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Ultrafast investigation of electron dynamics in the gold-coated two-layer metal films
Thin Solid Films 529 (2013) 209–216
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Ultrafast investigation of electron dynamics in the gold-coated two-layer metal films Anmin Chen a, Laizhi Sui a, Ying Shi a, Yuanfei Jiang a, Dapeng Yang b,⁎, Hang Liu a, Mingxing Jin a,⁎, Dajun Ding a a b
Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, People's Republic of China Key Laboratory of Geo-exploration Instrumentation Ministry of Education, College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130012, People's Republic of China
a r t i c l e
i n f o
Available online 12 June 2012 Keywords: Electron dynamics Transient reflectivity Two-layer film Two-temperature model Damage threshold
a b s t r a c t The gold-coated metal thin films are widely used in modern engineering applications. In this paper, the ultrafast electron dynamics of gold-coated two-layer thin films has been investigated by ultrafast time-resolved pump–probe experiment. The dependence of the surface electron temperature on the film structure was considered based on the two-temperature model at the different two-layer film structure. The effect of laser fluence (3, 6 and 17 mJ/cm2), and two-layer film thickness (the thickness of 50 nm and 100 nm gold layer) is considered. The theoretical predictions are compared with experimental data, which agree well with both thermal model and transient reflectivity. © 2012 Elsevier B.V. All rights reserved.
1. Introduction With the development of ultrashort laser based on chirped-pulse amplification [1], it is possible to carry out powerful femtosecond laser systems. The femtosecond pulsed lasers are widely used in a variety of fields including material processing [2], pulsed laser deposition [3], molecular spectroscopy [4,5], ionization and dissociation of polyatomic molecules [6,7], and so on. For the sake of increasing the output power of such femtosecond laser systems, an important limiting factor in the high power operation of lasers is the damage threshold of the optical components of the laser system. Hence, comparative damage threshold measurements on laser optical components are essential for the evaluation of different materials as well as different deposition techniques in respect to their applicability in high-power femtosecond laser systems. Due to the high reflectivity of gold surface in the infrared beyond 0.7 μm (an averaged reflectance is above 98%), gold coating optical components (mirrors and gratings, etc.) are widely used in femtosecond pulsed laser systems (for example, Ti:Sapphire laser system) and infrared optical systems (for example, Terahertz system [8]). The interaction of femtosecond laser and gold film has been a challenging research topic. During pulsed laser irradiation of gold film, the electron– electron interaction time is very short, on the order of femtoseconds, compared with electron–lattice interaction time, which is on the order of picoseconds. It has been assumed that the incident photon energy of
⁎ Corresponding authors. E-mail addresses: [email protected] (D. Yang), [email protected] (M. Jin). 0040-6090/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2012.06.027
the laser beam is absorbed instantaneously by the free electrons of the metal and is confined close to the surface. Hence, a strong nonequilibrium is created between the electrons and lattices. The thermal energy possessed by these “hot” electrons diffuses deeper into the film. Optical pump–probe measurement using femtosecond laser has been proven to be a very sensitive tool for the investigation of electron dynamics in metals. They have been used to study many phenomena of fundamental and applied interests such as optical orientation of spin, ultrafast demagnetization, and ultrafast excitation of coherent lattices. Their potential for material characterization is illustrated by measurements of the electron–lattice coupling constant in metals [9], hot electron linear and angular momentum relaxation times and nonlinear susceptibility tensor components in metals, and the spin wave mode spectrum of nanomagnets. For the interaction of the laser and metal, the investigation of ultrafast electron dynamics investigation has been reported using the pump–probe measurement by many researchers [10–13]. In these electron dynamics studies, the single-layer metals have been used. The electron dynamics of the multi-layer metal has been investigated by Ibrahim et al. [14]. The Au/Cr two-layer film had been experimentally studied by Qiu and Tien [15]. And the Au/glass two-layer film had been experimentally studied by Wang and Ma et al. [16]. However, the researches of the ultrafast electron dynamics are still lacking for the multi-layer metal films. In this paper, we report the experimental results of the transient reflectivity of the gold-coated two-layer film using the femtosecond pump–probe technique for three different pump powers. Experimental results show that the reflectivity change increases with the power of the pump laser. Numerical solutions of the two-temperature model (TTM) are compared with experimental results. The distributions of electron temperature and lattice temperature are considered. The results show that the substrate layer chrome film can influence the variation of gold film temperature.
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2. Mathematical model
ε 2 ¼ 2nκ
The theoretical method to investigate the ultrashort laser–matter interaction is the well-known two-temperature model [17]. Laser light is absorbed in metals by the conduction-band electrons within a few femtoseconds. After the fast thermalization of the laser energy in the conduction band, electrons may quickly diffuse and thereby transport their energy deep into the internal target (within a few femtoseconds). At the same time, the electrons transfer their energy to the lattice. The TTM describes the evolution of the temperature increase due to the absorption of a laser pulse within the solid and is applied to model physical phenomena like the energy transfer between electrons and lattice occurring during the target–laser interaction [18]. The one-dimension two-temperature equation is given below [19,20]:
and
∂T ∂ ∂T Ce e ¼ ke e −GðT e −T l Þ þ S ∂t ∂x ∂x
ð1Þ
∂T ∂ ∂T Cl l ¼ kl e þ GðT e −T l Þ ∂t ∂x ∂x
ð2Þ
" !2 # rffiffiffiffi t−2t p β ð1−RÞαI exp −xα−β π tp tp
ð3Þ
Where R = 0.369 (the wavelength of the pump beam is 400 nm) is the target reflection coefficient, tp is the full-width at the half maximum (FWHM) with the linear polarization, α is the absorption coefficient and I is the incident energy, β = 4 ln(2). The reflectivity (R) of metal is mainly due to the Drude free electron model. The electrical permittivity ε (dielectric function) of metals modeled as a plasma, is expressed as [23] ε ¼ ε1 þ iε2
ð4Þ 2 2
ε 1 ¼ 1−
ε2 ¼
ωp τ
1 þ ω2 τ 2 ω2p τ2
ω 1 þ ω2 τ
2
ð5Þ
ð6Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω is laser frequency, ωp ¼ ne e2 =ðme ε0 Þ is the plasma frequency, ne is the density of the free electrons, me is the mass of electron and ε0 is the electrical permittivity of free space. τ is the electron relaxation time. In general, for good conductors, the e–e collision rate may be determined by υe–e = ATe2 whereas the e–ph collision rate is independent of Te, but proportional to Tl, namely, υe–ph = BTl. Here A and B are constants, and both contribute to the electron collision frequency υ. A relationship between the electron relaxation time τ and the e–e and e−ph collision rates for electron temperatures below the Fermi temperature is given by 1 2 ¼ υ ¼ υe−e þ υe−ph ¼ AT e þ BT l : τ
ð7Þ
We then work out n and κ, the real and imaginary parts of the complex refractive index. These are: 2
ε1 ¼ n −κ
2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u ε þ ε21 þ ε22 t 1
n¼
ð10Þ
2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u t−ε1 þ ε21 þ ε22 κ¼ : 2
ð11Þ
The reflectivity depends on both n and κ and is given by ðn−1Þ2 þ κ 2 : ðn þ 1Þ2 þ κ 2
R¼
ð12Þ
The absorption coefficient is determined by κ, and is given by
Where t is the time, x is the depth, Ce is the electron heat capacity, Cl is the lattice heat capacity, ke is the electron thermal conductivity, Te is the electron temperature, Tl is the lattice temperature, G is the electron–lattice coupling factor [21], and S is the laser heat source. The heat source S can be modeled with a Gaussian temporal profile [22]: S¼
ð9Þ
ð8Þ
α¼
2κω : c
ð13Þ
The electron heat capacity is proportional to the electron temperature when the electron temperature is less than the Fermi temperature as Ce = γTe [24] and γ = π2nekB/2TF. ne is the density of the free electrons, kB is the Boltzmann's constant and TF is Fermi temperature. The lattice heat capacity is set as a constant because of its relatively small variation as the temperature changes. The electron heat conductivity can be expressed as ke = ke0BTe/(ATe2 + BTl) [25], where ke0, A and B are the constants. Many of the ultrafast laser heating analyses have been carried out with a constant electron–lattice coupling factor G. However, due to the significant changes in the electron and lattice temperatures caused by high-power laser heating, G should be temperature dependent (G = G0(A(Te + Tl)/B + 1), where G0 is the coupling factor at room temperature) [26]. The lattice thermal conductivity is therefore taken as 1% of the thermal conductivity of bulk metal since the mechanism of heat conduction in metal is mainly due to electrons [27]. As the temperature changes, the variety of the lattice heat conductivity is relatively small and it is assumed a constant. Considering a one-dimensional two-layered thin film, Fig. 1 shows the schematic view of the laser heating, which indicates a two-layer metal film with an interface at x = l. For the two-layer thin film, the two-temperature equation (Eqs. (1) and (2)) for studying thermal behavior in the thin film can be expressed as I
∂T e ∂ I ∂T e Ce ¼ k ∂t ∂x e ∂x I
Cl
I
Ce
I ∂T l I ∂ I ∂T l ¼ kl ∂t ∂x ∂x
II
I
!
I I I −G T e −T l þ S
!
I I þ G T e −T l
! II ∂T e II ∂ II ∂T e II II ¼ −G T e −T l ke ∂t ∂x ∂x
II ∂T l II ∂ II ∂T l Cl ¼ kl ∂t ∂x ∂x
!
II
II II þ G T e −T l :
ð14Þ
ð15Þ
ð16Þ
ð17Þ
To solve Eqs. (4)–(7), the following initial and boundary conditions must be used. Before irradiated by the laser pulse, the electron and lattice sub-systems are considered to be at the same initial temperature (T0 = 300 K) I
I
T e ðx; 0Þ ¼ T l ðx; 0Þ ¼ T 0
ð18Þ
A. Chen et al. / Thin Solid Films 529 (2013) 209–216
Fig. 1. The schematic of a two-layer metal film. The thickness of Au is l. The thickness of Cr is 200 nm.
II
II
T e ðx; 0Þ ¼ T l ðx; 0Þ ¼ T 0 :
ð19Þ
The energy of the convective and radiative losses from the front and back surfaces of the two-layer film, in addition, is negligible during the femtosecond transient. The boundary conditions are formulated, as follows ∂T e I ∂x
j
∂T l I ∂x
j
x¼0
x¼0
¼
∂T e II ∂x
¼
∂T l II ∂x
j
x¼L
j
x¼L
¼0
ð20Þ
¼ 0:
ð21Þ
At the interface of the film (x = l), the two-layer thin film is in perfect thermal contact. Therefore we set the boundary conditions of the interface, as follows Te Tl
I
ke
kl
I
I
I
j
j
x¼l
¼ Te
x¼l
¼ Tl
∂T e I ∂x ∂T l I ∂x
j
j
II
x¼l
x¼l
II
j
j
ð22Þ
x¼l
ð23Þ
x¼l
¼ ke
¼ kl
II
II
∂T e II ∂x
∂T l II ∂x
j
j
x¼l
x¼l
:
ð24Þ
ð25Þ
3. Experimental details A schematic diagram of the standard pump–probe experimental setup is shown in Fig. 2. The laser system was a regenerative amplified
211
Ti:Sapphire laser (Spectra Physics, Tsunami oscillator and Spitfire amplifier), which provides 90 fs pulses at 800 nm with 0.6 mJ per pulse and a repetition rate of 1 kHz. The laser beam was then split to generate pump and probe parts. The pump beam (400 nm) was obtained by second harmonic generation in a 0.5 mm thick β-BaB2O4 (BBO) crystal. The intensity of the pump beam can be controlled by a λ/2 plate in combination with a Glan prism. The residual 800 nm laser beam acts as a probe beam. In our experiment the intensity ratio of pump to probe beam is about 80:1. A computer-controlled translation stage (Physik instrumente, M-505) was used to control the time delay between the pump and the probe pulses with a resolution of 1 μm. The delay time may be changed from − 100 to 900 ps. By a combination of a Glan laser polarizer and a half-wave plate, the energy of each pulse can be attenuated to the desired value. The pump and probe pulses were directed by two concave mirrors (Focal length is 25 cm) and a beam splitter onto the sample with the focal diameter spots of 300 μm and 200 μm. The spots were carefully overlapped, while being viewed with a CCD camera. The metal target was mounted on a computer-controlled X–Y–Z stage, which can guarantee the sample location. All experiments are performed in air at atmospheric pressure. The angles of incidence of the pump and probe beams at the sample were very small. The pump and probe beams were reflected from the sample and filtered by a filter so that the 800 nm probe beam could be detected by a photodiode. Differential detection (ThorLabs PDB150A-AC) was used so as to cancel out the fluctuations of the laser output, leaving only the signal caused by the chopped pump beam. Thus, the lock-in amplifier (Stanford SR830) detects modulation in the received probe intensity that was caused only by the effect of the pump on the sample. The samples used in the experiments were double-layer gold and chrome thin films deposited on K9 glass. The two-layer metallic films were prepared using a physical vapor deposition method. The sample structure and general optical layout were shown in Fig. 1. The thickness of chrome film was 200 nm. The thickness of gold layer was 50 nm, and 100 nm, respectively. We substituted a BBO crystal (0.2 mm) for the sample to generate a sum-frequency pulse (267 nm) of pump and probe pulses. Through detecting the correlation signal, the time zero-point and the time resolution of our system could be evaluated. 4. Results In this experiment, the time dependence of transient relative reflectivities for 400 nm pump light and 800 nm probe light are displayed in Figs. 3 and 4 for both gold-coated two-layer films. The three different pump laser powers are 2 mW, 4 mW, and 12 mW, respectively. Fig. 3 (a and b) shows the normalized ΔR/R for the same
Fig. 2. The schematic drawing of the apparatus. Components include beam splitter (BS), concave mirror (CM), filter (F), Glan laser polarizer (G) and half-wave plate (HWP).
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Fig. 3. The normalized transient reflectivity data for both films recorded with three different laser powers: (a) the film is Au/Cr of 50 nm and 200 nm and (b) the film is Au/Cr of 100 nm and 200 nm.
gold film thickness. The normalized curves are calculated by dividing the minimum value of three curves. As shown in these figures, the reflectivity change process consists of three different time stages. Firstly, the transient relative reflectivity decreases rapidly for the delay time up to a few hundred femtoseconds and reaches the minimum point. Next, the increasing reflectivity occurs for the delay time of 2 ps. Finally, the reflectivity after delay time of 2 ps nears a constant. Fig. 4 (a–c) shows the normalized ΔR/R for the 50 nm and 100 nm Au/Cr two-layer films at the same laser power. These data are normalized at the peak reflectance to observe the difference between the electron cooling profiles at three different laser fluences. For the different thickness of gold layer, the surface electron temperatures rose rapidly with the maximum temperatures. Next, surface electron temperatures decreased with time. In the range of 0–2 ps, the variations of the surface electron temperature were almost same for the different thickness of gold layer [28]. The variation of the surface electron temperature is proportional to the variation of the reflectivity. It is the shape of the cooling profile after the maximum electron temperature that is related to the rate of electron–lattice equilibration; therefore, the normalization of the data is for clear comparison between the two data sets. The majority of the electron energy loss to the lattices occurs within 1–2 ps after laser heating. Differences in the data are seen within 2 ps after the maximum reflectance, indicating a difference in the cooling rate of the electron system during electron–lattice equilibration.
Fig. 4. The normalized transient reflectivity data for three laser powers recorded with both different two-layer films. The pump laser powers: (a) 2 mW, (b) 4 mW, and (c) 12 mW.
Two major processes of electron–electron collision and scattering process and electron–lattice coupling process occur in the interaction between the femtosecond laser and the thin film. The nonequilibrium temperature induced in the experiments can be predicted with the two temperature model. The mathematical model that is calculated by the finite difference method, given by Eqs. (1) and (2), describes
A. Chen et al. / Thin Solid Films 529 (2013) 209–216
the rate of energy exchange between the electrons and lattices in a metallic film. The temporal distributions of the electron are presented in Fig. 5 for both thin films. The laser fluences are 3 mJ/cm 2, 6 mJ/cm 2, and 17 mJ/cm 2, respectively. Table 1 [29–33] lists the values of thermal physical parameters of the two noble metals used in these calculations. One can see from Fig. 5 that the surface electron temperatures rose rapidly with maximum temperatures in the range of a few hundred femtoseconds. Consequently, surface electron temperature decreases with time due to the heat diffusion effect in the electron gas, at a short time delay (about 2 ps). The distributions of the surface electron temperature for three different laser fluences are noticeably different. The decay rate of electron temperature of the low laser fluence is less than that of the high laser fluence, and the thermal equilibrium time is extended.
5. Discussion Generally, the lattice cannot be affected by the absorption of a pump light, but a nonequilibrium process of hot electron and cold lattice will be created. The scattering among the hot electrons as well as from the lattices, defects, etc., results in the creation of the
213
Table 1 Thermal and optical physical parameters for gold and chrome. Au
Cr
Electron–lattice coupling coefficient G0 0.22 4.2 [1017 J m− 3 s− 1 K− 1] 68 194 Electron heat capacity coefficient γ[J m− 3 K− 2] Electron thermal conductivity coefficient ke0[J m− 1 s− 1 K− 1] 315 95 6 −3 −1 Lattice heat capacity Cl[10 J m K ] 2.5 3.3 −9 Penetration depth α[10 m] 17.7 7 −1 −2 A [10 s K ] 1.18 7.9 1.25 13.4 B[1011 s− 1 K− 1] Melting temperature Tm[103 K] 1.337 2.180
equilibrium electron distribution described by the Fermi–Dirac function [34,35] f FD ðE; T e Þ ¼
exp
1
E−EF ðT e Þ kB T e
þ1
ð26Þ
where, E is the electron energy, EF is the Fermi energy, and kB is the Boltzmann constant. At moderate temperatures, the Fermi energy varies with temperature as " EF ðT e Þ ¼ EF0 1−
# 2 π kB T e 2 : 12 EF0
ð27Þ
Where, EF0 is the Fermi energy at absolute zero temperature. The transient reflectivities are not affected by holes in the d-band which are initially created by optical excitation since the lifetime of these holes is vanishingly small [36]. When the electrons have been heated, the electron temperature can still be higher than that of the lattice. The main mechanism of the TTM is that the electron and lattice are well characterized by their respective temperatures which equalize with rate proportional to the electron–lattice coupling constant. The process is a very complex [37], since the specific heat capacity of electron is low. Irradiated by a laser beam, the electron temperature increases rapidly in an extremely short time, producing a great temperature difference between electron and lattice. The nonequilibrium energy transport, which is due to the electron–lattice coupling mechanism [38], will take place. The excess energy of the thermalized electron subsystem is equal to the product of the excess electron temperature ΔTe and the electron heat capacity Ce, which is in turn proportional to the electron temperature Te =Te + ΔTe. In the transient thermoreflectance experiments, it is the change in reflectivity ΔR resulting from a change in temperature in the sample that is measured. The change in reflectance of a metal can be related to the change in temperature through the change in the complex dielectric function Δε =Δε1 +iΔε2, here Δε1 and Δε2 are the real and imaginary part changes of the complex dielectric function. When the changes of ΔTe and ΔTl are small, Δεcan be expressed by ΔTe and ΔTl Δε ¼ Δε1 þ iΔε 2 ¼
∂ε1 ∂ε ∂ε2 ∂ε ΔT e þ 1 ΔT l þ i ΔT e þ 2 ΔT : ∂T e ∂T l ∂T e ∂T l
ð28Þ
The changed reflectivity can be expressed by the dielectric functions
ΔR 1 ∂R ∂R ¼ Δε1 þ Δε2 : R R ∂ε1 ∂ε2
ð29Þ
Combining Eqs. (28) and (29), the change of the reflectivity can be rewritten as [39,40] Fig. 5. The variation of surface electron temperature with the delay time for the different laser fluences by TTM predictions. The thickness of Au/Cr films: (a) 50 nm and 200 nm; (b) 100 nm and 200 nm.
ΔR ¼ aΔT e þ bΔT l R
ð30Þ
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A. Chen et al. / Thin Solid Films 529 (2013) 209–216
where a ∝ ∂ R/∂ Te and b ∝ ∂ R/∂ Tl. The electron and lattice temperatures directly relate to the change of the reflectivity. Compared with the change of the electron temperature, the change of the lattice temperature is very small and can be ignored. Eq. (30) can be simplified as ΔR ¼ aΔT e : R
ð31Þ
The original measured signals and theoretical results are shown in Figs. 3 and 4, and Fig. 5, respectively. As mentioned above, ΔTe/Te is proportional to ΔR/R. As a result, the transient reflectivity signals can be represented by the variation of the electron temperature with time. The electron temperature starts to rise when the pump pulse irradiates the surface of the target, and then the electron temperature decreases because of the non-equilibrium heat transport from the hot electrons to the cold lattices. In order to analyze the data, the electron temperature is normalized. In Fig. 6, we compare the calculations with experimental data. Agreement with experiment is rather satisfactory. However, it should be noted that the measured data are in fact a function not only of film thickness [41,42] (as expected from Fig. 4) but also of film morphology [43,44]. The morphology dependence is a subject of continuing study. In Fig. 6 (a), there is some disagreement between calculated and experimental data. This is due to electron–lattice coupling factor that governs the
Fig. 6. The comparison of theoretical and experimental results: (a) fixed film thickness with the different laser energy and (b) fixed laser energy with the different film thickness.
rate of energy transfer to the lattice from the hot electrons. In here, we use theoretical predictions that differ with the actual value. The two-layer film structure can change the damage threshold of the gold surface [45]. As shown in Fig. 4, for the fixed laser power, the ΔR/R of the thinner gold layer is less than that of the thicker gold layer at the thermal equilibrium. In contrast with the experimental results of Hohlfeld et al. [46], it is just contrary. In the Hohlfeld's experiment, the gold films were directly deposited on optical fused silica plates. However, we introduced the chrome film as the substrate layer in this experiment. The substrate layer will act as a heat sink absorbing the thermal energy transmitted through the interface and then coupling that energy to the lattice away from the heat affected area [47]. According to the previous theory, ΔTe/Te is proportional to ΔR/R, Fig. 4 (a–c) illustrates that the surface of the thicker gold layer will obtain higher temperature compared to that of the thinner gold layer. Subsequently, we calculate the variation of the lattice temperature with the depth of the two-layer film. Fig. 7 shows the distribution of the lattice temperature for both thin films at three different fluences. We notice that the lattice temperature distribution has big ups and downs in the interface region of the gold-layer and chrome-layer. This is due to the fact that the electron–lattice coupling factor is considerably higher or lower for the substrate layer film than that for the top layer. This results in the redistribution of the deposited laser energy from the gold film
Fig. 7. The distribution of the lattice temperature with the different laser fluences for both two-layer films. The thickness of Au/Cr films: (a) 50 nm and 200 nm; (b) 100 nm and 200 nm.
A. Chen et al. / Thin Solid Films 529 (2013) 209–216
layer to the substrate layer, where the energy of the excited electrons couples more effectively with the lattice vibrations, leading to the preferential or disadvantageous lattice heating in the substrate layer. Fig. 8 clearly shows the distribution of the lattice temperature
215
for the different thick gold layer. At the surface, the lattice temperature of 50 nm gold layer is lower than that of 100 nm for the twolayer films, the lattice of single-layer films are higher than that of the two-layer films. The results provide way for the improvement of gold surface damage threshold. 6. Conclusion In summary, the transient reflectivity of the gold-coated two-layer metal film is investigated by femtosecond time-resolved pump–probe technique. The two-layer structure is the 50 nm and 100 nm gold layers padding on the 200 nm chromes. Experiments are performed for three different pump powers. Experimental results show that the reflectivity change increases with the power of the pump laser. The experimental results are analyzed within the framework of the two-temperature model, which describes the energy relaxation in ultrafast heating. A comparison between the experimental results for both two-layer films revealed the difference of the thermoreflectivity signal at the thermal equilibrium. By the theoretical analysis, the introduced substrate layer will signify a reduction in the surface lattice temperature. Taking advantage of the two-layer structure, it is believed that the damage threshold of the gold film can be improved. Acknowledgment This project is supported by the Chinese National Fusion Project for ITER (Grant no. 2010GB104003) and the National Natural Science Foundation of China (Grant nos. 10974069, 11034003). References
Fig. 8. The comparison of the lattice temperature distribution for the single-layer Au films and the two-layer Au/Cr films at the different laser fluences. The fluence: (a) 3 mJ/cm2, (b) 6 mJ/cm2, and (c) 17 mJ/cm2.
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Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Ultrafast investigation of electron dynamics in the gold-coated two-layer metal films Anmin Chen a, Laizhi Sui a, Ying Shi a, Yuanfei Jiang a, Dapeng Yang b,⁎, Hang Liu a, Mingxing Jin a,⁎, Dajun Ding a a b
Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, People's Republic of China Key Laboratory of Geo-exploration Instrumentation Ministry of Education, College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130012, People's Republic of China
a r t i c l e
i n f o
Available online 12 June 2012 Keywords: Electron dynamics Transient reflectivity Two-layer film Two-temperature model Damage threshold
a b s t r a c t The gold-coated metal thin films are widely used in modern engineering applications. In this paper, the ultrafast electron dynamics of gold-coated two-layer thin films has been investigated by ultrafast time-resolved pump–probe experiment. The dependence of the surface electron temperature on the film structure was considered based on the two-temperature model at the different two-layer film structure. The effect of laser fluence (3, 6 and 17 mJ/cm2), and two-layer film thickness (the thickness of 50 nm and 100 nm gold layer) is considered. The theoretical predictions are compared with experimental data, which agree well with both thermal model and transient reflectivity. © 2012 Elsevier B.V. All rights reserved.
1. Introduction With the development of ultrashort laser based on chirped-pulse amplification [1], it is possible to carry out powerful femtosecond laser systems. The femtosecond pulsed lasers are widely used in a variety of fields including material processing [2], pulsed laser deposition [3], molecular spectroscopy [4,5], ionization and dissociation of polyatomic molecules [6,7], and so on. For the sake of increasing the output power of such femtosecond laser systems, an important limiting factor in the high power operation of lasers is the damage threshold of the optical components of the laser system. Hence, comparative damage threshold measurements on laser optical components are essential for the evaluation of different materials as well as different deposition techniques in respect to their applicability in high-power femtosecond laser systems. Due to the high reflectivity of gold surface in the infrared beyond 0.7 μm (an averaged reflectance is above 98%), gold coating optical components (mirrors and gratings, etc.) are widely used in femtosecond pulsed laser systems (for example, Ti:Sapphire laser system) and infrared optical systems (for example, Terahertz system [8]). The interaction of femtosecond laser and gold film has been a challenging research topic. During pulsed laser irradiation of gold film, the electron– electron interaction time is very short, on the order of femtoseconds, compared with electron–lattice interaction time, which is on the order of picoseconds. It has been assumed that the incident photon energy of
⁎ Corresponding authors. E-mail addresses: [email protected] (D. Yang), [email protected] (M. Jin). 0040-6090/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2012.06.027
the laser beam is absorbed instantaneously by the free electrons of the metal and is confined close to the surface. Hence, a strong nonequilibrium is created between the electrons and lattices. The thermal energy possessed by these “hot” electrons diffuses deeper into the film. Optical pump–probe measurement using femtosecond laser has been proven to be a very sensitive tool for the investigation of electron dynamics in metals. They have been used to study many phenomena of fundamental and applied interests such as optical orientation of spin, ultrafast demagnetization, and ultrafast excitation of coherent lattices. Their potential for material characterization is illustrated by measurements of the electron–lattice coupling constant in metals [9], hot electron linear and angular momentum relaxation times and nonlinear susceptibility tensor components in metals, and the spin wave mode spectrum of nanomagnets. For the interaction of the laser and metal, the investigation of ultrafast electron dynamics investigation has been reported using the pump–probe measurement by many researchers [10–13]. In these electron dynamics studies, the single-layer metals have been used. The electron dynamics of the multi-layer metal has been investigated by Ibrahim et al. [14]. The Au/Cr two-layer film had been experimentally studied by Qiu and Tien [15]. And the Au/glass two-layer film had been experimentally studied by Wang and Ma et al. [16]. However, the researches of the ultrafast electron dynamics are still lacking for the multi-layer metal films. In this paper, we report the experimental results of the transient reflectivity of the gold-coated two-layer film using the femtosecond pump–probe technique for three different pump powers. Experimental results show that the reflectivity change increases with the power of the pump laser. Numerical solutions of the two-temperature model (TTM) are compared with experimental results. The distributions of electron temperature and lattice temperature are considered. The results show that the substrate layer chrome film can influence the variation of gold film temperature.
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2. Mathematical model
ε 2 ¼ 2nκ
The theoretical method to investigate the ultrashort laser–matter interaction is the well-known two-temperature model [17]. Laser light is absorbed in metals by the conduction-band electrons within a few femtoseconds. After the fast thermalization of the laser energy in the conduction band, electrons may quickly diffuse and thereby transport their energy deep into the internal target (within a few femtoseconds). At the same time, the electrons transfer their energy to the lattice. The TTM describes the evolution of the temperature increase due to the absorption of a laser pulse within the solid and is applied to model physical phenomena like the energy transfer between electrons and lattice occurring during the target–laser interaction [18]. The one-dimension two-temperature equation is given below [19,20]:
and
∂T ∂ ∂T Ce e ¼ ke e −GðT e −T l Þ þ S ∂t ∂x ∂x
ð1Þ
∂T ∂ ∂T Cl l ¼ kl e þ GðT e −T l Þ ∂t ∂x ∂x
ð2Þ
" !2 # rffiffiffiffi t−2t p β ð1−RÞαI exp −xα−β π tp tp
ð3Þ
Where R = 0.369 (the wavelength of the pump beam is 400 nm) is the target reflection coefficient, tp is the full-width at the half maximum (FWHM) with the linear polarization, α is the absorption coefficient and I is the incident energy, β = 4 ln(2). The reflectivity (R) of metal is mainly due to the Drude free electron model. The electrical permittivity ε (dielectric function) of metals modeled as a plasma, is expressed as [23] ε ¼ ε1 þ iε2
ð4Þ 2 2
ε 1 ¼ 1−
ε2 ¼
ωp τ
1 þ ω2 τ 2 ω2p τ2
ω 1 þ ω2 τ
2
ð5Þ
ð6Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω is laser frequency, ωp ¼ ne e2 =ðme ε0 Þ is the plasma frequency, ne is the density of the free electrons, me is the mass of electron and ε0 is the electrical permittivity of free space. τ is the electron relaxation time. In general, for good conductors, the e–e collision rate may be determined by υe–e = ATe2 whereas the e–ph collision rate is independent of Te, but proportional to Tl, namely, υe–ph = BTl. Here A and B are constants, and both contribute to the electron collision frequency υ. A relationship between the electron relaxation time τ and the e–e and e−ph collision rates for electron temperatures below the Fermi temperature is given by 1 2 ¼ υ ¼ υe−e þ υe−ph ¼ AT e þ BT l : τ
ð7Þ
We then work out n and κ, the real and imaginary parts of the complex refractive index. These are: 2
ε1 ¼ n −κ
2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u ε þ ε21 þ ε22 t 1
n¼
ð10Þ
2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u t−ε1 þ ε21 þ ε22 κ¼ : 2
ð11Þ
The reflectivity depends on both n and κ and is given by ðn−1Þ2 þ κ 2 : ðn þ 1Þ2 þ κ 2
R¼
ð12Þ
The absorption coefficient is determined by κ, and is given by
Where t is the time, x is the depth, Ce is the electron heat capacity, Cl is the lattice heat capacity, ke is the electron thermal conductivity, Te is the electron temperature, Tl is the lattice temperature, G is the electron–lattice coupling factor [21], and S is the laser heat source. The heat source S can be modeled with a Gaussian temporal profile [22]: S¼
ð9Þ
ð8Þ
α¼
2κω : c
ð13Þ
The electron heat capacity is proportional to the electron temperature when the electron temperature is less than the Fermi temperature as Ce = γTe [24] and γ = π2nekB/2TF. ne is the density of the free electrons, kB is the Boltzmann's constant and TF is Fermi temperature. The lattice heat capacity is set as a constant because of its relatively small variation as the temperature changes. The electron heat conductivity can be expressed as ke = ke0BTe/(ATe2 + BTl) [25], where ke0, A and B are the constants. Many of the ultrafast laser heating analyses have been carried out with a constant electron–lattice coupling factor G. However, due to the significant changes in the electron and lattice temperatures caused by high-power laser heating, G should be temperature dependent (G = G0(A(Te + Tl)/B + 1), where G0 is the coupling factor at room temperature) [26]. The lattice thermal conductivity is therefore taken as 1% of the thermal conductivity of bulk metal since the mechanism of heat conduction in metal is mainly due to electrons [27]. As the temperature changes, the variety of the lattice heat conductivity is relatively small and it is assumed a constant. Considering a one-dimensional two-layered thin film, Fig. 1 shows the schematic view of the laser heating, which indicates a two-layer metal film with an interface at x = l. For the two-layer thin film, the two-temperature equation (Eqs. (1) and (2)) for studying thermal behavior in the thin film can be expressed as I
∂T e ∂ I ∂T e Ce ¼ k ∂t ∂x e ∂x I
Cl
I
Ce
I ∂T l I ∂ I ∂T l ¼ kl ∂t ∂x ∂x
II
I
!
I I I −G T e −T l þ S
!
I I þ G T e −T l
! II ∂T e II ∂ II ∂T e II II ¼ −G T e −T l ke ∂t ∂x ∂x
II ∂T l II ∂ II ∂T l Cl ¼ kl ∂t ∂x ∂x
!
II
II II þ G T e −T l :
ð14Þ
ð15Þ
ð16Þ
ð17Þ
To solve Eqs. (4)–(7), the following initial and boundary conditions must be used. Before irradiated by the laser pulse, the electron and lattice sub-systems are considered to be at the same initial temperature (T0 = 300 K) I
I
T e ðx; 0Þ ¼ T l ðx; 0Þ ¼ T 0
ð18Þ
A. Chen et al. / Thin Solid Films 529 (2013) 209–216
Fig. 1. The schematic of a two-layer metal film. The thickness of Au is l. The thickness of Cr is 200 nm.
II
II
T e ðx; 0Þ ¼ T l ðx; 0Þ ¼ T 0 :
ð19Þ
The energy of the convective and radiative losses from the front and back surfaces of the two-layer film, in addition, is negligible during the femtosecond transient. The boundary conditions are formulated, as follows ∂T e I ∂x
j
∂T l I ∂x
j
x¼0
x¼0
¼
∂T e II ∂x
¼
∂T l II ∂x
j
x¼L
j
x¼L
¼0
ð20Þ
¼ 0:
ð21Þ
At the interface of the film (x = l), the two-layer thin film is in perfect thermal contact. Therefore we set the boundary conditions of the interface, as follows Te Tl
I
ke
kl
I
I
I
j
j
x¼l
¼ Te
x¼l
¼ Tl
∂T e I ∂x ∂T l I ∂x
j
j
II
x¼l
x¼l
II
j
j
ð22Þ
x¼l
ð23Þ
x¼l
¼ ke
¼ kl
II
II
∂T e II ∂x
∂T l II ∂x
j
j
x¼l
x¼l
:
ð24Þ
ð25Þ
3. Experimental details A schematic diagram of the standard pump–probe experimental setup is shown in Fig. 2. The laser system was a regenerative amplified
211
Ti:Sapphire laser (Spectra Physics, Tsunami oscillator and Spitfire amplifier), which provides 90 fs pulses at 800 nm with 0.6 mJ per pulse and a repetition rate of 1 kHz. The laser beam was then split to generate pump and probe parts. The pump beam (400 nm) was obtained by second harmonic generation in a 0.5 mm thick β-BaB2O4 (BBO) crystal. The intensity of the pump beam can be controlled by a λ/2 plate in combination with a Glan prism. The residual 800 nm laser beam acts as a probe beam. In our experiment the intensity ratio of pump to probe beam is about 80:1. A computer-controlled translation stage (Physik instrumente, M-505) was used to control the time delay between the pump and the probe pulses with a resolution of 1 μm. The delay time may be changed from − 100 to 900 ps. By a combination of a Glan laser polarizer and a half-wave plate, the energy of each pulse can be attenuated to the desired value. The pump and probe pulses were directed by two concave mirrors (Focal length is 25 cm) and a beam splitter onto the sample with the focal diameter spots of 300 μm and 200 μm. The spots were carefully overlapped, while being viewed with a CCD camera. The metal target was mounted on a computer-controlled X–Y–Z stage, which can guarantee the sample location. All experiments are performed in air at atmospheric pressure. The angles of incidence of the pump and probe beams at the sample were very small. The pump and probe beams were reflected from the sample and filtered by a filter so that the 800 nm probe beam could be detected by a photodiode. Differential detection (ThorLabs PDB150A-AC) was used so as to cancel out the fluctuations of the laser output, leaving only the signal caused by the chopped pump beam. Thus, the lock-in amplifier (Stanford SR830) detects modulation in the received probe intensity that was caused only by the effect of the pump on the sample. The samples used in the experiments were double-layer gold and chrome thin films deposited on K9 glass. The two-layer metallic films were prepared using a physical vapor deposition method. The sample structure and general optical layout were shown in Fig. 1. The thickness of chrome film was 200 nm. The thickness of gold layer was 50 nm, and 100 nm, respectively. We substituted a BBO crystal (0.2 mm) for the sample to generate a sum-frequency pulse (267 nm) of pump and probe pulses. Through detecting the correlation signal, the time zero-point and the time resolution of our system could be evaluated. 4. Results In this experiment, the time dependence of transient relative reflectivities for 400 nm pump light and 800 nm probe light are displayed in Figs. 3 and 4 for both gold-coated two-layer films. The three different pump laser powers are 2 mW, 4 mW, and 12 mW, respectively. Fig. 3 (a and b) shows the normalized ΔR/R for the same
Fig. 2. The schematic drawing of the apparatus. Components include beam splitter (BS), concave mirror (CM), filter (F), Glan laser polarizer (G) and half-wave plate (HWP).
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Fig. 3. The normalized transient reflectivity data for both films recorded with three different laser powers: (a) the film is Au/Cr of 50 nm and 200 nm and (b) the film is Au/Cr of 100 nm and 200 nm.
gold film thickness. The normalized curves are calculated by dividing the minimum value of three curves. As shown in these figures, the reflectivity change process consists of three different time stages. Firstly, the transient relative reflectivity decreases rapidly for the delay time up to a few hundred femtoseconds and reaches the minimum point. Next, the increasing reflectivity occurs for the delay time of 2 ps. Finally, the reflectivity after delay time of 2 ps nears a constant. Fig. 4 (a–c) shows the normalized ΔR/R for the 50 nm and 100 nm Au/Cr two-layer films at the same laser power. These data are normalized at the peak reflectance to observe the difference between the electron cooling profiles at three different laser fluences. For the different thickness of gold layer, the surface electron temperatures rose rapidly with the maximum temperatures. Next, surface electron temperatures decreased with time. In the range of 0–2 ps, the variations of the surface electron temperature were almost same for the different thickness of gold layer [28]. The variation of the surface electron temperature is proportional to the variation of the reflectivity. It is the shape of the cooling profile after the maximum electron temperature that is related to the rate of electron–lattice equilibration; therefore, the normalization of the data is for clear comparison between the two data sets. The majority of the electron energy loss to the lattices occurs within 1–2 ps after laser heating. Differences in the data are seen within 2 ps after the maximum reflectance, indicating a difference in the cooling rate of the electron system during electron–lattice equilibration.
Fig. 4. The normalized transient reflectivity data for three laser powers recorded with both different two-layer films. The pump laser powers: (a) 2 mW, (b) 4 mW, and (c) 12 mW.
Two major processes of electron–electron collision and scattering process and electron–lattice coupling process occur in the interaction between the femtosecond laser and the thin film. The nonequilibrium temperature induced in the experiments can be predicted with the two temperature model. The mathematical model that is calculated by the finite difference method, given by Eqs. (1) and (2), describes
A. Chen et al. / Thin Solid Films 529 (2013) 209–216
the rate of energy exchange between the electrons and lattices in a metallic film. The temporal distributions of the electron are presented in Fig. 5 for both thin films. The laser fluences are 3 mJ/cm 2, 6 mJ/cm 2, and 17 mJ/cm 2, respectively. Table 1 [29–33] lists the values of thermal physical parameters of the two noble metals used in these calculations. One can see from Fig. 5 that the surface electron temperatures rose rapidly with maximum temperatures in the range of a few hundred femtoseconds. Consequently, surface electron temperature decreases with time due to the heat diffusion effect in the electron gas, at a short time delay (about 2 ps). The distributions of the surface electron temperature for three different laser fluences are noticeably different. The decay rate of electron temperature of the low laser fluence is less than that of the high laser fluence, and the thermal equilibrium time is extended.
5. Discussion Generally, the lattice cannot be affected by the absorption of a pump light, but a nonequilibrium process of hot electron and cold lattice will be created. The scattering among the hot electrons as well as from the lattices, defects, etc., results in the creation of the
213
Table 1 Thermal and optical physical parameters for gold and chrome. Au
Cr
Electron–lattice coupling coefficient G0 0.22 4.2 [1017 J m− 3 s− 1 K− 1] 68 194 Electron heat capacity coefficient γ[J m− 3 K− 2] Electron thermal conductivity coefficient ke0[J m− 1 s− 1 K− 1] 315 95 6 −3 −1 Lattice heat capacity Cl[10 J m K ] 2.5 3.3 −9 Penetration depth α[10 m] 17.7 7 −1 −2 A [10 s K ] 1.18 7.9 1.25 13.4 B[1011 s− 1 K− 1] Melting temperature Tm[103 K] 1.337 2.180
equilibrium electron distribution described by the Fermi–Dirac function [34,35] f FD ðE; T e Þ ¼
exp
1
E−EF ðT e Þ kB T e
þ1
ð26Þ
where, E is the electron energy, EF is the Fermi energy, and kB is the Boltzmann constant. At moderate temperatures, the Fermi energy varies with temperature as " EF ðT e Þ ¼ EF0 1−
# 2 π kB T e 2 : 12 EF0
ð27Þ
Where, EF0 is the Fermi energy at absolute zero temperature. The transient reflectivities are not affected by holes in the d-band which are initially created by optical excitation since the lifetime of these holes is vanishingly small [36]. When the electrons have been heated, the electron temperature can still be higher than that of the lattice. The main mechanism of the TTM is that the electron and lattice are well characterized by their respective temperatures which equalize with rate proportional to the electron–lattice coupling constant. The process is a very complex [37], since the specific heat capacity of electron is low. Irradiated by a laser beam, the electron temperature increases rapidly in an extremely short time, producing a great temperature difference between electron and lattice. The nonequilibrium energy transport, which is due to the electron–lattice coupling mechanism [38], will take place. The excess energy of the thermalized electron subsystem is equal to the product of the excess electron temperature ΔTe and the electron heat capacity Ce, which is in turn proportional to the electron temperature Te =Te + ΔTe. In the transient thermoreflectance experiments, it is the change in reflectivity ΔR resulting from a change in temperature in the sample that is measured. The change in reflectance of a metal can be related to the change in temperature through the change in the complex dielectric function Δε =Δε1 +iΔε2, here Δε1 and Δε2 are the real and imaginary part changes of the complex dielectric function. When the changes of ΔTe and ΔTl are small, Δεcan be expressed by ΔTe and ΔTl Δε ¼ Δε1 þ iΔε 2 ¼
∂ε1 ∂ε ∂ε2 ∂ε ΔT e þ 1 ΔT l þ i ΔT e þ 2 ΔT : ∂T e ∂T l ∂T e ∂T l
ð28Þ
The changed reflectivity can be expressed by the dielectric functions
ΔR 1 ∂R ∂R ¼ Δε1 þ Δε2 : R R ∂ε1 ∂ε2
ð29Þ
Combining Eqs. (28) and (29), the change of the reflectivity can be rewritten as [39,40] Fig. 5. The variation of surface electron temperature with the delay time for the different laser fluences by TTM predictions. The thickness of Au/Cr films: (a) 50 nm and 200 nm; (b) 100 nm and 200 nm.
ΔR ¼ aΔT e þ bΔT l R
ð30Þ
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A. Chen et al. / Thin Solid Films 529 (2013) 209–216
where a ∝ ∂ R/∂ Te and b ∝ ∂ R/∂ Tl. The electron and lattice temperatures directly relate to the change of the reflectivity. Compared with the change of the electron temperature, the change of the lattice temperature is very small and can be ignored. Eq. (30) can be simplified as ΔR ¼ aΔT e : R
ð31Þ
The original measured signals and theoretical results are shown in Figs. 3 and 4, and Fig. 5, respectively. As mentioned above, ΔTe/Te is proportional to ΔR/R. As a result, the transient reflectivity signals can be represented by the variation of the electron temperature with time. The electron temperature starts to rise when the pump pulse irradiates the surface of the target, and then the electron temperature decreases because of the non-equilibrium heat transport from the hot electrons to the cold lattices. In order to analyze the data, the electron temperature is normalized. In Fig. 6, we compare the calculations with experimental data. Agreement with experiment is rather satisfactory. However, it should be noted that the measured data are in fact a function not only of film thickness [41,42] (as expected from Fig. 4) but also of film morphology [43,44]. The morphology dependence is a subject of continuing study. In Fig. 6 (a), there is some disagreement between calculated and experimental data. This is due to electron–lattice coupling factor that governs the
Fig. 6. The comparison of theoretical and experimental results: (a) fixed film thickness with the different laser energy and (b) fixed laser energy with the different film thickness.
rate of energy transfer to the lattice from the hot electrons. In here, we use theoretical predictions that differ with the actual value. The two-layer film structure can change the damage threshold of the gold surface [45]. As shown in Fig. 4, for the fixed laser power, the ΔR/R of the thinner gold layer is less than that of the thicker gold layer at the thermal equilibrium. In contrast with the experimental results of Hohlfeld et al. [46], it is just contrary. In the Hohlfeld's experiment, the gold films were directly deposited on optical fused silica plates. However, we introduced the chrome film as the substrate layer in this experiment. The substrate layer will act as a heat sink absorbing the thermal energy transmitted through the interface and then coupling that energy to the lattice away from the heat affected area [47]. According to the previous theory, ΔTe/Te is proportional to ΔR/R, Fig. 4 (a–c) illustrates that the surface of the thicker gold layer will obtain higher temperature compared to that of the thinner gold layer. Subsequently, we calculate the variation of the lattice temperature with the depth of the two-layer film. Fig. 7 shows the distribution of the lattice temperature for both thin films at three different fluences. We notice that the lattice temperature distribution has big ups and downs in the interface region of the gold-layer and chrome-layer. This is due to the fact that the electron–lattice coupling factor is considerably higher or lower for the substrate layer film than that for the top layer. This results in the redistribution of the deposited laser energy from the gold film
Fig. 7. The distribution of the lattice temperature with the different laser fluences for both two-layer films. The thickness of Au/Cr films: (a) 50 nm and 200 nm; (b) 100 nm and 200 nm.
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layer to the substrate layer, where the energy of the excited electrons couples more effectively with the lattice vibrations, leading to the preferential or disadvantageous lattice heating in the substrate layer. Fig. 8 clearly shows the distribution of the lattice temperature
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for the different thick gold layer. At the surface, the lattice temperature of 50 nm gold layer is lower than that of 100 nm for the twolayer films, the lattice of single-layer films are higher than that of the two-layer films. The results provide way for the improvement of gold surface damage threshold. 6. Conclusion In summary, the transient reflectivity of the gold-coated two-layer metal film is investigated by femtosecond time-resolved pump–probe technique. The two-layer structure is the 50 nm and 100 nm gold layers padding on the 200 nm chromes. Experiments are performed for three different pump powers. Experimental results show that the reflectivity change increases with the power of the pump laser. The experimental results are analyzed within the framework of the two-temperature model, which describes the energy relaxation in ultrafast heating. A comparison between the experimental results for both two-layer films revealed the difference of the thermoreflectivity signal at the thermal equilibrium. By the theoretical analysis, the introduced substrate layer will signify a reduction in the surface lattice temperature. Taking advantage of the two-layer structure, it is believed that the damage threshold of the gold film can be improved. Acknowledgment This project is supported by the Chinese National Fusion Project for ITER (Grant no. 2010GB104003) and the National Natural Science Foundation of China (Grant nos. 10974069, 11034003). References
Fig. 8. The comparison of the lattice temperature distribution for the single-layer Au films and the two-layer Au/Cr films at the different laser fluences. The fluence: (a) 3 mJ/cm2, (b) 6 mJ/cm2, and (c) 17 mJ/cm2.
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