Ultrashort-pulsed Laser Heating Research Articles

Sub-Diffusion Two-Temperature Model and Accurate Numerical Scheme for Heat Conduction Induced by Ultrashort-Pulsed Laser Heating

In this study, we propose a new sub-diffusion two-temperature model and its accurate numerical method by introducing the Knudsen number (Kn) and two Caputo fractional derivatives (0<α,β<1) in time into the parabolic two-temperature model of the diffusive type. We prove that the obtained sub-diffusion two-temperature model is well posed. The numerical scheme is obtained based on the L1 approximation for the Caputo fractional derivatives and the second-order finite difference for the spatial derivatives. Using the discrete energy method, we prove the numerical scheme to be unconditionally stable and convergent with O(τmin{2−α,2−β}+h2), where τ,h are time and space steps, respectively. The accuracy and applicability of the present numerical scheme are tested in two examples. Results show that the numerical solutions are accurate, and the present model and its numerical scheme could be used as a tool by changing the values of the Knudsen number and fractional-order derivatives as well as the parameter in the boundary condition for analyzing the heat conduction in porous media, such as porous thin metal films exposed to ultrashort-pulsed lasers, where the energy transports in phonons and electrons may be ultraslow at different rates.

A generalized thermoelastic diffusion theory of porous materials considering strain, thermal and diffusion relaxation, and its application in the ultrashort pulse laser heating

A generalized thermoelastic diffusion theory of porous materials considering strain, thermal and diffusion relaxation, and its application in the ultrashort pulse laser heating

Analytical model for ultrashort pulse laser heating in a titanium nanofilm by implementing dual-phase-lag theory in mathematical analysis

Analytical model for ultrashort pulse laser heating in a titanium nanofilm by implementing dual-phase-lag theory in mathematical analysis

Neural network method for solving parabolic two-temperature microscale heat conduction in double-layered thin films exposed to ultrashort-pulsed lasers

Simulation of the micro/nanoscale heat conduction induced by ultrashort-pulsed laser heating has been attracting great attention. Additionally, machine and deep learning techniques are becoming an important tool in engineering and science research. This article presents an artificial neural network (ANN) method for solving the parabolic two-temperature heat conduction equations in double-layered thin films exposed to ultrashort-pulsed lasers. Convergence of the ANN solution to the analytical solution is theoretically analyzed. Finally, the ANN method is used to predict the electron and lattice temperatures in a gold film padding on a chromium film when exposed to ultrashort-pulsed lasers, which is based on the parabolic two-temperature heat conduction model.

High precision simulation and analysis of non-Fourier heat transfer during laser processing

With the rapid development of ultrashort-pulse laser heating and nanomaterials in science and engineering, the research on non-Fourier models to predict the anomalous heat conduction has attracted more and more attention. Among the existing non-Fourier models, the dual-phase-lag model can provide the best performance and it is more suitable for a short duration of heating. Considering the complexity of the equation, an efficient and accurate numerical method is proposed and applied to the analysis of the non-Fourier problems with complex geometry. The Cattaneo-Vernotte model and the dual-phase-lag model are selected and analyzed by the proposed method in the process of laser heating. Numerical simulations are made conducted for 1-D, 2-D, and 3-D problems in single-phase media exposed to laser pulses. The numerical results represent that the proposed method is accurate and stable to predict the thermal behavior of the plate irradiated by laser and other non-Fourier heat transfer problems.

Modeling the laser-polymer interaction of laser propulsion systems considering progressive surface removal, thermal decomposition and non-Fourier effect

During the laser-polymer interactions of laser propulsion systems, the surface of the target progressively recedes, which in turn necessitates accounting for the moving front boundary, and the decomposition rate varies with the temperature resolution, which accordingly updates the internal heat flux. The non-Fourier effect existing in ultra-short pulse laser heating also needs to account for the finite propagation speed of the thermal wave. Therefore, developing an accurate predictive simulation model that captures materials moving front, simultaneously updates the internal heat source, and characterizes the non-Fourier effect is an important and challenging task. In this study, a mathematical model of the laser-polymer interaction was numerically implemented using a two-dimensional finite volume method considering progressive surface removal, thermal decomposition, and non-Fourier effect. The proposed model utilizes a robust coupling scheme that enables us to track the moving boundary condition owing to the progressive surface material removal, simultaneously updates the internal heat source by varying the pyrolysis rate, and re-meshes the computational domain after the material surface is progressively removed. Moreover, the thermal relaxation time is introduced into the heat conduction equation to characterize the non-Fourier effect. In addition, the temperature-dependent material and optical properties of the target material were considered in the proposed model. Simulations were performed for the laser ablation of polyoxymethylene with a carbon dioxide laser under different parameters. The theoretical estimations of the ablation depths and area mass densities agree well with the experimental results.

Analytical solution of dual-phase-lag based heat transfer model in ultrashort pulse laser heating of A6061 and Cu3Zn2 nano film

The dual-phase-lag model provides the best performance among many existing non-Fourier models and it is particularly more suitable for a short duration of heating. The present literature survey certifies the availability of very few research papers specifically on the development of an exact analytical solution of the dual-phase-lag model illustrating the thermal analysis of ultrashort pulsed laser heating. To address such issues, the present work is intended to develop an exact solution of the thermal response based on the dual-phase-lag heat conduction model utilized for the femtosecond laser heating of nanofilm. The corresponding solution has been derived by a hybrid application of the Duhamel’s theorem and the finite integral transform approach. A comparative thermal analysis has been depicted for the laser heating of 5 nm thin A6061 and Cu3Zn2 nanofilm and the necessity of non-Fourier analysis over the Fourier’s model has been justified. Existing research works are mostly based on gold and chromium nanofilm. As multi-component microstructures of Cu and Al are scientifically proved to be excellent metallic properties (magnetic and optical) and exhibit strong response during energy driven-chemical reactions, the present analysis is focused on these two materials for the femtosecond laser irradiation. In the present analysis, optical properties (absorptivity and reflectivity) of substrate material have been taken into account to develop a better and realistic analytical model than the existing models. The research output notifies that at 0.1 ps of the laser pulse and 100 J m−2 of the laser intensity, developed temperature history reaches the melting point temperature of both the materials in combination with other thermophysical properties. The mathematical modeling also provides the appropriate information about the selection of thermal relaxation time lags for respective materials and this also justifies the experimental observation of relaxation time lags as reported in the literature. The thermal response has been captured for both A6061 and Cu3Zn2 material along the various depths of the nanofilm to evolve the irradiation capacity of the pulsed femtosecond laser source. The present research output is well validated through numerical and experimental research works of existing literature with a negligible variation. The inclusion of optical properties of materials in the present research work plays an important role as it is noticed that the maximum deviation of the temperature difference between with and without optical properties is evidenced as 38.86% and 57.70% for A6061 and Cu3Zn2 nanofilms, respectively.

Fractional parabolic two-step model and its accurate numerical scheme for nanoscale heat conduction

Simulation of nanoscale heat transfer phenomena has attracted great attention, particularly the nanoscale heat conduction induced by ultrashort-pulsed laser heating. In this article, we present a nanoscale fractional parabolic two-step model and obtain an accurate numerical scheme for nanoscale heat conduction in metals. The model is obtained by introducing the Knudsen number (Kn) and the fractional-order derivative in time to the original parabolic two-step energy transport, and then coupling them with the Kn dependent and temperature-jump boundary condition. The numerical scheme is developed based on the fourth-order compact finite difference method and the L1 approximation for fractional derivatives. The well-posedness of the model, and the stability and convergence of the scheme are analyzed theoretically. We finally test the accuracy and applicability of the new model and the obtained numerical method by two examples. By changing values of the Knudsen number and fractional-order derivative as well as the parameter in the boundary condition, the simulation could be a tool for analyzing the nanoscale heat conduction in porous media such as porous thin metal film exposed to ultrashort-pulsed lasers.

Parabolic two-step model and accurate numerical scheme for nanoscale heat conduction induced by ultrashort-pulsed laser heating

Simulation of nanoscale heat transfer phenomena has attracted great attention, particularly the nano-scale heat conduction induced by ultrashort-pulsed laser heating. In this article, we propose a nanoscale parabolic two-step model and an accurate numerical scheme for thermal analysis of the nanoscale heat conduction induced by ultrashort-pulsed laser heating. To this end, we first introduce the Knudsen number (Kn) into the original parabolic two-step heat conduction equations and couple them with the Kn-dependent and temperature-jump boundary condition. We then develop a fourth-order accurate compact finite difference method for solving the nanoscale model. Stability and convergence of the obtained numerical scheme are analyzed theoretically. We finally test the accuracy and applicability of the nanoscale model and the obtained numerical scheme in three examples. By choosing various values of the Kn and the parameter α in the boundary condition, the simulation could be a tool for analyzing the nanoscale heat conduction induced by ultrashort-pulsed laser heating.

Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film

This article proposes a time fractional dual-phase-lagging (DPL) heat conduction model in a double-layered nanoscale thin film with the temperature-jump boundary condition and a thermal lagging effect interfacial condition between layers. The model is proved to be well-posed. A finite difference scheme with second-order spatial convergence accuracy in maximum norm is then presented for solving the fractional DPL model. Unconditional stability and convergence of the scheme are proved by using the discrete energy method. A numerical example without exact solution is given to verify the accuracy of the scheme. Finally, we show the applicability of the time fractional DPL model by predicting the temperature rise in a double-layered nanoscale thin film, where a gold layer is on a chromium padding layer exposed to an ultrashort-pulsed laser heating.

Nonlocal thermoelastic semi-infinite medium with variable thermal conductivity due to a laser short-pulse

In this article, the thermoelastic interactions in an isotropic and homogeneous semi-infinite medium with variable thermal conductivity caused by an ultra-short pulsed laser heating based on the linear nonlocal theory of elasticity has been considered. We consider that the thermal conductivity of the material is dependent on the temperature. The surface of the surrounding plane of the medium is heated by an ultra-short pulse laser. Basic equations are solved along with the corresponding boundary conditions numerically by means of the Laplace transform technique. The influences of the rise time of the laser pulse, as well as the nonlocal parameter on thermoelastic wave propagation in the medium, have also been investigated in detail. Presented numerical results, graphs and discussions in this work lead to some important deductions. The results obtained here will be useful for researchers in nonlocal material science, low-temperature physicists, new materials designers, as well as to those who are working on the development of the theory of nonlocal thermoelasticity.

Probing phase lag effect in ultra-short pulse laser heating of nano-film

Advanced material processing using ultra-short pulse laser is ever increasing with miniature of the components due to its capability of high precision control on heat transfer and heat affected zone. The transient growth of heat affected zone is worthy to investigate for nano-scale devices under the application of femtosecond pulse laser. The cost of experiments is high at femtosecond time scale on nano-scale substrates. Hence, the physical model of heat transfer based on finite element method is developed considering non-Fourier effect. The phase lag effect in terms of two relaxation times is considered to study the heat transfer phenomena.

Finite element model for femtosecond laser pulse heating using dual phase lag effect

The ultrashort pulse laser in material processing of micro/nanoscale has emerged as a useful application due to its capability of high precision control on heating and heat affected zone. The non-Fourier effect in heat conduction becomes more predominant as the duration of heating becomes extremely small which is the case of ultrashort pulse laser. To analyze the heat transfer process by an ultrashort pulse laser, a three dimensional finite element based numerical model is developed assuming finite speed of thermal wave propagation with two phase lags. The present work also describes the finite element formulation using phase lag boundary conditions. The numerical model is developed indigenously using an Intel fortran compiler. The transient heating and cooling phenomena are analyzed for the effect of two relaxation times, variation of pulse width, and multiple pulses. The model results are validated with ultrashort pulse laser heating of a thin gold film. The accuracy of the computed results shows promising application of the developed numerical model for differential influence of process parameters in micro/nano scale heat transport by ultrashort pulse laser processing.

An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.

Numerical Analysis of Ultrashort Pulse Laser-Induced Thermomechanical Response of Germanium Thin Films

Ultrashort pulse laser heating of a germanium nanofilm was simulated using a combined continuum–atomistic method that couples the molecular dynamics and a self-consistent energy model for ultrafast laser–semiconductor interaction. Both a single pulse and a pulse burst were considered. To accurately describe laser energy deposition, the transient optical properties were computed based on the Drude formula. It was found that for a single pulse at low fluence (e.g., 0.02 J/cm2), the pulse duration had little impact on the lattice temperature response. In contrast, a higher lattice temperature could be obtained for a longer pulse (e.g., 5 ps) at higher fluences (e.g., 0.06 J/cm2) due to lower surface reflectivity. A strong thermal stress wave could be induced by the laser heating, with its maximum compression and tension occurring in the front and rear film regions, respectively. The investigations of laser burst heating revealed that a laser burst not only can retain the advantages of ultrashort pulse lasers but can enhance the photon efficiency for material melting as well.

Theoretical and experimental study of femtosecond pulse laser heating on thin metal film

Ultrashort pulse laser heating is not only capable of resolving and observing the ultrafast interaction of energy carriers, i.e. electrons, phonons, but also widely applied to material processing, i.e., laser ablation. However, the previous theories, i.e., two-temperature model, parabolic one-step model, can be applied only to some limited segments. In this paper, according to the two-temperature model and Fourier’s law, a general theoretical model is presented for the description of the entire heat relaxation process after the thin metal film deposited on the substrate has been heated by the ultrashort pulse laser. Moreover, the heat conduction process is also experimentally studied by using the rear-pump front-probe transient thermoreflectance technique on Au/glass and Au/SiC at 300 K, and the theoretical prediction accords well with the experimental result, which illustrates the validity of the present theoretical model. Based on the good agreement between theoretical predictions and experimental data, the electron-phonon coupling factor of the thin gold film and thermal boundary conductance of the Au/glass and Au/SiC interfaces are extracted and the measured results are in good agrement with the previous reported values. The electron-phonon coupling factor is close to that of the bulk material and does not exhibit size effect. The thermal boundary conductance is greater than the prediction of diffuse mismatch model, and the reasons responsible for the discrepancies are electrons participating in the interfacial heat conduction, interfacial atom diffusion and inelastic scattering.

Ultrafast thermoelectric properties of gold under conditions of strong electron-phonon nonequilibrium

The electronic scattering rates in metals after ultrashort pulsed laser heating can be drastically different than those predicted from free electron theory. The large electron temperature achieved after ultrashort pulsed absorption and subsequent thermalization can lead to excitation of subconduction band thermal excitations of electron orbitals far below the Fermi energy. In the case of noble metals, which all have a characteristic flat d-band several electron volts well below the Fermi energy, the onset of d-band excitations has been shown to increase electron-phonon scattering rates by an order of magnitude. In this paper, we investigate the effects of these large electronic thermal excitations on the ultrafast thermoelectric transport properties of gold, a characteristic noble metal. Under conditions of strong electron-phonon nonequilibrium (relatively high electron temperatures and relatively low lattice temperatures, Te⪢TL), we find that the Wiedemann–Franz law breaks down and the Seebeck coefficient is massively enhanced. Although we perform representative calculations for Au, these results are expected to be similar for the other noble metals (Ag and Cu) due to the characteristic large d-band separation from the Fermi energy.

Theoretical and experimental study on the heat transport in metallic nanofilms heated by ultra-short pulsed laser

In this paper the mechanism of heat transport in metallic nanofilms under ultra-short pulsed laser heating is examined theoretically and experimentally. In order to easily understand the non-equilibrium heat transport in metallic nanofilms the study of heat transport behavior is first carried out in dielectrics. The analyses indicate that there may be two kinds of wave phenomena in dielectrics subjected to a periodic surface temperature. One is the thermal wave governed by the C–V model based hyperbolic equation and the other is the diffusive wave governed by the Fourier model based parabolic equation. According to the hyperbolic two step model for non-equilibrium heat transport, such two kinds of wave phenomena can also occur simultaneously in the metallic nanofilms under pulsed laser heating, where the diffusive wave is induced by the electron temperature oscillation at the surface due to the non-equilibrium between electrons and lattices. Unlike the propagation speed of the thermal wave, the propagation speed of the diffusive wave depends not only on the medium properties but also the period of the temperature oscillation at the boundary. Hence, the propagation speed of the diffusive wave in the electron gas may be of as high as 10 6 m s −1, when the laser pulse duration is less than 1 ps. A transient thermoreflectance (TTR) system has been built to measure the transient electron temperature responses caused by the femtosecond laser heating and a pump–probe technique is used to ensure the femtosecond temporal resolution in the experiments. Different from the commonly used front heating-front detecting (FF) method for measuring the material properties, a rear heating-front detecting (RF) method is applied, so that measuring the propagation speed of heat becomes available. The non-equilibrium heat diffusion model is used to fit the measured normalized electron temperature profiles of 27.2 nm, 39.9 nm and 55.5 nm Au films. The best-fitted coupling factor G basically agrees with the theoretical value 2.3 × 10 16 W m −3 K −1. The propagation speed of the diffusive wave in the electron gas can be obtained by comparing the measured delay time of peak electron temperatures of Au films with different thicknesses. The average propagation speed of the temperature oscillation or diffusive wave in Au films for the range of thickness from 27.2 nm to 55.5 nm is equal to 8.1 × 10 5 m s −1, which is close to the value predicted by the non-equilibrium heat diffusion model.

Thermal analysis of thin multi-layer metal films during femtosecond laser heating

Multi-layer metals films are widely used in modern engineering applications such as gold-coated metal mirrors used in high power laser systems. A transient heat flux model is derived to analyze multi-layer metal films under laser heating. The two separate system composed of electrons and the lattice is considered to take into account the electron–lattice interaction. The present model predicted the effects of underlying chromium’s thermal properties on temperature rise of the top gold layer. The effects of two adjacent and different metals with different electron–lattice coupling factors are analyzed for the heating mechanism of different lattices. The derived transient model combined with the two different conservation equations for the lattice and electrons are applied for the ultra short-pulse laser heating of a multi-layer film composed of gold and chromium.

Contribution of Ballistic Electron Transport to Energy Transfer During Electron-Phonon Nonequilibrium in Thin Metal Films

AbstractWith the ever decreasing characteristic lengths of nanomaterials, nonequilibrium electron-phonon scattering can be affected by additional scattering processes at the interface of two materials. Electron-interface scattering would lead to another path of energy flow for the high-energy electrons other than electron-phonon coupling in a single material. Traditionally, electron-phonon coupling in transport is analyzed with a diffusion (Fourier) based model, such as the two temperature model (TTM). However, in thin films with thicknesses less than the electron mean free path, ballistic electron transport could lead to electron-interface scattering, which is not taken into account in the TTM. The ballistic component of electron transport, leading to electron-interface scattering during ultrashort pulsed laser heating, is studied here by a ballistic-diffusive approximation of the Boltzmann transport equation. The results for electron-phonon equilibration times are compared with calculations with TTM based approximations and experimental data on Au thin films.