Molecular-dynamics simulations of electronic sputtering
E. M. Bringa and R. E. Johnson
Engineering Physics, University of Virginia, Charlottesville, Virginia 22903
M. Jakas
Engineering Physics, University of Virginia, Charlottesville, Virginia 22903
and Departamento de Fı ´sica Fundamental y Experimental, Universidad de La Laguna, 38201 La Laguna Tenerife, Spain
Received 11 May 1999
Following electronic or collisional excitation of a solid by a fast ion, an energized cylindrical region is
produced which can lead to sputtering. Here ejection from such a region is studied via molecular-dynamics
simulations using Lennard-Jones and Morse potentials. Over the full range of excitations studied the yield vs
the energy release per unit path length in the solid, which we call dE / dx , is shown to scale with the binding
energy and with the density of the material for all materials studied and at all dE / dx . This allows the
simulation results to be applied to low-temperature, condensed-gas solids and to more refractory solids over a
broad range of dE / dx . The effect of a distribution of energies for the initial energizing events, and the effect
of a spatial distribution of such events for a given dE / dx are examined. Three regimes have been identified.
When the energy release per excitation event is greater than the escape energy, sputtering is linear in dE / dx at
low dE / dx . With increasing dE / dx a spikelike regime occurs in which the yield again becomes nonlinear with
dE / dx . For fixed cylindrical radius ejection then saturates so that at very high dE / dx the yield again becomes
nearly linear with dE / dx . In this regime the size of the yield increases with the initial radial extent of the track
and is determined by the removal of energy radially by the pressure pulse and by the transport of energy from
depth to the surface. Therefore, the clear nonlinearities observed in the knock-on sputtering yields by heavy
ions require consideration of the radial extent of the cascades. For electronic sputtering yields of condensed-gas
solids, the observed nonlinearity in the sputtering yield suggests that the radial extent of the excited region
varies in a manner different from that predicted or that the energy release to the lattice is nonlinear in the
stopping power. S0163-18299902146-3
I. INTRODUCTION
In two recent papers
1,2
hereafter I and II molecular-
dynamics MD simulations of a cylindrically energized re-
gion were carried out in order to describe the transport of
energy from a track of excitations produced by a fast ion and
to test ‘‘thermal’’ spike models for sputtering. Although
spike models have been used for over 50 years to describe
the nonlinear aspects of sputtering,
3,4
ion-beam induced
mixing,
5,6
and track formation
7,6
by fast ions, there have
been relatively few tests using atomistic simulations. One of
our goals is to understand the applicability of spike models
to laboratory results on the electronic sputtering of low-
temperature condensed-gas solids.
8–10
Such experiments pro-
vide one of the few means of determining the nonradiative
electronic relaxation pathways in molecular insulators.
8,9,11
The electronic sputtering of low-temperature ice is also of
interest as it produces atmospheres on the moons of Jupiter.
12
Laboratory studies of fast ions incident on low-
temperature condensed-gas solids show that the yields for
the molecular solids all exhibit a roughly quadratic depen-
dence on dE / dx at high dE / dx . Here dE / dx is the energy
deposited per unit path length by a fast ion and is also called
the stopping power.
13
Spike models, in which the energy
transport is diffusive, also give yields quadratic in dE / dx for
the cylindrical geometry appropriate to fast ions. In such
models, of course, dE / dx is the kinetic energy per unit path
length of the moving atoms or molecules in the spike. As-
suming this value of dE / dx is proportional to the stopping
power, the laboratory observations have been parametrized
using spike models.
14
This parametrization allows one to
beautifully scale data for different targets over a broad range
of dE / dx .
14
However, we found to our surprise that the yield
calculated using MD simulations for initial conditions asso-
ciated with a spike is not quadratic in dE / dx for those values
of dE / dx appropriate to the nonlinear electronic sputtering
regime.
15,2
Quite remarkably, the sputtering yields calculated
using MD for fixed track radius are nearly linear in dE / dx at
high dE / dx even though the transport processes are clearly
nonlinear. That is, above some ‘‘threshold’’ value of dE / dx
saturation sets in unlike in the analytic spike models. We
showed that the difference in the dependence of the yield on
dE / dx obtained in the MD simulations from that dependence
obtained using a spike model is not due to a lack of thermal
equilibration locally in the rapidly evolving spike, and we
showed earlier that local equilibration was not required in
order to obtain the quadratic dependence of the yield.
14
In
addition, Jakas
16
showed that the quadratic dependence in
spike models in which the energy transport is diffusive is
robust since it persists even when realistic thermal properties
which allow melting are used rather than the analytic model
properties typically used.
The difference between our MD simulations and the
spike models is due to two factors. First, the energy trans-
ported away from the excited cylindrical region at high
dE / dx cannot be described diffusively but is more closely
PHYSICAL REVIEW B 1 DECEMBER 1999-II VOLUME 60, NUMBER 22
PRB 60 0163-1829/99/6022/1510710/$15.00 15 107 ©1999 The American Physical Society