Copper, gold, and platinum under femtosecond irradiation: Results of first-principles calculations

The paper investigates the interaction of femtosecond laser pulses with the thin films of copper, gold, and platinum. It considers electron-phonon relaxation processes and melting in the metal system nonequilibrium heated by laser radiation. Instead of the approximated formula by Wang et al. [Phys. Rev. B 50, 8016 (1994)], which is widely used to determine the temperature dependence of the electron-phonon coupling factor, we propose an improved approach for its more accurate calculation from first principles. Comparison with experiments and other calculations shows our approach to provide good calculation accuracy. Melting time versus absorbed energy density was estimated for the films and shown to be markedly sensitive to latent heat at low absorbed energy densities $(<1$ MJ/kg). Our calculations taken to study the temporal evolution of the (220) diffraction peak intensity after femtosecond irradiation show good agreement between experimental and theoretical data, which was attained due to higher accuracy in our determination of the temperature dependence electron-phonon coupling factor.

Figure 1

Phonon DOS calculated in this work (solid lines) in comparison with experiment [33] (dashed-dotted lines) for Cu, Au, and Pt. Densities correspond to ambient conditions.

Figure 2

Electron-phonon coupling factor as a function of electron temperature $T_e$. The lines demonstrate various calculations: Solid line (our calculation), dash-dotted line [40], dotted line [19], stars connected with lines [41] for molten Cu with solid density ${\rho }_0$. The circle experiment [42]; diamonds, squares, and triangles experiment [21].

Figure 3

Melting temperature and Debye temperature versus electron temperature for copper from our calculations (solid lines). Dashed line ${\mathrm{\Theta }}_D$ from calculations [46].

Figure 4

Melting time versus absorbed energy density for copper from calculations with no account for the latent heat (solid line) and with its account (dashed line).

Figure 5

Electron heat capacity as a function of temperature $T_e$ for Cu from our calculations (solid line), and from other calculations: Dotted line [19] and dashed line [49]. Open circle is the experimental value [21].

Figure 6

Initial and final electron temperatures versus absorbed energy density from experiment [21] (circles and triangles, respectively), and from our calculation (solid lines) and calculation [21] (dashed line) for liquid copper with solid density.

Figure 7

Electron-phonon coupling factor versus electron temperature $T_e$ for gold from our calculation (solid line), and other calculations: Dashed-dotted line [45] and dotted line [19]. Open circle is the experiment [8].

Figure 8

Melting temperature and Debye temperature as a function of electron temperature for gold from our calculation (solid lines). Dashed line: Calculation of ${\mathrm{\Theta }}_D$ from Ref. [10].

Figure 9

Temporal evolution of (220) diffraction peak intensity from experiments (circles) [7] (top figures) and [4] (bottom figures) and calculations: Curve C1 obtained using $G\left(T_e\right)$ calculations by formula (5) and ${\mathrm{\Theta }}_D\left(T_e\right)$ by formulas (13) and (14); $\text{C}2G\left(T_e\right)$ from [45] and ${\mathrm{\Theta }}_D\left(T_e\right)$ by formulas (13) and (14); $\text{C}3G\left(T_e\right)$ from [19] and ${\mathrm{\Theta }}_D=\mathrm{const}.$; $\text{C}4G=\mathrm{const}.,{\mathrm{\Theta }}_D=\mathrm{const}.$, and $C_e=\gamma T_e$ [51]; $\text{C}5G\left(T_e\right)$ from formula (5) and ${\mathrm{\Theta }}_D=\mathrm{const}.$ (see the text for details).

Figure 10

Melting time versus absorbed energy density for gold. Solid and dashed lines (our calculations) with no account for the latent heat and with its account, respectively. MD simulations: Black circles [51], blue star [13], and blue triangle [32]. Experimental data: Open orange triangles and green circles experiments [7], closed red circles, black squares, and violet diamonds [4], open square [53] (see the text for details).

Figure 11

Electron-phonon coupling factor as a function of $T_e$ for platinum from our calculation (the solid line), calculations [19] (dashed line), and experiments [8] (circle) and [55] (diamond).

Figure 12

Melting temperature versus pressure for platinum from our calculation (solid red line) and ab initio MD calculations [56] (diamonds) and [57] (triangles). Closed and open circles experiments [57, 58].

Figure 13

Melting temperature and Debye temperature versus electron temperature for platinum.

Figure 14

Melting time versus absorbed energy density for platinum from our calculation with no account for latent heat (solid line) and with its account (dashed line).