DOS calculatd from VASP, th sharp incras of th numbr of stats at nrgis that ar highr than th high-nrgy dg of th squar function, ε = -. V, and th contribution of d band stats at around th rmi lvl, ig. 1 and Rf. [17], rsult in th highr valus of th chmical potntial as compard to th ons obtaind with th squar function approximation of th d band. - C,(J7T, C,(Tjwithsqiarfunction DOS C,(jwith DOS fromvasp calculation 30 - // /, -7, /7 /7 / V 7,1 -p I!!!! 05 I 1.5 Elctron Tmpratur Ta, 104K igur 3. Elctron hat capacity of Au as a function of th lctron tmpratur calculatd using C = γt with γ = 71 Jm -3 K - [18] and with th sam two approximations of DOS for Au as in ig.. In ig. 3 th tmpratur dpndncs of th lctron hat capacity, calculatd from Eq. (3), ar shown for thr approximations of DOS discussd abov and usd in th calculation of th chmical potntial in ig.. Th diffrnc in th tmpratur dpndncs of th prdictd lctron hat capacity can b undrstood from th fact that at a sufficintly high tmpratur significant xcitation occurs from th d band in Au, which contains a larg numbr of lctron stats. Calculations prformd with th squar function approximation of th d band giv a similar tmpratur dpndnc for th lctron hat capacity but undrstimat th valus of th hat capacity du to lack of a complt dscription of th d band. Larg dviations of th lctron hat capacity from th linar dpndnc at lctron tmpraturs that can b radily achivd by ultrashort lasr pulss suggst that th application of commonly usd linar approximation C( T ) = γt could rsult in a significant ovrstimation of th transint valus of th lctron tmpratur during th tim of th lctron-lattic nonquilibrium. Th lctron thrmal conductivity is also affctd by th thrmal xcitation of lowr band lctrons as it is rlatd to th lctron hat capacity through th Drud modl rlationship, κ ( T, Tl ) = vc ( T ) τ ( T, Tl ) / 3 [10], whr v is th rmi vlocity and τ ( T, Tl ) is th total lctron scattring tim with othr lctrons and th lattic. Th total lctron scattring tim is dfind by th lctron-lctron scattring tim, τ, and th lctron-phonon scattring tim, τ, and can b valuatd from th sum of th scattring rats, ph 1/ τ = 1/ τ + 1/ τ ph = AT + BT, l whr A and B ar constants [8,10]. Th dviation of th lctron hat capacity from th linar tmpratur dpndnc, ig. 3, would also rsult in a fastr lctronic hat transfr during th initial stag of th lctron-phonon nonquilibrium. In th xampl problm considrd in Sction 3 (lasr intraction with 0 nm fr standing Au film), howvr, a uniform distribution of th lctron tmpratur is stablishd in th film on th timscal of th lctronphonon thrmalization and th lctron thrmal conductivity dos not play a rol in this cas.. Tmpratur dpndnc of th lctron-phonon coupling factor Whil th lctron-phonon coupling has bn undr activ invstigations in th fild of suprconductivity for svral dcads, it has also attractd a rnwd intrst with th fast growth of fmtoscond lasr applications, in which th rat of th nrgy transport btwn hot lctrons and th lattic has dirct implications on lasr inducd procsss. Thortical invstigations hav bn focusd on dscribing th nrgy xchang through lctron-phonon collision Proc. of SPIE Vol U-4

5 quations that charactriz th phonon mission and absorption procsss. Th lctron-phonon nrgy xchang within th fr lctron gas modl was first addrssd by Kaganov t al. [19]. It was found that th nrgy xchang rat could b xprssd in trms of th lctron rlaxation tim at T and T l. At lattic and lctron tmpraturs much highr than th Dby tmpratur and T >> T l, th rat of th nrgy transfr from th lctrons to th lattic pr unit volum is E t = G( T T ), / l G π mcs n0 =, (6) 6 τ ( T ) T whr m is th ffctiv lctron mass, C s is th spd of sound, n 0 is th numbr dnsity of th lctrons, and τ(t ) is th lctron rlaxation tim dfind as th lctron-phonon scattring tim and valuatd undr th assumption that th lattic tmpratur is qual to th lctron tmpratur [19]. Th lctron-phonon scattring is proportional to th invrs of th phonon tmpratur and, undr th condition of T = T l, τ(t ) ~ 1/T, lading to a constant valu of th coupling factor givn by th Kaganov s xprssion [1]. Whil a constant valu for th lctron-phonon coupling factor is usd in most of currnt computational and thortical studis of short-puls lasr intractions with mtals, thr is growing xprimntal vidnc suggsting that th applicability of th constant lctron-phonon coupling may b limitd to low lasr intnsitis (low lctronic tmpraturs). or xampl, th coupling constant is usd as a fitting paramtr in Rf. [0] to obtain an agrmnt btwn th calculatd and xprimntal valus of th ablation thrshold in Au, whras an mpirical G(T ) dpndnc is introducd in Rf. [1] to provid a good dscription of lctron photomission data. Svral approachs hav bn proposd in ordr to account for th tmpratur dpndnc of th lctronphonon coupling factor. Basd on th Kaganov s xprssion for th lctron-phonon nrgy xchang rat, Eq. (6), Chn t al. [] introducd a phnomnological modl in which both lctron-lctron and lctron-phonon scattring rats ar includd in th valuation of th lctron rlaxation tim, τ(t ) in Eq. (6). Th lctron-lctron scattring, indd, starts to significantly contribut to th total lctron scattring rat at high lctron tmpraturs, abov ~1 V. Whil this contribution dirctly affcts th lctron transport proprtis (thrmal and lctrical conductivitis), th rlvanc of th lctron-lctron scattring to th lctron-phonon coupling factor is qustionabl. Similarly, th valuation of th lctron rlaxation tim τ(t ) basd on th tmpratur dpndnc of th lctrical or thrmal conductivity [1,3,4] includs th contribution of lctron-lctron scattring and is inappropriat for th calculation of th lctron-phonon coupling at high lctron tmpraturs. As discussd abov, in Sction.1, in th high lctron tmpratur rgim, a quantitativ analysis of th lctron rlaxation dynamics in mtals with low-laying d bands should go byond th fr lctron modl and should includ th considration of th lctron DOS ffcts. Thus, th discussion providd in Sction.1 for th lctron hat capacity and chmical potntial should b xtndd to th lctron-phonon coupling. A gnral dscription of th lctron-phonon nrgy xchang involving arbitrary lctron DOS was dvlopd by Alln [5] basd on th lctronphonon collisions quations. Th rat of th nrgy xchang btwn th lctrons and th lattic can b thn xprssd as E t p 4π = hωq M kk S( k, k ) δ ( ε k ε k + hωq ) (7) hn c k, k whr M kk is th lctron-phonon scattring matrix lmnt [6], N c is th numbr of unit clls in th sampl, k and Q dnot th lctron and phonon quantum numbrs, rspctivly. S( k, k ) = ( k k ) N Q k (1 k ) is th socalld thrmal factor that charactrizs th phonon absorption and mission procsss in th lctron-phonon scattring, whr k and N Q ar th rmi-dirac and Bos-Einstin distribution functions, rspctivly. Assuming that nar room tmpratur only lctron stats around th rmi nrgy contribut to th scattring procsss, Eq. (7) can b rwrittn in trms of th lctron-phonon spctral function α ( Ω) from th suprconductivity thory [5]: E t p ) 0 = π N g( ε α ( Ω)( hω) [ N( Ω, T ) N( Ω, T )] dω (8) c l Proc. of SPIE Vol U-5

6 By dfining E / t = G ( T )( Tl T ) and.. G(T) from squar function DOS making a Taylor xpansion of Eq. (8) in trms of G(Tj from DOS calculatd by VASP B and, on could obtain th lctron-phonon / B l 7 7 coupling constant: G / 0 = πhk B λ ω g( ε ), whr λ is th 7 / lctron-phonon coupling constant usd in th / / 7 suprconductivity thory and <ω > is th scond momnt /7 /7 of th phonon spctrum dfind by McMillan [7]. or Au, with th valu λ<ω >=3±4 mv masurd in Rf. [8] and DOS shown in ig. 1, w can dtrmin th room tmpratur lctron-phonon coupling constant, G 0 = /,.5 10 /7 Wm -3 K -1, which is consistnt with th on obtaind from rflctivity xprimnts: G=(.± 0.3) Wm -3 K -1 7 at low lctron tmpraturs (a fw thousand K) [18]. or high T situations, it is ncssary to tak into , account th lctron nrgy dpndnc of th lctronphonon spctral function, i.. α ( ε, ε, Ω). In ordr to xplicitly account for th d band lctrons in Au, Wang t al. [8] proposd an approximation of th spctral function basd on th assumption that th magnitud of M kk is Elctron Tmpratur T, 104K igur 4. Elctron-phonon coupling factor as a function of th lctron tmpratur calculatd for DOS obtaind with VASP (solid lin) and squar function approximation for th 5d band (dash-dottd lin). indpndnt of th lctron stats, which lads to: α ( ε, ε, Ω) = [ g( ε ) g( ε ) / g ( ε )] α ( ε, ε, Ω). An xprssion for th tmpratur dpndnt lctron-phonon coupling factor could b thn obtaind using th approach discussd in Rf. [5]: πhkbλ ω f G( T ) = g ε dε g ε ( )( ) ( ) ε (9) It is asy to vrify that at low lctron tmpraturs, f / ε rducs to a dlta function and Eq. (9) givs a constant valu, rcovring th xprssion G 0 givn by Alln, whras at high lctron tmpraturs, f / ε for ε away from ε can no longr b nglctd, lading to a tmpratur dpndnc of th lctron-phonon coupling factor. Th rsults for G(T ) in Au obtaind with Eq. (9) using two diffrnt dscriptions of th d band lctrons discussd in Sction.1, ar shown in ig. 4. In both cass th lctron-phonon coupling factor rmains approximatly constant at T blow ~3000 K. This obsrvation is consistnt with th rsults shown in igs. and 3 for th lctron hat capacity and chmical potntial, whr th contribution from th thrmal xcitation of th d band lctrons also bcoms significant only whn T bcoms largr than ~3000 K. This fact also implis that at low xcitation lvls, whr th lctron tmpratur only rachs svral thousand K, th assumption of th constant lctron-phonon coupling factor provids a vry good dscription of th rat of th lctron-lattic nrgy xchang. Howvr, as th lctron tmpratur incrass abov ~3000 K, th valu for th lctron-phonon coupling factor with th full dscription of th lctron DOS starts to significantly dviat from th constant valu. Th lctron-phonon factor calculatd with th full dscription of DOS xcds th room tmpratur valu by a factor of 5.8 at T = K and by a factor of 8.9 at T = 10 4 K. As apparnt from ig. 4, th dtaild dscription of lctron DOS obtaind in th lctronic structur calculation givs a consistntly highr valu of th lctron-phonon coupling than th on using th squar function approximation for d band lctrons. A significant incras in th lctron-phonon coupling in th rang of lctron tmpraturs typically ralizd in fmtoscond lasr matrial procssing applications may lad to important practical implications. Th fastr nrgy transfr from th hot lctrons to th lattic can rsult in th thrmal nrgy confinmnt in a smallr surfac rgion of th irradiatd targt, gnration of strongr thrmolastic strsss, rduction of th thrshold fluncs for th onst of lasr mlting and ablation, and changs in th timscals of th lasr inducd phas transformations. Som of th implications of th tmpratur dpndnc of th thrmophysical paramtrs discussd in this sction ar illustratd in th TTM-MD simulations prsntd in Sction 3. Proc. of SPIE Vol U-6

7 3. TTM-MD SIMULATIONS O LASER MELTING O A THIN Au ILM In ordr to tst th ffct of th modifid tmpratur dpndnc of th lctron hat capacity and th lctron-phonon coupling factor discussd abov on th matrial rspons to th ultrashort puls lasr irradiation, w incorporatd th rsults illustratd in igs. 3 and 4 into th TTM-MD computational modl [] and prformd simulations of lasr mlting of a 0 nm frstanding Au film. Th conditions of th simulations ar chosn to b similar to th ons ralizd in rcnt tim-rsolvd lctron diffraction xprimnts prformd in th transmission mod for thin frstanding films [9]. Th rsults of th simulations obtaind with and without taking into account th DOS ffcts ar rlatd to th xprimntal obsrvations. 3.1 Computational modl Simulations of lasr mlting of a 0 nm frstanding Au film irradiatd by a 00 fs lasr puls at an absorbd flunc of 9.5 J/m ar prformd with a combind TTM MD modl dscribd in dtails lswhr []. Brifly, th modl is basd on th TTM quations in which th classical MD mthod substituts th TTM quation for th lattic tmpratur, Eq. (). Th quation for th lctron tmpratur, Eq. (1), is solvd by a finit diffrnc mthod simultanously with th MD intgration of quations of motion of atoms. Th lctron tmpratur ntrs a coupling trm that is addd to th MD quations of motion to account for th nrgy xchang btwn th lctrons and th lattic. Th clls in th finit diffrnc discrtization ar rlatd to th corrsponding volums of th MD systm and th local lattic tmpratur is dfind for ach cll from th avrag kintic nrgy of th thrmal motion of atoms. Irradiation by a lasr puls is rprsntd in th continuum part of th modl by a sourc trm with a Gaussian tmporal profil. Th lctron man fr path in Au is largr than th optical pntration dpth and th ballistic nrgy transport dfins th ffctiv lasr nrgy dposition dpth, stimatd to b on th ordr of 100 nm [18]. This dpth of ffctiv lctronic xcitation xcds th thicknss of th Au film considrd in this work, 0 nm. Th rflction of th ballistic lctrons from th back surfac of th film rsults in a uniform distribution of th lctronic tmpratur stablishd on th timscal of th lctron thrmalization. Th ffct of th ballistic nrgy transport and th finit siz of th film ar accountd for in th sourc trm dscribing th lasr irradiation []. Th initial MD computational cll is an CC crystal, consisting of 80,000 atoms with dimnsions of nm and priodic boundary conditions imposd in th dirctions paralll to two (001) fr surfacs. Th priodic boundary conditions simulat th situation in which th lasr spot diamtr is sufficintly larg so that th nrgy rdistribution in th latral dirctions, paralll to th fr surfacs of th film, can b nglctd on th tim-scals considrd in th simulations. An additional simulation with a largr, nm, MD computational cll consisting of 500,000 atoms is also prformd to provid a bttr visual pictur of th mlting procss. Th intratomic intraction in th MD part of th modl is dscribd by th mbddd atom mthod (EAM) [30]. Th choic of th intratomic potntial dfins all th thrmal and lastic proprtis of th matrial. Thrmodynamic proprtis of th EAM Au rlvant to th lasr hating and mlting procsss ar givn in Rf. [4]. Bfor applying lasr irradiation, all systms ar quilibratd at 300 K and zro prssur. To illustrat th practical implications of ffct of th lctron DOS on th thrmophysical paramtrs of th matrial discussd in Sction, th TTM-MD simulations wr prformd for thr sts of paramtrs of th TTM quation for th lctron tmpratur. On simulation was prformd for th paramtrs that corrspond to th fr lctron gas modl with only s band lctrons takn into account. In this cas th linar tmpratur dpndnc of th lctronic hat capacity, C = γt with γ = 71 Jm -3 K - (ig. 3), and a constant lctron-phonon coupling constant takn as th room tmpratur valu calculatd from th Alln s xprssion (Eq. 8), G c = Wm -3 K -1 ar usd. In two othr simulations, th tmpratur dpndncs of th lctron hat capacity and th lctron-phonon coupling factor accounting for thrmal xcitations of th d band lctrons and calculatd with th squar function approximation for th d band in on cas and with th dtaild DOS obtaind with VASP in anothr cas (igs. 3 and 4) ar usd. 3. Transint volution of lctron and lattic tmpraturs Th volution of th lattic and lctron tmpraturs, prdictd in TTM-MD simulations, is shown for thr diffrnt tratmnts of th lctron DOS for Au in ig. 5. Th maximum lctron tmpratur achivd by th nd of th lasr puls is significantly, by ~35%, ovrstimatd in th modl whr th convntional linar dpndnc of th hat capacity on lctron tmpratur is usd. As discussd in Sction.1 and illustratd in ig. 3, th contribution of Proc. of SPIE Vol U-7

8 jn Gandc(T)7T N - - squar function DOS DOS from VASP calculation 8000 N 1800 l750 I I I I I GandC(TyT squar function DOS DOS from VASP calculation K4060T Tim, ps (a) (b) Tim, ps igur 5. Evolution of th lctron (a) and lattic (b) tmpraturs in 0 nm Au film irradiatd with a 00 fs lasr puls at an absorbd flunc of 9.5 J/m. Th lattic tmpratur in (b) is normalizd to th quilibrium mlting tmpratur of EAM Au. Th tmpraturs ar avragd ovr th thicknss of th film. Th arrows show th tim of th onst of mlting. Th paramtrs usd in th simulations ar calculatd using thr diffrnt approximations of DOS for Au: DOS obtaind with VASP (solid lin), squar function approximation for th 5d band (dash-dottd lin), and nglcting th contribution of th d lctrons (dashd lin), as shown in igs. 3 and 4. th 5d band lctrons to th lctron hat capacity bcoms significant at high lctron tmpraturs and rsults in smallr valus of th lctron tmpratur during th tim of th initial lctron-lattic quilibration, ig. 5a. Th rat of th initial incras of th lattic tmpratur, shown in ig. 5b, is also significantly affctd by th choic of th approximation usd in th modl. In th simulations that account for th tmpratur dpndnc of th lctron-phonon coupling (ig. 4), th lattic tmpratur ris is much fastr, th tim whn th onst of th fast homognous mlting of th film is obsrvd shifts from ~16 ps to ~6 ps, and th tim of th saturation of th lattic tmpratur dcrass from ~35 ps to ~0 ps. Whil th volution of th lctron and lattic tmpraturs rflcts th rat of th nrgy xchang btwn th lctrons and th lattic, th lctron nrgy profils shown in ig. 6 provid mor dirct information on th lctron-phonon nrgy transfr rat and th tim of th lctron-lattic quilibration. It is apparnt from ig. 6 that th nrgy transfr is much fastr whn th thrmal xcitation of th d band lctrons is takn into account and th tmpratur dpndnt lctron-phonon coupling factor is usd in th TTM-MD simulations. Basd on th lctron nrgy plots, th lctron-phonon quilibration tim can b stimatd to b 33 ps, 35 ps, and 50 ps for th thr plots shown in ig. 6. 0) 0) = 0) = o t 0) 1 I I GandC(T)yT - - squar function DOS DOS from VASP calculation 0-) \ 15 E z0.\ Tim, ps igur 6. Evolution of th lctron nrgy in th sam thr simulations illustratd in ig. 5. Th lctron nrgis ar normalizd to th total lasr nrgy absorbd by th film, E tot = abs S, whr S is th surfac ara of th TTM-MD computational cll, and abs is th absorbd lasr flunc. Proc. of SPIE Vol U-8

9 E -5 = a ' P, OPa l Dpth (nm) I'J - - I!!!! I :0 M M 0 t W Tim (ps) (a) (b) Tim (ps) igur 7. Contour plots showing th spatial and tmporal volution of prssur in simulations of lasr mlting of a 0 nm Au film irradiatd with a 00 fs lasr puls at an absorbd flunc of 9.5 J/m. Th simulations ar prformd with two sts of paramtrs: (a) C (T ) and G(T ) calculatd with DOS from VASP and shown by solid lins in igs. 3 and 4; (b) C = γt with γ = 71 Jm -3 K - and G c = Wm -3 K -1. Solid and dashd lins show th bginning (90% of th crystal phas, as dfind by th local ordr paramtr []) and th nd (10% of th crystal phas) of th mlting procss. Lasr puls is dirctd along th Y-axs, from th top of th contour plots. Th stpwis shap of th contour plot boundaris is rlatd to th discrtization of th msh ovr which th avrag tmpratur and prssur valus ar calculatd. Although th initial lctron-phonon quilibration of th dpositd lasr nrgy is compltd by ps aftr th lasr puls, th insts in ig. 5 show long-trm oscillations of th lattic and lctron tmpraturs. Th oscillations ar strongr in th simulations whr d band lctrons ar takn into account and a tmpratur dpndnt lctron phonon coupling factor is usd. Th tmpratur oscillations can b rlatd to th rlaxation of th lasrinducd thrmolastic strsss. Th prssur contour plot in ig. 7 shows that th fast lattic hating rsults in th build up of a comprssiv strsss insid th film within th first ~5 ps. or a 0 nm frstanding Au film, 5 ps corrsponds to th tim of th mchanical rlaxation, i.. th tim ndd for two unloading wavs to cross a half of th dpth of th film. During th first svral picosconds th lattic hating taks plac undr conditions of th inrtial strss confinmnt [5], lading to th buildup of comprssiv strsss in th cntral part of th film, ig. 7. Th initial comprssiv prssur drivs th xpansion of th film, with tnsil strsss concntrating in th cntral part of th film. Th following gradually dissipating oscillations of th film continu byond th tim of th simulation. Th oscillation of th lattic and lctron tmpraturs shown in th insts in ig. 5, ar dirctly rlatd to th prssur oscillations in ig. 7. Comprssion lads to th incras of th lattic tmpratur whras xpansion corrsponds to cooling. Th lctronic tmpratur lags bhind th lattic tmpratur oscillations, inst in ig. 5b, with th dlay dfind by th strngth of th lctron-phonon coupling. Quantitativ thrmodynamic analysis prformd in Rfs. [,3] confirms that th tmpratur variations with prssur can b attributd to th adiabatic/isntropic xpansion of th film. As discussd abov, th charactristic tim of th mchanical rlaxation of th film is ~5 ps and, thrfor, th amount of nrgy transfrrd from th hot lctrons to th lattic during this tim dfins th magnitud of th initial comprssiv prssur and th amplitud of th prssur oscillations. Th fraction of th lasr nrgy transfrrd from th lctrons to th lattic during th first 5 ps can b obtaind from th lctron nrgy plots shown in ig. 6 and is 54% in th simulation prformd with paramtrs that account for th DOS ffcts and 3% in th simulation prformd with a constant lctron-phonon coupling factor and a linar tmpratur dpndnc of th lctron hat capacity. As a rsult, in th formr simulation th fast transfr of mor than a half of th dpositd lasr nrgy to th thrmal nrgy of atomic motions during th first 5 ps taks plac undr conditions of th inrtial strss confinmnt and lads to th buildup of strong comprssiv strsss, ig. 7a, whras in th lattr simulation th film xpands during th lattic hating, th initial prssur is wak and th oscillations can b hardly obsrvd in ig. 7b. Proc. of SPIE Vol U-9

10 Th diffrnc in th prssur oscillations in ig. 7 is rflctd in th diffrnc in th tmpratur oscillations in ig. 5, whr much wakr tmpratur oscillations ar obsrvd in th simulation prformd with paramtrs that do not account for th ffct of th d band lctrons. Not that at lowr lasr fluncs, blow th thrshold for lasr mlting, th lasr-inducd lastic oscillations of th film would rsult in priodic oscillations of th diffraction pak positions th ffct that has bn rcntly prdictd in simulations [31] and obsrvd in tim-rsolvd lctron diffraction xprimnts [3]. 3.3 Ultrafast mlting procss Th atomic-lvl pictur of th mlting procss prdictd in a TTM-MD simulation using C (T ) and G(T ) calculatd with DOS from VASP is prsntd in ig. 8. Th visual analysis of th snapshots takn during th mlting procss shows that at ~6 ps th growth of liquid rgions first occurs at two fr surfacs of th film, whr th kintic nrgy barrir is absnt for liquid nuclation. Howvr, du to th fast rat of th lattic hating, th propagation of mlting fronts from th fr surfacs of th film dos not mak any significant contribution to th ovrall mlting procss. By th tim of 6 ps, th lattic tmpratur xcds th ovrhating that corrsponds to th limit of th crystal stability of th EAM Au, α=t/t m ~1.5 [], lading to a spontanous homognous nuclation of a larg numbr of small liquid rgions throughout th film and a rapid collaps of th crystallin structur within th subsqunt 3-4 ps. As discussd in Rfs. [,4], th rlativ contribution of th homognous and htrognous mlting mchanisms in lasr mlting is controlld by th rat of th lattic hating and th tmpratur dpndnt vlocity of th propagation of th mlting fronts from th fr surfacs of th film. Th valu of lasr flunc usd in th simulations prsntd in this papr significantly, by ~75%, xcds th flunc ndd for th complt mlting of a 0 nm Au film [4]. At this lvl of lasr xcitation, th fast homognous mlting within 3-4 ps, similar to th on illustratd in ig. 8, is also obsrvd in th simulation prformd with a smallr constant valu of th lctron-phonon coupling factor. A larg diffrnc btwn th simulations prformd with and without taking into account th ffct of th thrmal xcitation of d band lctrons, howvr, is found in th tim of th onst of th mlting procss. Th diffrnc in th tim of th bginning of th mlting procss is apparnt from igs. 5b and 7, whr th onsts of mlting ar markd by arrows and solid lins, rspctivly. A mor clar rprsntation of th timscals of th mlting procss is givn in ig. 9, whr th volution of th fraction of th crystal phas is shown for simulations prformd with two sts of C (T ) and G(T ) paramtrs. In th cas of constant G and γ, th mlting starts at ~13 ps, th fraction of atoms in th liquid phas rachs 10% by 15 ps, 90% by 18 ps, and th crystallin rgions compltly disappar by 19 ps. In th simulation prformd with C (T ) and G(T ) prdictd using th lctron DOS obtaind in lctronic structur calculation, th mlting starts at ~6 ps, th fraction of atoms in th liquid phas rachs 10% by 7 ps, 90% by 9 ps, and th crystallin rgions compltly disappar by 10 ps. Th larg diffrnc in th starting tim of th mlting procss obsrvd btwn th two simulations discussd abov provids a good opportunity for xprimntal vrification of thortical modls discussd in Sction 3. In particular, th rsults of th simulations discussd in this sction can b dirctly rlatd to rcnt tim-rsolvd lctron diffraction masurmnts prformd for a 0 nm Au film irradiatd by a 00 fs lasr puls at an absorbd lasr flunc of 119 J/m [9]. In ordr to quantitativly rlat th simulation conditions to th xprimntal ons, w us th sam ovrhating paramtr α=t/t m =1.9 as in th xprimnt. Th ovrhating paramtr is dfind as a ratio of th maximum achivabl lattic tmpratur (obtaind undr th assumption that no mlting occurs) to th quilibrium mlting tmpratur, T m [33]. Using th thrmodynamic paramtrs of th EAM Au matrial [4], th valu of th absorbd flunc corrsponding to α=1.9 is found to b 9.5 J/m [34]. Th xprimntal rsults show th prsnc of th long-rang corrlations in th diffraction profils up to ~7 ps and th fast disapparanc of th diffraction paks corrsponding to th crystal ordring during th tim btwn 7 ps and 10 ps [9]. Ths xprimntal obsrvations ar in xcllnt agrmnt with th simulation rsults accounting for th thrmal xcitation of d band lctrons. W can conclud, thrfor, that th commonly usd approximations of th constant lctron-phonon coupling factor and th linar tmpratur dpndnc of th lctron hat capacity ar not appropriat for a ralistic dscription of ultrashort puls lasr-matrial intractions in th high-flunc rgim, whr lctron DOS ffcts start to play an important rol in dfining th timscals and othr paramtrs of lasr-inducd procsss. Proc. of SPIE Vol U-10

11 S 0 Distanc from th irradiatd surfac (nm) S PS S 0 Distanc from th irradiatd surfac (nm) BPS S 0 Distanc from th irradiatd surfac (nm) 7 p S 0 Distanc from th irradiatd surfac (nm) 8 p S 0 Distanc from th irradiatd surfac (nm) 9 ps S 0 Distanc from th irradiatd surfac (nm) D p5 igur 8. Snapshots of atomic configurations during th mlting procss in a 0 nm Au film irradiatd with a 00 fs lasr puls at an absorbd flunc of 9.5 J/m. Atoms ar colord according to th local ordr paramtr - blu atoms hav local crystallin surroundings, rd atoms blong to th liquid phas. Th lasr puls is dirctd from th right to th lft sids of th snapshots. Th simulation is prformd with C (T ) and G(T ) calculatd with DOS from VASP. Proc. of SPIE Vol U-11

12 In this study no attmpt has bn mad to account for th chang in th lctron DOS du to th modification of th lctronic structur at high lctron tmpraturs. Th modifications of th lctron structur would not affct th ssntial physics rsponsibl for th chang of th lctron hat capacity and lctron-phonon coupling causd by th thrmal xcitation of lowr band lctrons. Morovr, in th irradiation rgim considrd in this work th ffct of th variations of th lctron DOS on th calculatd physical proprtis is small. Rcnt invstigation of th modification of th lctronic structur at much highr lctron tmpraturs (~6 V) [35] shows that th d band shifts towards lowr nrgis whil th width of th d band dcrass. As a rsult, th contribution from th thrmal xcitation of d band lctrons to th lctron hat capacity and th lctronphonon coupling factor can b xpctd to b rducd at ths xtrm lctron tmpraturs. In th cas of transition mtals, such as Ni or Pt, du to th unfilld d stats in th lctronic configurations, th rmi lvl cuts through th d band [10]. Thus, th ffct of th thrmal xcitation of lctrons at high lctron tmpraturs could affct th lctron hat capacity and lctron-phonon coupling in a vry diffrnt way as compard to what is discussd in Sction 3 for Au. In particular, th lctron hat capacity would b smallr than th valus givn by th linar dpndnc on th lctron tmpratur, as shown raction of crystal phas, % P P P P igur 9. Th volution of th fraction of th crystal phas as a function of tim in simulations prformd with two sts of paramtrs: (Solid lin) C (T ) and G(T ) calculatd with DOS from VASP; (Dashd lin) C =γt with γ = 71 Jm -3 K - and G c = Wm -3 K -1. Th atoms in th crystal phas ar distinguishd from th ons in th liquid phas basd on th local ordr paramtr. for Pt in Rf. [1], whil th thrmal xcitation of lctrons may lad to th dcras of th lctron-phonon coupling with incrasing lctron tmpratur [36]. (0 II 4. SUMMARY Th tmpratur dpndncs of th lctron-phonon coupling factor and th lctron hat capacity ar invstigatd for Au basd on th lctronic structur calculation prformd within th dnsity functional thory. Thrmal xcitation of d band lctrons lads to a significant (up to an ordr of magnitud) incras in th lctronphonon coupling factor and maks a considrabl contribution to th lctron hat capacity in th rang of lctron tmpraturs typically ralizd in fmtoscond lasr matrial procssing applications. Th rsults of th analysis of th thrmophysical proprtis of Au at high lctron tmpraturs ar incorporatd into TTM-MD modl and applid for simulations of lasr mlting of thin Au films. Th incras in th strngth of th lctron-phonon coupling at high lctron tmpraturs lads to a fastr lattic hating, gnration of strongr thrmolastic strsss and a highr amplitud of long-trm oscillations of th film thicknss, as wll as significant changs in th tim of th onst of th mlting procss. Th lattr can b dirctly rlatd to th rsults of rcnt tim-rsolvd lctron diffraction xprimnts. Th xprimntal tim of th mlting onst and th duration of th mlting procss ar in xcllnt agrmnt with th rsults of th simulations in which th thrmal xcitation of d band lctrons is accountd for. A simulation prformd with commonly usd approximations of a constant lctron-phonon coupling factor and a linar tmpratur dpndnc of th lctron hat capacity, on th othr hand, is found to significantly (by a factor of ) ovrprdict th tim of th bginning of th mlting procss, supporting th importanc of th lctron DOS ffcts and thrmal xcitation of lowr band lctrons for ralistic modling of fmtoscond puls lasr procssing. ACKNOWLEDGEMENTS inancial support of this work is providd by th National Scinc oundation through th Thrmal Transport and Thrmal Procsss Program of th Chmical and Transport Systms Division (Award No. CTS ). Proc. of SPIE Vol U-1

13 REERENCES [1] S. I. Anisimov, B. L. Kapliovich, and T. L. Prl'man, Elctron mission from mtal surfacs xposd to ultrashort lasr pulss, Sov. Phys. JETP 39, , [] D. S. Ivanov and L. V. Zhigili, Combind atomistic-continuum modling of short puls lasr mlting and disintgration of mtal films, Phys. Rv. B 68, , 003. [3] D. S. Ivanov and L. V. Zhigili, Th ffct of prssur rlaxation on th mchanisms of short puls lasr mlting, Phys. Rv. Ltt. 91, , 003. [4] Z. Lin and L. V. Zhigili, Tim-rsolvd diffraction profils and atomic dynamics in short puls lasr inducd structural transformations: Molcular dynamics study, Phys. Rv. B 73, , 006. [5] E. Lvugl, D. S. Ivanov, and L. V. Zhigili, Photomchanical spallation of molcular and mtal targts: molcular dynamics study, Appl. Phys. A 79, 1643, 004. [6] L. V. Zhigili, D. S. Ivanov, E. Lvugl, B. Sadigh, and E. M. Bringa, Computr modling of lasr mlting and spallation of mtal targts, High-Powr Lasr Ablation V, Proc. SPIE 5448, 505, 004. [7] L. V. Zhigili and D. S. Ivanov, Channls of nrgy rdistribution in short-puls lasr intractions with mtal targts, Appl. Surf. Sci. 48, 433, 005. [8] X. Y. Wang, D. M. Riff, Y. S. L, and M. C. Down, Tim-rsolvd lctron-tmpratur masurmnt in a highly xcitd gold targt using fmtoscond thrmionic mission, Phys. Rv. B 50, 8016, [9] A. N. Smith and P. M. Norris, Numrical solution for th diffusion of high intnsity, ultrashort lasr pulss within mtal films, Procdings of 11 th Intrnational Hat Transfr Confrnc 5, 41, [10] N. W. Ashcroft and N. D. Mrmin, Solid Stat Physics (Holt, Rinhart and Winston, Nw York, 1976). [11] K. M. Ho and K. P. Bohnn, Stability of th missing-row rconstruction on fcc (110) transition-mtal surfacs, Phys. Rv. Ltt. 59, 1833, [1] T. Tsuchiya and K. Kawamura, irst-principls lctronic thrmal prssur of mtal Au and Pt, Phys. Rv. B 66, , 00. [13]. Kirchhoff, M. J. Mhl, N. I.Papanicolaou, D. A. Papaconstantopoulos, and.s.khan, Dynamical proprtis of Au from tight-binding molcular-dynamics simulations, Phys. Rv. B 63, , 001. [14] G. K. Wrthim and D. N. E. Buchanan, Cor-lctron binding nrgis of adsorbd mtallic monolayrs: Au/Ag(111), Phys. Rv. B 33, 914, [15] G. Krss and J. Hafnr, Ab initio molcular dynamics for liquid mtals, Phys. Rv. B 47, 558, [16] D. Vandrbilt, Soft slf-consistnt psudopotntials in a gnralizd ignvalu formalism, Phys. Rv. B 41,789, [17]. Ladstädtr, U. Hohnstr, P. Puschnig, and C. Ambrosch-Draxl, irst-principls calculation of hot-lctron scattring in mtals, Phys. Rv. B 70, 3515, 004. [18] J. Hohlfld, S.-S. Wllrshoff, J. Gudd, U. Conrad, V. Jahnk, and E. Matthias, Elctron and lattic dynamics following optical xcitation of mtals, Chm. Phys. 51, 37-58, 000. [19] M. I. Kaganov, I. M. Lifshitz, and L. V. Tanatarov, Rlaxation btwn lctrons and crystallin lattics, Sov. Phys. JETP 4, 173, [0] J. K. Chn and J. E. Braun, Modling of ultrashort lasr ablation of gold films in vacuum, J. Opt. A: Pur Appl. Opt. 5, 168, 003. [1] J. P. Girardau-Montaut and C. Girardau-Montaut, Thory of ultrashort nonlinar multiphoton photolctric mission from mtals, Phys. Rv. B 51, 13560, Proc. of SPIE Vol U-13

14 [] J. K. Chn, W. P. Latham and J. E. Braun, Th rol of lctron-phonon coupling in ultrafast lasr hating, J. Lasr Applications, 17, 63, 005. [3] D. Y. Tzou, Macro- to Microscal Hat Transfr: Th Lagging Bhavior (Washington, DC: Taylor & rancis, 1997). [4] Z. G. Wang, Ch. Dufour, E. Paumir, and M. Toulmond, Th S snsitivity of mtals undr swift-havy-ion irradiation: a transint thrmal procss, J. Phys.: Condns. Mattr 6, 6733, [5] P. B. Alln, Thory of thrmal rlaxation of lctrons in mtals, Phys. Rv. Ltt. 59, 1460, [6] J. M. Ziman, Elctrons and Phonons (Oxford Univ. Prss London, 1960). [7] W. L. McMillan, Transition tmpratur of strong-coupld suprconductors, Phys.Rv.167, 331, [8] S. D. Brorson, A. Karoonian, J. S. Moodra, D. W. ac, T. K. Chng, E. P. Ippn, M. S. Drsslhaus and G. Drsslhaus, mtoscond room-tmpratur masurmnt of th lctron-phonon coupling constant λ in mtallic suprconductors, Phys. Rv. Ltt. 64, 17, [9] J. R. Dwyr, C. T. Hbisn, R. Ernstorfr, M. Harb, V. Dyirmnjian, R. E. Jordan and R. J. D. Millr, mtoscond lctron diffraction: making th molcular movi, Phil. Trans. R. Soc. A 364, 741, 006. [30] X. W. Zhou, H. N. G. Wadly, R. A. Johnson, D. J. Larson, N. Tabat, A. Crzo, A. K. Ptford-Long, G. D. W. Smith, P. H. Clifton, R. L. Martns, and T.. Klly, Atomic scal structur of sputtrd mtal multilayrs, Acta Matr. 49, 4005, 001. [31] Z. Lin and L. V. Zhigili, Tim-rsolvd diffraction profils and structural dynamics of Ni film undr short lasr puls irradiation, J. Phys.: Confrnc Sris, in prss. [3] H. Park, X. Wang, S. Ni, R. Clinit, and J. Cao, Mchanism of cohrnt acoustic phonon gnration undr nonquilibrium conditions, Phys. Rv. B 7, (R), 005. [33] B. Rthfld, K. Sokolowski-Tintn, D. von dr Lind, and S. I. Anisimov, Ultrafast thrmal mlting of lasrxcitd solids by homognous nuclation, Phys. Rv. B 65, 09103, 00. [34] In simulations, th calculation of th ovrhating paramtr α=1.9 is don with a tmpratur dpndnt lattic hat capacity dtrmind for th EAM Au matrial [4], whras in Rf. [9] a constant hat capacity is assumd. Using an xprimntal tmpratur dpndnt hat capacity for Au [8], a smallr ovrhating factor of 1.7 can b obtaind for th absorbd lasr flunc of 119 J/m usd in th xprimnt [9]. Nvrthlss, this discrpancy dos not affct th physical intrprtations and conclusions drivd from th comparison of th simulations and xprimnts prsntd in this papr. In th simulation prformd at a lowr ovrhating of 1.7 with C (T ) and G(T ) calculatd with DOS from VASP, th timscal of th mlting procss is vry similar to th on at α=1.9: th mlting starts at ~8 ps, th fraction of atoms in th liquid phas rachs 10% by 10 ps, 90% by 14 ps, and th crystallin rgions compltly disappar by ~15 ps. [35] V. Rcouls, J. Clérouin, G. Zérah, P. M. Anglad, and S. Mazvt, Effct of intns lasr irradiation on th lattic stability of smiconductors and mtals, Phys. Rv. Ltt. 96, , 006. [36] Z. Lin and L. V. Zhigili, unpublishd. Proc. of SPIE Vol U-14