Metal Ablation by ps-Laser-Pulses: A Hybrid Simulation

Boundary condition

t = 0.5       1.0         1.5         2.0         2.8         3.2          4.0         10.0 ps

The compressive pressure wave (red colored) travels with the velocity of sound through the crystal. After 3.2 ps the wave reaches the terminating zone, where calculation of the forces is changed. The high pressure is reduced to the nominal crystal pressure. The local pressures is in units of the bulk modulus, B=137 GPa.

 
• Animation (293 kB)

A Hybrid Simulation

Motivation

• The simulation of laser ablation of metals requires the modelling of both the electron and the atom system of the metal
• Simulation allows to study the strong non-equilibrium processes occurring during ablation: pressure wave, spallation, boiling, ...

Method

• Hybrid simulation: Molecular dynamics of the atomic system, coupled to finite-difference scheme for electron heat conduction

Molecular-dynamics (MD):

• Cu crystal, l=72 nm deep, 2.2 nm wide, with periodic boundary conditions
• Non-reflecting boundary conditions [Zhigilei and Garrison, 2000] are used at the bottom side, x=l, to prevent pressure wave reflection.

Finite-difference scheme (FD):

• electron heat transport down to a depth of L=400 nm
• electron heat conductivity dependent on electron and atom temperatures [Anisimov and Rethfeld, 1996]

Coupling:

• electron-phonon coupling introduced as a velocity-dependent force in MD [Häkkinen and Landman, 1993]
• electron-phonon coupling introduced as a gain/loss-term in FD
• atomic heat calculated in FD and coupled to electron heat between l < x < L

System:

• 0.5 ps irradiation of Cu with 250 nm laser, fluence between 100 and 450 mJ/cm². Laser penetration depth: lambda=14 nm.

a) Pressure

t = 29.4     30.4       31.4       32.4       33.4       34.4       35.0      35.8 ps

b) Temperature

t = 29.4     30.4       31.4       32.4       33.4       34.4       35.0      35.8 ps

Atomistic view of part of the laser-irradiated solid, at a time t = 32 ps, immediately after ablation occurred. Cross sections through the simulation volume (height 6 nm, width 2.1 nm, thickness 1 nm) are shown at various times after laser irradiation at a depth of 23 nm. Atoms are colored (a) according to their local pressures, in units of the bulk modulus, B = 137 GPa, and (b) according to their local temperature, in units of the melting point of copper, T_m = 1358 K. The local temperature of an atom is defined as the average kinetic energy of all atoms around the central atom within a radius of 6.2 A (cutoff of the interaction potential), in the center of mass system. Analogously, local pressures are defined as an average over the atomic virials.

• Animation (a) (450 kB)
• Animation (b) (419 kB)

• Animation (459 kB)

• Animation (541 kB)

Results

• Electron-phonon coupling heats the atomic system in a time scale of around 5 ps down to depths of around 10 lambda.
• Ablation is triggered by the unloading wave following the strong pressure pulse traveling down into the target.
• Ablation occurs by spallation in a depth of around 20 nm. For higher laser fluence multiple spallation occurs.
• The ablation threshold is 170mJ/cm², in good agreement with experiment.
• The ablation rate is a factor of 3 - 5 too high. Possible reasons:
• Simulation: single shot - Experiment: > 100 pulses
• Simulation: in the laser focus - Experiment: averaged laser diameter > 100 µm.
• Plasma shielding?
• Surface modification due to laser irradiation.