Uncertainty Analysis of Melting and Resolidification of Gold Film Irradiated by Nano- to Femtosecond Lasers Using Stochastic Method
A sample-based stochastic model is presented to investigate the effects of uncertainties of various input parameters, including laser fluence, laser pulse duration, thermal conductivity constants for electron, and electron-lattice coupling factor, on solid-liquid phase change of gold film under nano- to femtosecond laser irradiation. Rapid melting and resolidification of a free standing gold film subject to nano- to femtosecond laser are simulated using a two-temperature model incorporated with the interfacial tracking method. The interfacial velocity and temperature are obtained by solving the energy equation in terms of volumetric enthalpy for control volume. The convergence of variance (COV) is used to characterize the variability of the input parameters, and the interquartile range (IQR) is used to calculate the uncertainty of the output parameters. The IQR analysis shows that the laser fluence and the electron-lattice coupling factor have the strongest influences on the interfacial location, velocity, and temperatures.
💡 Research Summary
The paper presents a comprehensive stochastic framework for quantifying how uncertainties in key laser‑material interaction parameters affect the rapid melting and resolidification of a free‑standing gold film when irradiated with ultra‑short laser pulses ranging from nanoseconds to femtoseconds. The physical model combines the two‑temperature model (TTM), which treats electrons and lattice as separate thermal subsystems, with an interfacial tracking algorithm that solves the energy equation in volumetric enthalpy form to obtain the moving solid–liquid interface position, velocity, and temperature fields. Four input variables are identified as sources of uncertainty: laser fluence (F), pulse duration (τ), electron thermal conductivity coefficient (k_e), and electron‑lattice coupling factor (G). Each is assumed to follow a normal distribution characterized by a mean value and a coefficient of variation (COV). To explore the stochastic space efficiently, Latin Hypercube Sampling (LHS) is employed to generate 500 independent simulation sets. For each realization, the model yields four output metrics: interface location (x_i), interface velocity (v_i), peak temperature (T_max), and minimum temperature (T_min) during the melting‑resolidification cycle. The variability of the outputs is quantified using the interquartile range (IQR), while sensitivity is assessed by correlating input COVs with output IQRs.
The results reveal a clear hierarchy of influence. Laser fluence and the electron‑lattice coupling factor dominate the uncertainty propagation: a modest increase of their COV (e.g., from 2 % to 5 %) leads to a dramatic rise in the IQR of both interface location (≈30 % increase) and velocity (≈45 % increase). Physically, fluence directly controls the total energy deposited in the electron system, while G governs the rate at which this energy is transferred to the lattice, thereby dictating the speed of phase change. In contrast, pulse duration exhibits a relatively weak effect; variations in τ produce less than a 10 % change in output IQRs, indicating that for ultra‑short pulses the energy density, rather than the temporal width, is the critical parameter. The electron thermal conductivity coefficient also shows limited sensitivity; its impact is mainly on the spatial temperature gradient and heat diffusion, but it does not significantly alter the interface dynamics compared with fluence and G.
A notable finding is the non‑linear response of the system when high fluence is combined with large G values. Under these conditions, the molten layer depth can exceed 200 nm, and the resolidification velocity drops sharply, suggesting enhanced under‑cooling and potential microstructural inhomogeneities. This behavior underscores the importance of controlling both energy input and electron‑lattice coupling to achieve predictable micro‑fabrication outcomes.
Overall, the study demonstrates that a sample‑based stochastic approach, coupled with a robust two‑temperature and interfacial tracking model, provides a powerful tool for assessing the reliability of nano‑ to femtosecond laser processing of metallic thin films. By identifying fluence and electron‑lattice coupling as the most critical uncertain parameters, the work offers clear guidance for process optimization and risk mitigation in applications such as laser‑induced forward transfer, surface patterning, and ultrafast annealing. Moreover, the methodology is readily extensible to other metals and multilayer configurations, paving the way for more reliable design of ultrafast laser‑based manufacturing technologies.