Dynamics of thermalization in Au-Ti double-layered film excited by a femtosecond laser pulse

Yan Ou; Feng Chen; Guangqing Du; Qing Yang; Yanmin Wu; Yu Lu; Xun Hou

doi:10.3788/COL201513.S21414

Double-layered metals are widely used in engineering applications such as photo/microelectronic devices and microelectromechanical switches (MEMS)^[1–4]. For example, gold-coated metal mirrors are often used in femtosecond laser systems^[5,6]. Compared with single-metal layers, double-layered metals have significant advantages because the substrate layer reduces the lattice temperature rise of the top layer significantly^[7,8]. Therefore, it is very important to investigate the dynamics of thermalization in each layer during laser irradiation.

In recent years, several strategies have been developed for the thermalization dynamics of femtosecond laser heating of gold-coated metals^[9–12]. The aim of the exploitation of the thermalization dynamics in different double layers is to reduce the surface temperature and increase the damage threshold. Qiu et al. reported that a substrate Cr layer can reduce the phonon temperature rise of the top Au layer^[9,10]. Chen et al. investigated the influence of Ag, Cu, and Ni substrate layer material with different thermal physical properties on the phonon temperature distribution of the top Au layer^[11]. They also revealed that the electron-phonon coupling factor (G) of the substrate layer is the most important for changing the phonon temperature^[12]. A substrate layer with a higher electron-phonon coupling factor (G) can greatly reduce the phonon temperature of the top Au layer. Therefore, the physical properties of substrate layer have important effect on the top layer^[13]. Ti is a promising material as the substrate layer due to its high electron-phonon coupling factor and high melting point^[14,15]. However, it is currently challenging to understand the characteristics of the thermalization dynamics in Au-Ti double-layered film excited by a femtosecond laser pulse.

In this Letter, the dynamics of the thermalization in Au-Ti double-layered film excited by a femtosecond laser pulse is numerically investigated using the finite element method (FEM). The 2D temperature field evolution of Au-Ti double-layered film in the picosecond time domain was obtained. The results illustrate the energy transfer between two layers with different thickness of the Au film. This is because the thickness can affect the energy transfer between two layers. Moreover, the maximum phonon temperature on the surface of the Au film and the Ti film also can be tuned by changing the thickness of the top film. The results provide a theoretical guideline for optimizing the resistance of mirrors to thermal damage in applications of high-power lasers.

The theoretical method can be described by the well-known two-temperature model, as follows^[16,17]: $C_{e} \frac{\partial T_{e}}{\partial t} = \nabla (K_{e} \nabla T_{e}) - G (T_{e} - T_{p}) + S,$ (1) $C_{p} \frac{\partial T_{p}}{\partial t} = G (T_{e} - T_{p}),$ (2)where $T_{e}$ is the electron temperature, $T_{p}$ is the phonon temperature, $K_{e} = K_{0} (T_{e} / T_{p})$ is the temperature-dependent electron heat capacity^[18], $C_{e} = A_{e} T_{e}$ is the electronic heat capacity^[19], $C_{p}$ is the phonon heat capacity, and $G$ is the electron-phonon coupling strength.

For a Gaussian spatial distribution of the laser heat source, $S$ is the spatial energy absorption rate given as^[20] $S (x, y) = \sqrt{\frac{4 \ln 2}{π}} \frac{1 - R}{t_{p} (δ + δ_{b})} F \times \exp [- \frac{x}{δ + δ_{b}} - {(\frac{y - y_{0}}{y_{s}})}^{2}],$ (3)where $δ$ is the optical penetration depth, $δ_{b} = 100 nm$ is the electron ballistic transport length for an Au film, $t_{p}$ is the full width at half maximum (FWHM) pulse duration, $F$ is the incident fluence of the pulse train, $y_{0}$ is the coordinate of the light front center at the Au film surface, and $y_{s}$ is the profile parameter.

For the 2D Au-Ti double-layered film, Fig. 1(a) shows a schematic of the model that can be expressed as $C_{e}^{I} \frac{\partial T_{e}^{I}}{\partial t} = \nabla (K_{e}^{I} \nabla T_{e}^{I}) - G (T_{e}^{I} - T_{p}^{I}) + S^{I},$ (4) $C_{p}^{I} \frac{\partial T_{p}^{I}}{\partial t} = G (T_{e}^{I} - T_{p}^{I}),$ (5) $C_{e}^{II} \frac{\partial T_{e}^{II}}{\partial t} = \nabla (K_{e}^{II} \nabla T_{e}^{II}) - G (T_{e}^{II} - T_{p}^{II}),$ (6) $C_{p}^{II} \frac{\partial T_{p}^{II}}{\partial t} = G (T_{e}^{II} - T_{p}^{II}) .$ (7)

Figure 1.(a) Schematic of the Au-Ti double-layered film. The thickness of the Au layer is $x$ . The thickness of the Ti layer is $l = 500 nm$ . (b) The phonon temperature field on an Au film surface irradiated by a femtosecond laser pulse at 15 ps with a gold thickness of 500 nm. The laser fluence $F = 0.2 J / {cm}^{2}$ , pulse duration $t p = 100 fs$ , and the laser wavelength $λ = 800 nm$ .

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The initial temperatures of electrons and phonons are set to room temperature: $T_{e}^{I} (x, y, 0) = T_{p}^{I} (x, y, 0) = 300 K,$ (8) $T_{e}^{II} (x, y, 0) = T_{p}^{II} (x, y, 0) = 300 K .$ (9)

It is reasonable to neglect heat losses from the surface of the metal film. Therefore, the boundary conditions can be expressed as ${\frac{\partial T_{e}^{I}}{\partial n} |}_{Ω} = {\frac{\partial T_{p}^{I}}{\partial n} |}_{Ω} = 0,$ (10) ${\frac{\partial T_{e}^{II}}{\partial n} |}_{Ω} = {\frac{\partial T_{p}^{II}}{\partial n} |}_{Ω} = 0 .$ (11)

Here, $Ω$ represents the four boundary lines of the Au film.

The phonon temperature field on the Au film surface irradiated by a femtosecond laser pulse at 15 ps with a gold thickness of 500 nm is shown in Fig. 1(b). There is a sharp change in the region near the interface of the two layers. During the heating process the laser energy is transferred to the electron and then transferred to the phonon due to electron-phonon coupling. However, the electron-phonon coupling factor of the substrate Ti layer is greatly higher than the top Au layer. This results in the redistribution of the energy in the double-layered film. In the substrate Ti layer, the energy of the excited electron can more effectively couple to the phonon, leading to a higher phonon temperature.

The electron and phonon temperature field distributions at the time of 15 ps along the depth of the Au-Ti double-layered film are shown in Fig. 2. It can be seen from Fig. 2(a) that the electron temperature sharply drops at the Au-Ti interface, but the substrate Ti layer keeps to room temperature. This is attributed to the fact that the electron energy can be less transferred to Ti because the electron thermal conductivity coefficient of Ti is less than that of Au. It can be seen from Fig. 2(b) that the phonon temperature sharply changed at the interface region of the double-layered film. The reason is that the electron-phonon coupling factor for the Ti substrate is much higher than the Au layer. Therefore, the energy coupling efficiency of the Ti substrate is much higher than that of the Au layer, which causes the redistribution of the laser energy between the Ti substrate and the top Au layer. The results show that the preferential phonon heating in the Ti substrate can reduce the phonon temperature of the Au film, leading to the depression of the damage threshold.

Figure 2.Electron and phonon temperature field distributions at 15 ps along the depth of Au-Ti double-layered film; the gold thickness $x = 500 nm$ . The laser fluence $F = 0.2 J / {cm}^{2}$ , pulse duration $t p = 100 fs$ , and the laser wavelength $λ = 800 nm$ .

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Figure 3(a) shows the maximum phonon temperature change at point A (laser spot center on surface) and point B (laser spot center on interface), as shown in Fig. 1, of the Au-Ti double-layered film as a function of the Au layer thickness. It can be seen that the maximum phonon temperature at point A decreases, with the thickness of the top Au film increasing from 250 to 500 nm. However, the maximum phonon temperature at point B increases with thickness increasing when the thickness is less than 300 nm. This is because the energy absorption efficiency increases with thickness increasing when the thickness is less than 300 nm. In addition, the energy absorption efficiency decreases with thickness increasing when the thickness is less than 300 nm. Figure 3(b) shows the dependence of the temperature difference ( $Δ T$ ) of the phonon temperature across the Au layer at three different relaxation times. The temperature difference decreases with thickness increasing. This is because the thermal gradient across the Au layer is relatively small. A new way to increase the energy absorption efficiency is provided by adjusting the thickness of the double-layered film.

Figure 3.Dependence of phonon temperature and temperature difference across the gold layer of Au-Ti double-layered film on the Au layer thickness. The laser fluence $F = 0.2 J / {cm}^{2}$ , pulse duration $t p = 100 fs$ , and the laser wavelength $λ = 800 nm$ .

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Figure 4 shows the maximum phonon temperature change at the surface of the Au layer as a function of the laser fluence with three different Au layer thicknesses. It can be seen that the maximum phonon temperature presents a linear growth as the laser fluence increases. In the range of lower laser fluence, the temperature difference across the thickness of the Au layer is indistinctive. However, with high laser fluence, the thicker Au layer has a slower increasing slope. The results indicate that the thickness of the double-layered film can significantly affect the phonon thermalization of the Au layer. Therefore, the damage threshold can be tuned by adjusting the thickness of the double-layered film.

Figure 4.Maximum phonon temperature change at the surface of the Au layer as function of the laser fluence with three different Au layer thicknesses. The laser pulse duration $tp = 100 fs$ and the laser wavelength $λ = 800 nm$ .

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This study theoretically investigate the thermalization dynamics in double-layered Au-Ti film irradiated by a femtosecond laser. It is revealed that the maximum phonon temperature of the Ti film with a thickness of 300 nm is higher than that of the other thicknesses. The mechanism is mainly attributed to the enhancement of phonon temperature being related to the higher energy absorption efficiency of the double-layered Au-Ti film. Further, the maximum phonon temperature of the top Au film and the substrate Ti layer with a thickness of the top Au layer of 500 nm is lower than that for other thicknesses. The maximum phonon temperature can be flexibly tuned by using the optimal thickness of the Au film for a laser power. The study provides the basic strategy for understanding the fundamental thermalization processes of the Au-Ti double-layered film for well-optimizing laser micro- and nanofabrication.

Category: Lasers and Laser Optics

Received: Jan. 19, 2015

Accepted: Mar. 10, 2015

Published Online: Aug. 8, 2018

The Author Email: Feng Chen (chenfeng@mail.xjtu.edu.cn)

DOI:10.3788/COL201513.S21414