Energy Relaxation and Electron–Phonon Coupling in Laser-Excited Metals

Jia Zhang,Wenjun Zhu,Jan Vorberger,Rui Qin

doi:10.3390/ma15051902

Abstract

The rate of energy transfer between electrons and phonons is investigated by a first-principles framework for electron temperatures up to = 50,000 K while considering the lattice at ground state. Two typical but differently complex metals are investigated: aluminum and copper. In order to reasonably take the electronic excitation effect into account, we adopt finite temperature density functional theory and linear response to determine the electron temperature-dependent Eliashberg function and electron density of states. Of the three branch-dependent electron–phonon coupling strengths, the longitudinal acoustic mode plays a dominant role in the electron–phonon coupling for aluminum for all temperatures considered here, but for copper it only dominates above an electron temperature of = 40,000 K. The second moment of the Eliashberg function and the electron phonon coupling constant at room temperature K show good agreement with other results. For increasing electron temperatures, we show the limits of the approximation for the Eliashberg function. Our present work provides a rich perspective on the phonon dynamics and this will help to improve insight into the underlying mechanism of energy flow in ultra-fast laser–metal interaction.

Highlights

With the advent of femtosecond pump–probe setups, remarkable progress has been made in the study of ultrashort laser–matter interaction during recent decades [1–6]
As can be seen from expression (9), the evaluation of electron–phonon coupling factor is related to the specific phonon states that receive the energy and are determined by the phonon density of states F(ω) and the electron–phonon coupling as incorporated in the Eliashberg function α2F(ω)
The deviations between Te = 315 K and Te ∼ 20,000 K remain small. This justifies in this range the often applied approximation of using the ground state Eliashberg function for the energy transfer rate at all electron temperatures

Summary

Introduction

With the advent of femtosecond pump–probe setups, remarkable progress has been made in the study of ultrashort laser–matter interaction during recent decades [1–6]. Regarding the dynamical response of laser-excited materials, the electrons are accelerated by the laser pulse and thermalize within femtoseconds at a level of several tens of thousands Kelvin while leaving the ions in their initial state. If the initial state is a solid, the lattice is heated due to electron–phonon energy transfer to a new thermal equilibrium over several (tens to hundreds of) picoseconds. During this evolution, many interesting effects such as the ultrafast electron and non-equilibrium phonon dynamics [11–19], changes in lattice stability [20–24], phase transitions [25–30], and non-equilibrium electron–phonon interactions [31–40] take place. We concentrate on the microscopic energy flow related to the electron-phonon interaction

Methods

Results

Conclusion