. State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China . Optics Valley Laboratory, Wuhan 430074, China
Photoacoustic detection has shown excellent performance in measuring thickness and detecting defects in metal nanofilms. However, existing research on ultrafast lasers mainly focuses on using picosecond or nanosecond lasers for large-scale material processing and measurement. The theoretical study of femtosecond laser sources for photoacoustic nondestructive testing (NDT) in nanoscale thin film materials receives much less emphasis, leading to a lack of a complete physical model that covers the entire process from excitation to measurement. In this study, we developed a comprehensive physical model that combines the two-temperature model with the acoustic wave generation and detection model. On the basis of the physical model, we established a simulation model to visualize the ultrafast laser-material interaction process. The damage threshold of the laser source is determined, and the effect of key parameters (laser fluence, pulse duration, and wavelength) for AlCu nanofilms on the femtosecond photoacoustic NDT process is discussed using numerical results from the finite element model. The numerical results under certain parameters show good agreement with the experimental results.
Optical penetration depth for a wavelength of 920 nm
zs
9.640
nm
Poisson’s ratio
υ
0.350
–
Specific heat of the lattice
Cl
2.42 × 106
J/m3·K
Electron–lattice coupling factor
G
3.10 × 1017
–
Young’s modulus
E
70 × 109
Pa
Shear modulus
μ
26 × 109
Pa
Thermal expansion coefficient
α
23.1 × 10−6
1/K
Density
ρ
2.70 × 103
kg/m3
Tab.1 Thermophysical and optical properties of AlCu nanofilms
Fig.3 (a) Profile of the laser heat source in various depths. (b) Temporal and spatial distribution of the laser heat source. (c) Temporal and spatial distribution of the electron temperature. (d) Temporal and spatial distribution of the lattice temperature.
Fig.4 (a) Profile of longitude stress in the nanofilm at various times. (b) Temporal and spatial distribution of the strain in the nanofilm.
Fig.5 Temporal evolution of the change in surface reflectivity.
Fig.6 (a) Maximum effective stress in nanofilms under varying laser fluence. (b) Maximum electron and lattice temperatures in nanofilms under varying laser fluence.
Fig.7 (a) Electron and lattice heating time in nanofilms under varying laser fluence. (b) Maximum electron and lattice temperatures in nanofilms under varying laser fluence. (c) Maximum effective stress in nanofilms under varying laser fluence. (d) Signal intensity of δR under varying laser fluence.
Fig.8 (a) Surface reflectivity and absorptivity of AlCu nanofilms under varying laser wavelength. (b) Optical penetration depth of AlCu nanofilms under varying laser wavelength.
Fig.9 (a) Electron and lattice heating time in nanofilms under varying laser wavelength. (b) Maximum electron and lattice temperatures in nanofilms under varying laser wavelength. (c) Maximum effective stress in nanofilms under varying laser wavelength. (d) Signal intensity of δR under varying laser wavelength.
Fig.10 (a) Electron and lattice heating time in nanofilms under varying pulse duration. (b) Maximum electron and lattice temperatures in nanofilms under varying pulse duration. (c) Maximum effective stress in nanofilms under varying pulse duration. (d) Signal intensity of δR under varying laser pulse duration.
Fig.11 Comparison diagram of experimental and simulated signals.
Abbreviations
NDT
Nondestructive testing
TTM
Two-temperature model
Variables
B
Bulk modulus
C0
Reference specific heat of the electron
Ce
Electron specific heat
Cl
Lattice specific heat
E
Young’s modulus
G
Electron–lattice coupling factor
J0
Peak fluence carried by laser pulse
k
Free-space wave number
L
Film thickness
Complex refractive index
Q
Volumetric laser heat source
RS
Reflectivity of the sound pulse
r0
Reflection coefficient
Te
Electron temperature
Tl
Lattice temperature
t0
Transmission coefficient
tp
Laser pulse duration
vl
Longitude velocity of acoustic wave
ze
Acoustic impedance of emergent medium
zi
Acoustic impedance of incident medium
zs
Optical penetration depth
α
Thermal expansion coefficient
ε
Strain
κe
Electron thermal conductivity
κl
Lattice thermal conductivity
δ
Surface reflectivity
δR
Change in reflectivity
λ
Lamé constant
δij
Kronecker delta function
ρ
Density
σeff
Effective stress
μ
Shear modulus
υ
Poisson’s ratio
1
C Thomsen, H T Grahn, H J Maris, J Tauc. Surface generation and detection of phonons by picosecond light pulses. Physical Review B, 1986, 34(6): 4129–4138 https://doi.org/10.1103/PhysRevB.34.4129
2
M Dubois, Jr Drake. T E. Evolution of industrial laser-ultrasonic systems for the inspection of composites. Nondestructive Testing and Evaluation, 2011, 26(3–4): 213–228 https://doi.org/10.1080/10589759.2011.573552
S Manohar, D Razansky. Photoacoustics: a historical review. Advances in Optics and Photonics, 2016, 8(4): 586–617 https://doi.org/10.1364/AOP.8.000586
5
D H Hurley. Pump-probe laser ultrasonics: characterization of material microstructure. IEEE Nanotechnology Magazine, 2019, 13(3): 29–38 https://doi.org/10.1109/MNANO.2019.2904772
6
K X Zhang, D Chen, S Wang, Z J Yao, W Feng, S F Guo. Flexible and high-intensity photoacoustic transducer with PDMS/CSNPs nanocomposite for inspecting thick structure using laser ultrasonics. Composites Science and Technology, 2022, 228: 109667 https://doi.org/10.1016/j.compscitech.2022.109667
7
G A Antonelli, H J Maris, S G Malhotra, J M E Harper. Picosecond ultrasonics study of the vibrational modes of a nanostructure. Journal of Applied Physics, 2002, 91(5): 3261–3267 https://doi.org/10.1063/1.1435831
8
K Y Chou, C L Wu, C C Shen, J K Sheu, C K Sun. Terahertz photoacoustic generation using ultrathin nickel nanofilms. Journal of Physical Chemistry C, 2021, 125(5): 3134–3142 https://doi.org/10.1021/acs.jpcc.0c09303
9
G N Ji, W Y Zhu, X X Jia, S F Ji, D P Han, Z X Gao, H Liu, Y Wang, T Han. AuNP/Cu-TCPP(Fe) metal-organic framework nanofilm: a paper-based electrochemical sensor for non-invasive detection of lactate in sweat. Nanoscale, 2023, 15(10): 5023–5035 https://doi.org/10.1039/D2NR06342E
10
S Zheng, C G Wang, J X Li, W Q Wang, Q Yu, C W Wang, S Q Wang. Graphene oxide-based three-dimensional au nanofilm with high-density and controllable hotspots: a powerful film-type SERS tag for immunochromatographic analysis of multiple mycotoxins in complex samples. Chemical Engineering Journal, 2022, 448: 137760 https://doi.org/10.1016/j.cej.2022.137760
11
R A Rodriguez-Davila, R A Chapman, Z H Shamsi, S J Castillo, C D Young, M A Quevedo-López. Low temperature, highly stable ZnO thin-film transistors. Microelectronic Engineering, 2023, 279: 112063 https://doi.org/10.1016/j.mee.2023.112063
12
E G Gamaly. The physics of ultra-short laser interaction with solids at non-relativistic intensities. Physics Reports, 2011, 508(4–5): 91–243 https://doi.org/10.1016/j.physrep.2011.07.002
13
S I Anisimov, B L Kapeliovich, T L Perel’man. Electron emission from metal surfaces exposed to ultrashort laser pulses. Journal of Experimental and Theoretical Physics, 1974, 39(2): 375–377
14
L A Falkovsky, E G Mishchenko. Electron-lattice kinetics of metals heated by ultrashort laser pulses. Journal of Experimental and Theoretical Physics, 1999, 88(1): 84–88 https://doi.org/10.1134/1.558768
15
J K Chen, J E Beraun, L E Grimes, D Y Tzou. Modeling of femtosecond laser-induced non-equilibrium deformation in metal films. International Journal of Solids and Structures, 2002, 39(12): 3199–3216 https://doi.org/10.1016/S0020-7683(02)00242-1
16
M E Povarnitsyn, N E Andreev, E M Apfelbaum, T E Itina, K V Khishchenko, O F Kostenko, P R Levashov, M E Veysman. A wide-range model for simulation of pump-probe experiments with metals. Applied Surface Science, 2012, 258(23): 9480–9483 https://doi.org/10.1016/j.apsusc.2011.07.017
17
A Ancona, S Döring, C Jauregui, F Röser, J Limpert, S Nolte, A Tünnermann. Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers. Optics Letters, 2009, 34(21): 3304–3306 https://doi.org/10.1364/OL.34.003304
18
G Heise, D Trappendreher, F Ilchmann, R S Weiss, B Wolf, H Huber. Picosecond laser structuring of thin film platinum layers covered with tantalum pentoxide isolation. Journal of Applied Physics, 2012, 112(1): 013110 https://doi.org/10.1063/1.4733467
Fatti N Del, C Voisin, D Christofilos, F Vallée, C Flytzanis. Acoustic vibration of metal films and nanoparticles. The Journal of Physical Chemistry A, 2000, 104(18): 4321–4326 https://doi.org/10.1021/jp994051y
21
S Yamaguchi, T Tahara. Coherent acoustic phonons in a thin gold film probed by femtosecond surface plasmon resonance. Journal of Raman Spectroscopy, 2008, 39(11): 1703–1706 https://doi.org/10.1002/jrs.2078
22
M Grossmann, M Schubert, C He, D Brick, E Scheer, M Hettich, V Gusev, T Dekorsy. Characterization of thin-film adhesion and phonon lifetimes in Al/Si membranes by picosecond ultrasonics. New Journal of Physics, 2017, 19(5): 053019 https://doi.org/10.1088/1367-2630/aa6d05
23
M Grossmann, M Klingele, P Scheel, O Ristow, M Hettich, C He, R Waitz, M F Schubert, A E Bruchhausen, V E Gusev, E Scheer, T Dekorsy. Femtosecond spectroscopy of acoustic frequency combs in the 100-GHz frequency range in Al/Si membranes. Physical Review B, 2013, 88(20): 205202 https://doi.org/10.1103/PhysRevB.88.205202
24
T Saito, O Matsuda, O B Wright. Picosecond acoustic phonon pulse generation in nickel and chromium. Physical Review B, 2003, 67(20): 205421 https://doi.org/10.1103/PhysRevB.67.205421
25
K E O'hara, X Y Hu, D G Cahill. Characterization of nanostructured metal films by picosecond acoustics and interferometry. Journal of Applied Physics, 2001, 90(9): 4852–4858 https://doi.org/10.1063/1.1406543
26
C J K Richardson, M J Ehrlich, J W Wagner. Interferometric detection of ultrafast thermoelastic transients in thin films: theory with supporting experiment. Journal of the Optical Society of America B: Optical Physics, 1999, 16(6): 1007–1015 https://doi.org/10.1364/JOSAB.16.001007
27
A Devos, C Lerouge. Evidence of laser-wavelength effect in picosecond ultrasonics: possible connection with interband transitions. Physical Review Letters, 2001, 86(12): 2669–2672 https://doi.org/10.1103/PhysRevLett.86.2669
28
S I Anisimov, B Rethfeld. Theory of ultrashort laser pulse interaction with a metal. In: KonovV I, Libenson M N, eds. Nonresonant Laser-Matter Interaction (NLMI-9). St. Petersburg: SPIE, 1997, 192–203
29
T Q Qiu, C L Tien. Femtosecond laser heating of multi-layer metals—I. Analysis. International Journal of Heat and Mass Transfer, 1994, 37(17): 2789–2797 https://doi.org/10.1016/0017-9310(94)90396-4
30
T Q Qiu, T Juhasz, C Suarez, W E Bron, C L Tien. Femtosecond laser heating of multi-layer metals—II. Experiments. International Journal of Heat and Mass Transfer, 1994, 37(17): 2799–2808 https://doi.org/10.1016/0017-9310(94)90397-2
31
O Matsuda, O B Wright. Reflection and transmission of light in multilayers perturbed by picosecond strain pulse propagation. Journal of the Optical Society of America B: Optical Physics, 2002, 19(12): 3028–3041 https://doi.org/10.1364/JOSAB.19.003028
32
Z B Lin, L V Zhigilei, V Celli. Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium. Physical Review B, 2008, 77(7): 075133 https://doi.org/10.1103/PhysRevB.77.075133
33
J K Chen, J E Beraun, D Y Tzou. Thermomechanical response of metal films heated by ultrashort-pulsed lasers. Journal of Thermal Stresses, 2002, 25(6): 539–558 https://doi.org/10.1080/01495730290074289
34
C Kittle. Introduction to Solid State Physics. New York: John Wiles & Sons, 1967
35
J Y Zhang, X Zhang, G Liu, R H Wang, G J Zhang, J Sun. Length scale dependent yield strength and fatigue behavior of nanocrystalline Cu thin films. Materials Science and Engineering: A, 2011, 528(25–26): 7774–7780 https://doi.org/10.1016/j.msea.2011.06.083
36
K M McPeak, S V Jayanti, S J P Kress, S Meyer, S Iotti, A Rossinelli, D J Norris. Plasmonic films can easily be better: rules and recipes. ACS Photonics, 2015, 2(3): 326–333 https://doi.org/10.1021/ph5004237
