Molecular dynamics simulation of ultrafast laser ablation of fused silica

Transcription

1 IOP Publishing Jounal of Physics: Confeence Seies 59 (27) 1 14 doi:1.188/ /59/1/22 Eighth Intenational Confeence on Lase Ablation Molecula dynamics simulation of ultafast lase ablation of fused silica C Cheng, A Q Wu and X Xu School of Mechanical Engineeing, Pudue Univesity, 585 Pudue Mall, West Lafayette, IN 4797, USA xxu@ecn.pudue.edu Abstact. Ultafast lase ablation of fused silica is studied using molecula dynamics simulations. Ionization and geneation of fee electons, absoption of the lase enegy by fee electons and enegy coupling between fee electons and ions ae consideed. The BKS potential is used to descibe molecula inteactions and is modified to include the effect of fee electons. Tempeatue, density, and mateial emoval ae computed, and the themal and non-themal mechanisms of ultafast lase ablation of fused silica ae discussed. PACS: 2.7.Ns; b; Jm; 79.2.Ds; 42.7.Ce. 1. Intoduction Fused silica is an impotant mateial that has been widely used in industy. Howeve, it is vey difficult to machine with taditional abasive tools because of its mechanical and themal popeties. In the ecent decades, ultafast lases have been used to successfully fabicate wide bandgap dielectics, including fused silica [1-3]. The machining esults ae clean, pecise and epoducible, which shows that ultafast lase is capable of micoscale fabication of glass. The pocess of lase ablation o dielectic beakdown is usually involved in ultafast lase machining of dielectics. Common dielectic mateials ae tanspaent to longe pulse o continue-wave lase beams. Howeve, duing ultafast iadiation, the high intensity of the lase pulse fist excites valence electons in the mateial to the conduction band via photoionization and avalanche ionization. The excited fee electons will absob lase enegy, and tansfe its enegy to the lattice, esulting in the tempeatue ise. When tempeatue is aised to a cetain degee, volumetic phase change and mateial decomposition will occu. This pocess is consideed as themal ablation because it is caused by the high tempeatue in the mateial. On the othe hand, because of the fee electon geneation, Coulomb foces exist among the atoms. This will esult in intenal epulsive foce and may cause sepaation of the taget mateial, which is the non-themal ablation. Both themal and non-themal (Coulomb explosion) ablation pocesses have been discussed in the liteatue [e.g., 4]. Recently, molecula dynamics (MD) has shown its potential in the investigation of femtosecond lase ablation [5 7]. MD tacks the motion of each molecule o atom at evey time step, so the detailed ablation phenomenon is taced and captued. In this wok, MD simulations ae pefomed to study the ablation of fused silica. Inteactions among atoms in fused silica ae modeled using the BKS potential [8]. Geneation of fee electons inside the mateial and e-combination of fee electons with ions, and enegy tansfe fom fee electons to the lattice ae consideed. The main goal of this wok is to illustate the ultafast lase ablation pocess of fused silica, and to eveal the mechanisms leading to the mateial s emoval. 27 IOP Publishing Ltd 1

2 11 2. Numeical Appoach 2.1 MD model In MD calculation, all atoms inteact with each othe via a potential function, and the motion of each atom is govened by the Newtonian motion law. Positions, velocities and foces of all atoms ae tacked at each time step, and ae used to evaluate macoscopic paametes such as tempeatue, pessue and density fom statistical data pocessing. The potential function applied in this wok to simulate fused silica is the widely-used BKS potential [8] expessed as * qiq j C, A e b BKS (1) 6 Hee, atoms i and j can be Si o O atom. is the distance between atoms, and A, b and C ae constants with values A Si-Si =, A Si-O = ev, A O-O = ev, b Si-O = Å -1, b O-O = 2.76 Å -1, C Si-Si =, C Si-O = ev Å -6, and C O-O = 175 ev Å -6. q is the chage of an atom in a SiO 2 molecule as q Si = +2.4 and q O * = is the constant fo Coulomb enegy calculation with the value /(4π8.8542) ev Å. To coect the well-known dawback of BKS potential [9] that the potential enegies of Si-O and O-O bonds fall to negative infinity when is small, the oiginal potential is modified by a Lennad-Jones 18-6 tem [9] 18 6, M, BKS 4 (2) 2.2 Fee electon effect Duing femtosecond lase ablation of fused silica, valence electons in the mateial will absob photons in the lase beam and become fee electons in the conduction band. These fee electons have two effects to the ablation pocess: themal and non-themal. Fo themal, fee electons absob lase enegy and tansfe the enegy to the lattice so that the tempeatue of the mateial is inceased and the phase change occus. At the same time, the negative changes of fee electons change the foce acting on atoms. When fee electons ae not geneated evenly (paticulaly in the diection along the lase popagation diection), they fom an electonic field. These effects may influence the mateial s emoval pocess and need to be consideed in the MD simulation. The pocesses of lase enegy absoption and geneation of fee electons ae calculated by solving a 2D axisymmetic wave popagation equation coupled with a ate equation of fee electon geneation [1]. The tansient distibutions of absobed lase enegy and fee electon density obtained fom that calculation ae used in this wok. Due to the geneation of fee electons, the net chage of the Si and O atoms in a SiO 2 molecule is changed, modifying the Coulomb inteaction among atoms. To account fo this modification, in the fist tem in the BKS potential (Equation 1), the q value of the Si atom is changed fom +2.4 to +2.8, while that fo the two O atoms is changed fom -1.2 to -.9. These values ae chosen so that the summay of the change of the SiO 2 molecule becomes +1, coesponding to the unit positive chage due to the absence of a fee electon. The numbe of fee electons and the numbe of SiO 2 molecules whose potentials need to be modified with espect to depth and time ae obtained fom the wave equation calculation and ae andomly distibuted into the x-y plane (the plane pependicula to the lase popagation diection) of the MD computational domain. Since fee electons ae not distibuted evenly along the lase popagation diection, they fom an electonic field which exets an exta foce to all chaged paticles (atoms o ions). This exta foce can be estimated by adding up the electostatic foce vectos fom all electons, and is calculated as: 2 n k nk Fc 2 e q (4) A k k A k kk A k whee q A is the chage of the paticle, k is the index of the stuctue laye, n k is the numbe of fee electons in laye k, and k is the distance of the paticle fom the cente of laye k. k A is the stuctue laye whee paticle A is located. Recombinations between fee electons and ions ae consideed as decaying exponentially with time, with a time constant of 5 ps. Afte ecombination, q values ae changed back to

3 12 the nomal values (fom +2.8 to +2.4 fo Si atoms and fom -.9 to -1.2 fo O atoms). Accodingly, the enegy in fee electons is tansfeed to the lattice with a time constant of 5 ps. 3. Results and discussions In this wok, the initial thickness of the taget is 198 nm, while the lateal dimension is 3.42 nm x 3.42 nm togethe with peiodic bounday conditions. The lase beam has a unifom spatial distibution and a tempoal Gaussian distibution of 1 fs FWHM centeed at 1 ps. The wavelength is 8 nm. The absoption depth of the lase pulse in fused silica is assumed to be 3 nm. Befoe lase heating, the mateial is fist equilibated at 3 K. Fist, the snapshots of the taget at diffeent time steps ae shown in Figue 1. Each Si o O atom is epesented by a black dot. The lase beam is incident pependiculaly onto the ight suface. The bottom of the taget is always located at x = nm. The absobed fluence is calculated as.5241 J/cm 2 fom Refeence [1]. Note that the scale in the x diection is 3 times smalle than that in the othe diection so that a bigge length can be shown. It is seen that at 11 ps, a void occus at x = 141 nm, about 95 nm below the suface. This void gows lage at late time steps and sepaates the mateial into two pats. The suface pat on the ight is ejected at a speed of about 6 m/s, causing the mateial ablation. Mateials sepaation unde the suface has been seen in lase ablation of othe mateials such as metal [11] due to a combination of themal and themomechanical effect, although hee the electonic effect also plays a ole as will be shown below. Figue 1. Snapshots of mateial. Lase enegy:.5 μj. The tempeatue distibutions at diffeent time steps ae shown in Figue 2. The fluctuation of tempeatue at the location aound 14 nm at 12 and 16 ps is due to the existence of the void demonstated in Figue 1. 1 ps 2 ps 8 ps 1 ps

4 13 12 ps 16 ps Figue 2. Tempeatue distibutions. To futhe eveal the mechanism of the void geneation and ablation shown in Figue 1, a elated calculation is pefomed whee fee electon effects ae excluded. Specifically, the geneation and ecombination of fee electons ae not consideed, which means all atoms do not change thei q values in thei potentials, and the exta foce fom electon density gadient expessed in Equation 4 is not applied. The incident and absobed lase fluences ae the same as in the pevious case. Results of snapshots of the atomic distibution at diffeent time steps ae shown in Figue 3. The most significant diffeence between Figue 1 and Figue 3 is that a void is geneated when the fee electon effect is consideed; while no void is seen when fee electon effects ae excluded. Futhe, we can compae the tempeatue distibution fo these two cases: the tempeatue distibutions at two time steps ae shown in Figue 4. It is seen that the tempeatue distibutions ae almost the same egadless of the fee electon effect. Theefoe, it can be concluded that the fee electon effects play a significant ole in mateial s sepaation. Geneation of fee electons changes the net chage caied by Si and O atoms in fused silica, causing epulsive Coulomb foce between them. This additional epulsive inteaction contibutes to the sepaation of the mateial which is heated by the lase beam. Figue 3. Snapshots of mateial..5 μj, no electon effect consideed. 9 5 ps 9 1 ps 7 7 T (K) T (K) 5 with electons no electons 5 with electons no electons Figue 4. Compaison of tempeatue distibution with and without consideing the fee electon effects. The above computations and discussions focus on a lase fluence (4.5 J/cm 2 ) that is found to be ight above the ablation theshold fom expeiments [1, 12]. Moe analyses on lase ablation at highe fluences ae being conducted in ode to obtain a moe complete pictue of ultafast lase ablation of fused silica. 4. Conclusion Femtosecond lase ablation of fused silica is simulated using the molecula dynamics technique, with the consideation of fee electon geneation and ecombination. The electostatic foce caused by fee electons is consideed in MD calculations, and is found to play an impotant ole in mateial s sepaation.

5 14 Fom calculation esults, the non-themal (Coulomb) effect is clealy shown fo a lase fluence ight above the ablation theshold. Refeences [1] Kote F, Sebin J, Koch J, Egbet A, Fallnich C, Ostendof A and Chichkov B N Appli. Phys. A [2] Lenzne M, Küge J, Satania S, Cheng Z, Spielmann Ch, Mouou G, Kautek W and Kausz F 1998 Phys. Rev. Lett [3] Pey M D, Stuat B C, Banks P S, Feit M D, Yanovsky V and Rubenchik A M 1999 J. Appli. Phys [4] Stoian R, Rosenfeld A, Ashkenasi D, Hetel I V, Bulgakova N M and Campbell E E B 22 Phys. Rev. Lett [5] Wang X and Xu X 22 Int. J. Heat Mass Tansfe [6] Zhigilei L V 23 Appl. Phys. A [7] Jeschke H O, Gacia M E and Bennmann K H 21 Phys. Rev. Lett [8] van Beest B W H, Kame G J and van Santen R A 199 Phys. Rev. Lett [9] Guissani Y and Guillot B 1996 J. Chem. Phys [1] Wu A Q, Chowdhuy I H and Xu X 25 Phys. Rev. B [11] Cheng C and Xu X 25 Phys. Rev. B accepted [12] Chowdhuy I H, Wu A Q, Xu X, and Weine A M 25 Appl. Phys. A Accepted