Applied Surface Science 258 (2012) 9288–9291
Contents lists available at SciVerse ScienceDirect
Applied Surface Science
jou rn al h om epa g e: www.elsevier.com/locate/apsusc
Numerical simulation of laser ablation for photovoltaic materials
P. Stein
a,∗
, O. García
a
, M. Morales
a
, H.P. Huber
b
, C. Molpeceres
a
a
Centro Láser, Universidad Politécnica de Madrid, Spain
b
Munich University of Applied Sciences, Germany
a r t i c l e i n f o
Article history:
Available online 28 September 2011
Keywords:
Ultra-short laser pulses
Two-temperature model
Numerical simulation
Abaqus
a b s t r a c t
The objective of this work is to help understanding the impacts of short laser pulses on materials of
interest for photovoltaic applications, namely aluminum and silver. One of the traditional advantages of
using shorter laser pulses has been the attempt to reduce the characteristic heat affected zone generated
in the interaction process, however the complex physical problem involved limitates the integration of
simplified physical models in standard tools for numerical simulation. Here the interaction between short
laser pulses and matter is modeled in the commercial finite-element software Abaqus. To describe ps and
fs laser pulses properly, the two-temperature model (TTM) is applied considering electrons and lattice as
different thermal transport subsystems. The Material has been modeled as two equally sized and meshed
but geometrically independent parts, representing each the electron and the lattice domain. That means,
both domains match in number and position of the respective elements as well as in their shape and
their size. The laser pulse only affects the electron domain so that the lattice domain remains at ambient
temperature. The thermal connection is only given by the electron-phonon coupling, depending on the
temperature difference between both domains. It will be shown, that melting and heat affected zones
getting smaller with decreasing pulse durations.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
With their rapid development over the last decades, ultra-fast
lasers with pulse durations in the range between a few ps and
∼100 fs gained more and more importance in a number of appli-
cations such as material processing. Laser processing is often the
method of choice as its contactless nature allows precision and
processing speeds, which can hardly be reached by mechanical
means. In material microprocessing for example, ultra-short laser
pulses are being employed and as it was shown [1], using ps-
or fs-pulses leads to much better results for the quality of drill
holes, instead of using ns-pulses. Processing transparent mate-
rials also becomes available with IR and UV laser [2], as well
as highintensity ultra-short laser pulse systems are deployed for
microstructuring thin-films, for example in photovoltaic technolo-
gies [3]. When talking about ultra-short laser pulses and their
interaction with metals one has to consider that the occurring
physical processes differ from standard heat transfer models. In
this work we will demonstrate the successful implementation of
the two-temperature model [4] into the commercial finite-element
software Abaqus.
∗
Corresponding author.
2. Light absorption in metals
The dynamics in metals after the optical excitation by high
intensity laser radiation can be described by the TTM which
considers metals as two separate thermal transport subsystems
representing each electrons and the lattice connected only by
electron-phonon coupling. Incident light waves interact with
unbound delocalized electrons at the metal surface. Due to
their small heat capacity compared to the lattice heat capacity
(c
el
/c
la
≈ 10
-2
at T = 300 K) the excited electrons rapidly heat up set-
ting the system into a state of a thermal non-equilibrium. Mainly
by electron-electron scattering these high temperature electrons
return to a thermal equilibrium within the thermalization time.
The energy transfer between electrons and the lattice occurs via
electron-phonon coupling.
According to Anisimov the energy exchange in metals can be
described as a coupled system of two differential equations giving
the temporal evolution of the energy density of both the electrons
and lattice:
C
el
∂T
el
∂t
= -∇ (
el
∇T
el
) - G (T
el
- T
la
) + S (x, z, t ) (1)
C
la
∂T
la
∂t
= -∇ (
la
∇T
la
) + G (T
el
- T
la
) (2)
The term ∇ (∇T ) describes the energy dissipation within
the electron and the lattice domain respectively. However the
0169-4332/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.apsusc.2011.09.014