Modelling thermal energy transfer in a femtosecond pulsed laser ablation of metal using a coupled spring-mass oscillator

Abstract

Femtosecond pulsed laser ablation (fs-PLA) is an interesting but complicated field of study especially for undergraduate students entering the field. Hence, a bridging concept using classical and mechanical analog will be helpful. In this paper, we modelled the thermal energy transfer between electron and lattice system in a fs-PLA of metal described by two temperature model (TTM) using a coupled spring-mass oscillator. This was achieved by providing correspondence of TTM parameters to the coupled spring-mass oscillator, with temperature as position, electron thermal conductivity as coefficient of friction, electron-phonon coupling factor as spring term, electron/lattice heat capacity as the mass $m_1$/$m_2$ respectively, and laser source term as the driving force. The thermophysical properties considered are temperature dependent leading to position dependent parameters of coupled spring-mass oscillator. Results showed that the coupled spring-mass oscillator exhibit many behavior similar to the TTM. Additionally, maximum positions achieved by $m_2$ behave similarly with maximum lattice temperature after achieving certain threshold value. However, many features of TTM such as spatial dependence and crater formation are not observed in the coupled spring-mass oscillator. Despite its limitation, the coupled spring-mass oscillator model was able to represent many features of the thermal energy transfer of fs-PLA, and could be an easy and useful model in understanding fs-PLA.