Effect of Intense Laser Irradiation on the Lattice Stability of Al 2 Au

Transcription

1 Commun. Theor. Phys. 59 (2013) Vol. 59, No. 5, May 15, 2013 Effect of Intense Laser Irradiation on the Lattice Stability of Al 2 Au SHEN Yan-Hong ( ), GAO Tao (Ô ), and WANG Ming-Ming ( ) Institute of Atomic and Molecular Physics, Sichuan University, Chengdu , China (Received November 1, 2012; revised manuscript received December 26, 2012) Abstract The structural, electronic and lattice-dynamical properties of the intermetallic Al 2Au at different electronic temperatures have been investigated via density functional calculations. The results of electronic density of state indicate that, although its value changes considerably, Al 2Au is still of metal with the increasing of electronic temperature. The acoustic mode of Al 2Au gets negative which leads to lattice dynamical instability when the electronic temperature is beyond 1.44 ev. Moreover, with the increasing of the electronic temperature, the vibrational frequencies of the T 1u optical mode (triply degenerate) of Al 2Au at Γ point decrease first and increase then, the turning point is at T e = 1.40 ev. T 2g optical mode at Γ point has a similar situation, but the turning point is at T e = 1.80 ev. The predicted melting temperatures of Al 2Au undergo a sharp decrease from 1333K at normal temperature to 1172 K at T e = 1.8 ev after intense laser irradiation. PACS numbers: A- Key words: lattice stability, laser irradiation, density functional calculation 1 Introduction The research on ultra-fast phenomena and laserinduced phase transitions of material submitted to intense laser irradiation has attracted considerable attention, which includes laser micromachining, surface treatment, or even surger. [1 2] The investigation of the properties of various materials under intense laser irradiation is favorable for applications. In recent years, the electronic structures and dynamical behaviors that take place in the metals Al and Au under intense laser irradiation have been studied by many groups due to the relevant technological importance and the theoretical interest of the laser-annealing effect. [3 6] At the meantime, the Al-Au alloys are also extensively studied, because of not only the technological application of gold-aluminum interconnects in the electronic packing industries, [7] but also their important practical use as the metallization schemes. [8] However, the Al-Au bimetallic system is, to the best of our knowledge, relatively poorly researched on the change of its electronic and latticedynamical properties after intense laser irradiation. In this work, we focus our attention on the lattice stability of the intermetallic Al 2 Au in laser-induced ultra-fast irradiation. In fact, Al 2 Au has been experimentally studied for their structures, optical properties and oxidation behavior. [9 15] Fuggle et al. [9] investigated systematically the band structures of Al 2 Au, by measuring the X-ray photoelectron spectra (XPS) and Al K and L 2,3 soft-xay emission spectral (SXS). Switendick et al. [10] applied a significant improvement over the free-electron model to study the nonrelativistic energy band structure of cubic AuAl 2. Tütüncü et al. [11] calculated the structural and electronic properties of AuAl 2 using ab initio pseudopotential method. Vishnubhatla et al. [12] reported the optical properties of the purple compound Al 2 Au by making use of mechanically polished reported bulk samples of AuAl 2. The oxidation behavior of Al 2 Au during a 3- month laboratory air exposure was characterized by Piao et al. [13] using SIMS, XPS, and XANES. Sritharam et al. [14] used X-ray photoelectron spectroscopy to observe the oxidation of Al 2 Au in the air and found an increasing trend of oxidation in Al-Au alloys as the Au content increases. Supansomboon et al. [15] analyzed the optical properties and technologies of Al 2 Au coatings which were prepared by vacuum deposition onto heated substrates. Theoretically, there are limited calculations for the effect of intense laser irradiation on Al 2 Au in the literature. In this paper, in order to check the correctness of our theoretical calculation method, we have also calculated the structural, electronic and lattice-dynamical properties of Al and Au after intense laser radiation. The results are in a good agreement with the calculations of Recoules et al. [2] The main aim of this work is to employ ab initio pseudopotential method and the density functional perturbation theory (DFPT) [16] to obtain a complete set of first-principle-based data for the electronic and lattice dynamical properties of Al 2 Au under the intense laser irradiation. When intense laser interacts with Al 2 Au, the electrons are excited within a few tens of femtoseconds. The energy subsequently transfers between the excited electrons and the ions leading to the thermal melting of the lattice mainly as a result of the electron-phonon coupling. The alloy has a dramatic modification of the interatomic potential and reaches its electronic temperature T e due to electron-electron and electron-hole collisions. The Corresponding author, gaotao@scu.edu.cn c 2013 Chinese Physical Society and IOP Publishing Ltd

2 590 Communications in Theoretical Physics Vol. 59 electronic properties of Al 2 Au are calculated at different electronic temperatures. Moreover, the evolution of the phonon spectrum as a function of the electronic temperature is calculated using linear response method. 2 Computation Details The computational studies have been performed using the well-known ABINIT code based on a planewave pseudopotential method within the density functional theory (DFT). [17 18] The local density approximation (LDA) [19] is used to describe the exchange correlation interactions. The interaction of valence electrons with ionic cores is described with norm-conserving pseudopotential technique. [20] The 3s, 3p and 5d, 6s are retained as valence for, respectively, aluminum and gold. [2] We have optimized the equilibrium lattice parameters before calculating electronic and lattice dynamical properties. The valence pseudowave functions are expanded in plane waves up to a kinetic energy cutoff of 20 hartree for Al 2 Au. A Monk horst-pack mesh of k points is used. Convergence tests show that the BZ sampling and the kinetic energy cutoff are sufficient to guarantee an excellent convergence. In the following calculations, we use the optimized lattice parameter determined by minimizing the crystal total energy. The linear-response method within the DFPT is used in the calculations of the phonon dispersion curves and density of states of Al 2 Au. The phonondispersion curves are calculated along the Γ-X-Γ-L-X-W- L high symmetry points. Compared with the direct approach (or frozen phonon approach), the linear-response method avoids the time-consuming supercell calculations and has important advantages in the calculation of the dynamical matrix at arbitrary q vectors. Dynamical matrices are later used for a Fourier interpolation to obtain the phonon frequencies in reciprocal space. 3 Results and Discussion 3.1 Lattice Optimization Al 2 Au has the CaF 2 structure with a space group of Fm3m (No. 225), [11] which is similar to the face-centered cubic structures of Al and Au. But the unit cell of Al 2 Au has three atoms with lattice constant a = 5.99 Å. [11] The Au atom is located in the 1a Wyckoff site (0, 0, 0) and the Al atom occupies the 2c (1/4, 1/4, 1/4) site. Firstly, by minimization of the total energy with respect to the unit-cell volume, we obtain the equilibrium lattice constant. The volume is directly related to the lattice constant. Because Al 2 Au has very high symmetry, we have not optimized the atomic position. The exchange correlation interactions are described by LDA. Our calculated equilibrium lattice parameter for Al 2 Au is Å, which is slightly smaller than the experimental value of 5.99 Å. [11] The comparison with experimental data shows an underestimate of the equilibrium lattice parameter by 0.18%. In this work, we have also optimized the lattice constants of Å and Å for, respectively, Al and Au, which are very close to the experimental values of Å [2] and Å. [2] These results are largely sufficient to allow the further study of electronic and dynamical properties. 3.2 Electronic Properties For metals, the intense femtosecond laser irradiation can give rise to electronic excitation in a few tens of femtoseconds. The energy subsequently transfers between the excited electrons and the ions leading to the thermal melting of the lattice. This transition can be showed to the change in density of states (DOS) as the electronic temperature increases. Fig. 1 (Color online) Density of state of Al, Au and Al 2Au at the different electronic temperatures. The black curves are the spectrum for T e = 0 ev. The red curves are for T e = 6 ev.

3 No. 5 Communications in Theoretical Physics 591 Figure 1 shows the total density of states of Al, Au and Al 2 Au at the electron temperatures T e = 0 ev and T e = 6 ev. In Fig. 1, we find that the smaller width of the DOS for Au induces the Fermi level shift towards higher energies which may be induced by the excitation of 5d electrons making the effective electron-ion potential more attractive. For Al, the DOS does not change, and the Fermi level moves to lower energy as the elevation of the electron temperature (Fig. 1). As can be seen, aluminum is almost independent of the temperature of the electron gas dielectric constant in the density and temperature range. For the purpose of keeping the number of electrons constant, the Fermi level shifts towards lower energy. For Au and Al, our calculated results are in conformity with the results discussed by Recoules et al. [2] Furthermore, it can be clearly seen that the Fermi level of Al 2 Au goes through the conduction band from Fig. 1, which demonstrates that Al 2 Au is of metal. When the electronic temperature T e is shifted from 0 ev to 6 ev, the band moves to the lower energies and the Fermi level moves towards higher energies. This may be caused by the large mass difference between Au and Al atoms which have a significant modification of the interatomic bonds after the laser pulse interaction. 3.3 Lattice Dynamical Properties In order to describe the changes of lattice stability induced by intense femtosecond laser irradiation, the phonon-dispersion curves of Al, Au and Al 2 Au at T e = 0 ev and T e = 6 ev are computed (Fig. 2). We observe that the phonon spectrums of Al and Au have the same change trend in the amplitude (Fig. 2). The phonon frequencies of Al and Au have a very strong increase as the increase of the electronic temperature. In Table 1, we give the calculated phonon frequencies (THz) at the high-symmetry L point at T e = 0 ev and T e = 6 ev and compare the results with the theoretical calculations of Recoules et al. [14] using linear-response method. We note that the results are in a good agreement with the work of Recoules et al. [2] Fig. 2 (Color online) Phonon spectrums of Al and Au at different electronic temperatures. The black curves are the spectrum for T e = 0 ev. The red curves are for T e = 6 ev. However, the results for Al 2 Au are quiet different. There are 3 atoms in the primitive cell of Al 2 Au with 9 normal modes of vibrations. According to grouptheoretical analysis, the irreducible representations of the vibrational modes at Γ point are given as follows: Γ aco = T 1u (Inactive), Γ opt = T 1u (IR) + T 2g (R). There are 3 acoustic modes and 6 optical modes. The T 1u ((Inactive) mode (triply degenerate) correspond to the acoustic modes that are mainly characterized by Au atoms and the frequencies are equal to zero at Γ point. The optical modes include two triply degenerate modes: T 1u (infraredactive) mode and T 2g (Raman-active) mode which are due to the motions of Al atoms against each other. [11,21] Table 1 The phonon spectrum (THz) of Al and Au at L point at the different electron temperatures and their comparisons with the theoretical calculations of Recoules et al. [2] Metals T c L L a (ev) TA LA TA a Al Au a Ref. [2]. Fig. 3 (Color online) Phonon spectrums of Al 2Au at different electronic temperatures. The black curves are the spectrum for T e = 0 ev. The red curves are for T e = 6 ev.

4 592 Communications in Theoretical Physics Vol. 59 When the electronic temperature is elevated, the phonon frequencies of Al 2 Au change greatly. Firstly, the calculated phonon frequencies (THz) of Al 2 Au at T e = 0 ev are in excellent agreement with the theoretical calculations by Tütüncü et al. [11] For Γ point, we calculate two optical values with 6.96 THz and 8.26 THz at T e = 0 ev, which are very close to the calculated values of 6.93 THz and 8.03 THz by Tütüncü et al. [11] At the same time, our calculated optical values of Al 2 Au at Γ point at T e = 6 ev correspond to 9.16 THz (T 1u ) and THz (T 2g ), respectively. Furthermore, the acoustic mode of Al 2 Au gets negative which leads to lattice dynamical instability when the electronic temperature is beyond 1.44 ev. Figures 4(a) and 4(b) show the frequencies of acoustic branch TA mode and LA mode of Al 2 Au at X point as a function of T e. The frequencies of the TA mode of Al 2 Au at X point shift uniformly down as the elevation of the electronic temperature and become imaginary at T e = 2.23 ev (Fig. 4(a)). While the frequencies of the LA mode of Al 2 Au at X point have different change trend with the increase of the electron temperature: the curve decreases first and increases then, the turning point is at T e = 1.83 ev (Fig. 4(b)). Fig. 4 (a) Frequency of a TA phonon of Al 2Au at X point as a function of T e. (b) Frequency of a LA phonon of Al 2Au at X point as a function of T e. (c) Frequency of the T 1u mode of Al 2Au at Γ point as a function of T e. (d) Frequency of the T 2g mode of Al 2Au at the Γ point as a function of T e. Fig. 5 Debye temperature variation as a function of T e for Au and Al 2Au. On the right-hand side is the corresponding melting temperature (T m). Moreover, the vibrational frequencies of the optical branches T 1u mode and T 2g mode of Al 2 Au at Γ point have similar situations with the acoustic branch LA mode of Al 2 Au at X point (Figs. 4(c) and 4(d)). The turning points of optical branch T 1u mode and T 2g mode are at T e = 1.40 ev and T e = 1.80 ev, respectively. The results are different from theoretical calculations of the semiconductor silicon made by Recoules et al. [2] When the electronic temperature is beyond 1.44 ev, the electronic thermal motion becomes more fiercely and the energy of system is elevated, which induces the lattice instability, as indicated by the results of the acous-

5 No. 5 Communications in Theoretical Physics 593 tic modes and the optical modes. To our knowledge, the experimental data of Al 2 Au at different electronic temperatures is not available in the literatures. Therefore, we present the calculated results, and hope that our work will be helpful in guiding the experimental explorations. 3.4 Debye Temperature Calculations The lattice-dynamical properties of Al 2 Au have been determined in detail by the phonon spectrum, while a quantitative assessment of Al 2 Au can be described by the constant-volume specific heat C v. In the present work, the harmonic approximations per unit cell are given [22] as follows: C V ( T Θ D ) = 9R ( T ) 3 Θ D ΘD/T 0 ξ 4 e ξ (e ξ 1) 2 dξ, where T is the ionic temperature, Θ D is the Debye temperature. When the electronic temperature is close to room temperature, the heat capacity can be fitted to a Debye function. [2] In Fig. 5, we note that a Debye temperature Θ D = 183 K of Au is very near to the results obtained from the experimental values [23] and other calculations. [2,24] For Au, the Debye temperature increases as the elevation of T e. However, a similar calculation for Al 2 Au yields very different results. The Debye temperature decreases when increasing radiation intensity (see Fig. 5). According to Lindermann melting criterion, T m is related to Θ D as: [2] T m = AΘ 2 D, where A depends only upon the density and the atom mass. It can be seen that the melting temperature evolves like the squares of Θ D. So we can obtain the corresponding melting temperature at the different Debye temperature from the relation: T m (T e = nev ) ( ΘD (T e = nev ) ) 2 =, (n > 0) T m Θ D (T m and Θ D are the corresponding values at normal temperature) (see Fig. 5). We find that the predicted melting temperatures of Al 2 Au undergo a sharp decrease from 1333 K at normal temperature to 1172 K at T e = 1.8 ev. The lattice of Al 2 Au becomes unstable as the elevation of radiation intensity. This is consistent with the preceding discussions about the phonon spectrum. 4 Conclusions In summary, we have performed ab initio calculations of the structural, electronic and lattice-dynamical properties of Al 2 Au at different electronic temperatures. Although the total densities of state of Al 2 Au changes considerably when electronic temperature is elevated, it is of interest to note that Al 2 Au is still of metal. For Al 2 Au, it should be pointed out that the intense laser irradiation induces the lattice instability, as indicated by the phonon frequencies of the acoustic modes and the optical modes. We find that the lattice of Al 2 Au becomes imaginary as the electronic temperature is beyond 1.44 ev. Moreover, with the increasing of the electronic temperature, the vibrational frequencies of optical branch T 1u mode and T 2g mode of Al 2 Au at Γ point both decrease first and increase then, the turning points are T e = 1.40 ev and T e = 1.80 ev, respectively. Finally, the change of the predicted melting temperatures of Al 2 Au also implies that the lattice of Al 2 Au becomes unstable as the increasing of the electron temperature. References [1] Q. Feng, Y. Picard, H. Liu, S. Yalisove, G. Mourou, and T. Pollock, Scr. Mater. 53 (2005) 511. [2] V. Recoules, J. Clérouin, G. Zérah, P. M. Anglade, and S. Mazevet, Phys. Rev. Lett. 96 (2006) [3] U. Zastrau, et al., Phys. Rev. E. 78 (2008) [4] A.W. DeSilva and J.D. Katsouros, Phys. Rev. E. 57 (1998) [5] E.M. Apfelbaum, Contrib. Plasma. Phys. 52 (2012) 41. [6] M.W.C. Dharma-Wardana, Phys. Rev. E. 73 (2006) [7] H. Piao, N.S. McIntyre, G. Beamson, M.L. Abel, and J.F. Watts, J. Electron Spectrosc. Relat. Phenom. 125 (2002) 35. [8] J.M. Vandenberg and R.A. Hamm, J. Vac. Sci. Technol. 19 (1981) 84. [9] J.C. Fuggle, E. Kallne, L.M. Watson, and D.J. Fabian, Phys. Rev. B 16 (1977) 750. [10] A.C. Switendick and A. Narath, Phys. Rev. Lett. 22 (1969) [11] H.M. Tütüncü, H. Altuntas, G.P. Srivastava, and G. Uğr, Phys. Stat. Sol. 11 (2004) [12] S.S. Vishnubhatla and J.P. Jan, Philos. Mag. 16 (1967) 45. [13] H. Piao and N.S. McIntyre, Surf. Interface. Anal. 31 (2001) 874. [14] T. Sritharan, Y.B. Li, C. Xu, and S. Zhang, J. Mater. Res. 23 (2008) [15] S. Supansomboon, A. maaroof, and M.B. Cotie, Gold Bulletin 41 (2008) 4. [16] S. Baroni, S.de Gironcoli, A. Dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73 (2001) 515. [17] X. Gonze, Phys. Rev. B 55 (1997) [18] P. Hohenberg and W. Kohn, Phys. Rev. B. 864 (1964) 136. [19] J.P. Perdew and A. Zunger, Phys. Rev. B 23 (1981) [20] D. Vanderbilt, Phys. Rev. B. 32 (1985) [21] M.M. Sinha, J. Alloys Compd. 493 (2010) 577. [22] Kun Huang and Ru-Qi Han, Solid State Physics, Higher Education Press, Beijing (1988) p [23] A. Balema and S. Mobilio, Phys. Rev. B 34 (1986) [24] G. Kästle, H.G. Boyen, A. Schröder, A. Plettl, and P. Ziemann, Phys. Rev. B. 70 (2004)