Available online at www.sciencedirect.com
Surface Science 602 (2008) 156–161
www.elsevier.com/locate/susc
Sputtering of ice by low-energy ions
M. Famá *, J. Shi, R.A. Baragiola
Laboratory for Atomic and Surface Physics, University of Virginia, Charlottesville, VA 22904, USA
Received 17 August 2007; accepted for publication 1 October 2007
Available online 5 October 2007
Abstract
We measured the total sputtering yield Y of amorphous water ice at 80 K for 0.35–4 keV He and Ar ions. We found that Y depends
linearly on the elastic stopping cross section at low energies as predicted by the standard linear cascade theory of sputtering. As the
energy increases, a quadratic dependence with the electronic stopping cross section arises due to cooperative effects between excitations
produced by the projectile. We also studied how sputtering depends on the projectile incidence angle and found that Y follows a cosf(h)
dependence with f = 1.45 ± 0.05 for 2 keV He+ and f = 1.78 ± 0.08 for 2 keV Ar+. Measurements of Y for 2 keV ions vs. ice temperature
between 30 and 140 K show the same temperature dependence as that reported previously for high-energy ions. We introduce a general
formula to calculate Y below 100 keV once the ice temperature, projectile type, energy and angle of incidence are known. This formula
can be used for modeling the production of extended neutral atmospheres around astrophysical icy bodies subject to ion bombardment.
2007 Elsevier B.V. All rights reserved.
Keywords: Ion bombardment; Stopping power; Sputtering; Water; Ice
1. Introduction
The erosion or sputtering of water ice by energetic particles is an important process in the outer solar system,
where icy bodies are constantly exposed to magnetospheric
ions, the solar wind and cosmic rays. Sputtering, together
with sublimation, is responsible for the production of tenuous, extended neutral atmospheres of water molecules
ejected from icy satellites and ice grains embedded in planetary magnetospheres [1,2]. Such atmospheres have been
detected around icy satellites of Jupiter [3] and Saturn [4].
Modeling the production of tenuous atmospheres requires
accurate laboratory data for sputtering yields of ice at ion
energies and ice temperatures relevant to those astrophysical environments.
The ejection of surface molecules by sputtering is characterized by the yield Y, or number of molecules ejected
per incident ion. Sputtering occurs by either direct momen*
Corresponding author. Tel.: +1 434 9822335; fax: +1 434 9241353.
E-mail address: [email protected] (M. Famá).
0039-6028/$ - see front matter 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2007.10.002
tum transfer by the projectile to a target atom (elastic) or
due to long lived repulsive electronic excitations which lead
to atomic or molecular motion (electronic) [5,6]. While
elastic sputtering is well understood and described by the
standard linear cascade theory [7] (see review books [8,9])
electronic sputtering is still a subject of discussion due to
the lack of identification of the repulsive electronic states.
Electronic sputtering of ice was discovered three decades
ago by Brown et al. [10], who found that Y of water ice
bombarded by MeV protons was orders of magnitude
higher than predicted by the linear cascade theory, and
was proportional to the square of the electronic energy
deposition near the surface. Sputtering of water ice has
been extensively studied since this pioneering work, and
the extant literature is consistent with the total electronic
sputtering yield Y being proportional to S 2e [11], where
Se = dE/Ndx is the electronic stopping cross section, dE/
dx is the projectile energy loss per unit path length and N
is the target number density. The quadratic dependence
has been thought to signal that sputtering is dominated
by the interaction of pairs of excitations, such as the
M. Famá et al. / Surface Science 602 (2008) 156–161
screened Coulomb repulsion of ionized molecules. An
alternative of historical interest is the suggestion that the
quadratic behavior is caused by ‘‘thermal spikes’’ [12], temporary hot regions caused by the energy deposition of the
projectile, from which evaporation can transiently occur.
This has been disproved by detailed molecular dynamic
simulations which, instead, support the view that the sputtering yield is quadratic in the repulsive energy deposited
per unit path length near the surface [13]. Deviations from
the S 2e at low ion velocities have been attributed to different
projectile charge states and synergism between electronic
and elastic collision processes, among others [11]. Recently,
we proposed that the electronic sputtering yield at low
velocities is indeed dominated by (screened) Coulomb
repulsion, but enhanced by the additional ionization produced close to the surface by electron capture by the projectile ion [14].
In contrast with the numerous studies of electronic sputtering of ice (a guide to the literature can be found in Ref.
[11]), elastic sputtering by very low-energy ions (from hundreds eVs to few keVs) has been barely studied, in spite of
its importance to understand the interaction of solar wind
ions and cold plasmas with comets, icy ring particles and
satellites. Bar-Nun et al. [15] performed experiments using
0.5–6 keV Hþ
2 and neon ions and a quadrupole mass spectrometer to measure the flux of the ejected species during
bombardment. This method, based on the measurement
of the partial pressure of water in vacuum conditions and
the relation of the vapor pressure of ice vs. temperature,
may not be reliable in terms of absolute values for the sputtering yield. They found that the sputtering yield of water
molecules ejected intact does not depend on the ice temperature between 30 and 140 K. They indicate that the main
contribution to the total sputtering yield is due to radiolytic
production of O2 and H2. However, the molecular oxygen
synthesized in ice by ion bombardment contributes less
than 10% to the total yield for temperatures below 100 K
[16,17]. Christiansen et al. [18] measured the sputtering
yield of H2O, CO2 and N2O at 78 K under 2–6 keV Ar+,
Ne+, N+ and He+ bombardment at 45 incident angle from
the total ion fluence needed to remove a film of known
thickness. They found that the linear cascade theory agrees
with the experimental results only for ice water. On the
other hand, Haring et al. [19] found that water molecules
sputtered from ice by 6 keV ions have energies much lower
than predicted by the linear cascade theory, although still
much higher than thermal. They explained this difference
as resulting from a lower (by a factor of 2–3) ‘effective’ surface-binding energy. However, this was not reconciled with
the fact that yields agree with theory using normal binding
energies.
Here we present an experimental study of the total
sputtering yield of water ice at 80 K by low-energy ions
(0.35–4 keV) of significantly different masses, He and Ar.
The yields are obtained from the change in mass of the
ice films during irradiation with a known fluence. Together with previous published data at higher energies,
157
our results show the transition from elastic to electronic
sputtering of water ice for both ions. We also measured
the angular and temperature dependences of the sputtering yield. We used these results to introduce a simplified
model containing the main physical features of the process, which reproduces the available experimental data
from several laboratories with surprising accuracy. We
give an empirical formula that can be used to model the
production of sputtered tenuous H2O atmospheres around
icy bodies embedded in magnetospheres of the outer solar
system.
2. Experimental
The measurements were done in an ultra-high vacuum
chamber (base pressure 3 · 1010 Torr), equipped with
a 6 MHz gold-coated quartz-crystal microbalance (QCM)
with a sensitivity of 0.05 ML [20] (1 ML corresponds to
a single, closely packed layer of molecules 1 · 1015 molecules/cm2). The microbalance is mounted at the tip of a
LHe-cooled rotary manipulator. The water films were vapor deposited onto the microbalance at 80 K with a deposition rate of 0.4 ML/s by dosing pure H2O gas through a
microcapillary array and at normal incidence. The mass
per unit area of the condensed films was determined by
measuring the shift in the resonance frequency of the
quartz-crystal during deposition. Within these conditions,
films densities are likely >0.9 g/cm3, implying an upper limit for porosity of 4% [21]. Electrostatic charging effects
may be present on insulators under particle bombardment;
in particular, water ice can be charged up to several hundreds volts before dielectric breakdown occurs, depending
on film thickness and projectile range [22]. For this reason,
we used two different film thicknesses (100 and 3000 ML)
for Ar+ to test the influence of charging effects upon the
total sputtering yield. The ion beam is produced with a differentially-pumped electron impact ionization gun (Nonsequitur 1401) and scanned uniformly over the area of the
quartz-crystal. The films were irradiated at fluxes between
1011 and 1012 ions cm2 s1. The total sputtering yield is
obtained converting the mass loss given by the microbalance to number of water molecules and dividing it by the
number of incident particles. The sputtering yield measured
by the crystal microbalance Ym was corrected for the mass
due to implanted projectiles using the equation: Y = Ym +
n1m1/m2; where m1 and m2 are the masses of the projectile
and a water molecule and n1 the projectile trapping probability. For large fluences, trapping may be neglected
(n1 = 0) and the total sputtering yield is given directly by
the frequency change of the crystal. For small fluences we
assume that all projectiles are retained (n1 = 1), since reflection coefficients are very low; thus Y = Ym + m1/m2. We
did not measure n1; therefore we use an average value for
n1 = 1/2, which means that the error bars in the figures include both the experimental uncertainties and the small
constant term 1/2m1/m2. The sputtering yields were insensitive to ion beam current.
158
M. Famá et al. / Surface Science 602 (2008) 156–161
3. Results and discussion
3.5
3.1. Temperature dependence
3.0
3.2. Angular dependence
Fig. 2 shows measurements of the normalized sputtering
yield of ice at 80 K irradiated by 2 keV He+ and 2 keV Ar+,
as a function of the projectile incidence angle h. The results
were fitted to a cosf(h) dependence with f = 1.45 ± 0.05
for He+ and f = 1.78 ± 0.08 for Ar+. There is only one previous experimental report of the angular dependence of the
sputtering yield of water ice, and it corresponds to the electronic regime (100 keV protons) [24]. There, the authors
2.6
+
2.4
Ar (2 keV)
+
He (2 keV)
+
Ar (30 keV)
+
He (30 keV)
Normalized Sputtering Yield
2.2
2.0
1.8
1.6
He
Ar
Y(θ) / Y(θ = 0)
Fig. 1 shows the normalized total sputtering yield of ice
for He+ and Ar+ vs. ice temperature between 30 and 140 K.
Data from the compilation of Baragiola et al. [11] at
30 keV (mostly electronic processes) and from the present
measurements at 2 keV (elastic collisions) indicate that
the sputtering yield has a universal behavior as a function
of the ice temperature, irrespective of the excitation mechanism. The data was fitted with the expression Y =Y 0 ¼ 1þ
Y 1 =Y 0 eEa =kT , where k is Boltzmann’s constant, Y1/Y0 =
220 and Ea = 0.06 eV. These values are similar to those
found in Ref. [11]. The temperature dependence is thought
to originate in the formation and consequent behavior of
radicals and molecular products (H2, O2) during irradiation [16,17,23], but a detailed description is lacking.
2.5
2.0
1.5
1.0
0
10
20
30
40
50
60
Angle (deg)
Fig. 2. Normalized sputtering yield as a function of the incidence angle of
2 keV He+ and Ar+ ions. The lines are fits to Y(h)/Y(0) = cosf(h) with
f = 1.45 for He+ and 1.78 for Ar+.
state that Y(h) also follows a cosf(h) distribution with
f = 1.29 ± 0.02 (1.32 ± 0.05) at 20 (100) K. Another study
of electronic sputtering, but for solid oxygen irradiated
with 2 MeV He+, reports f 1.6 [25].
The factor f > 1 is caused by the near-surface variation in
the energy density along the incident direction [24,26]. For
electronic sputtering this is in part due to the forward directedness of the fast secondary electrons produced by the projectile, that relocate the electronic energy deposited near
the surface into the bulk of the ice and to the near-surface
variation in the Se due to changes in the incident ions charge
state. The effect of the secondary electrons should disappear
at low projectile velocities, since most of the secondary electrons cannot produce further ionizations. For elastic collisions, the standard linear cascade theory also predicts a
cosf(h) dependence for the sputtering yield, where f depends
on the spatial shape of the distribution of deposited energy
and is nearly independent of the projectile energy. Results
of f for metals irradiated by noble-gas ions at low energies
were found to be between 1 and 2 [27] but they may not
be strictly comparable since water ice is a molecular solid
with strong internal bonds and weak intermolecular bonds.
1.4
3.3. Energy dependence
1.2
Figs. 3 and 4 show measurements of the total sputtering
yields of ice at 80 K irradiated by 0.35–4 keV He+ and Ar+,
together with previous results of Christiansen et al. at 78 K
[18] at 45 incidence (the data were multiplied by
cos(45)1.78, see Section 3.2), Baragiola et al. at 60 K [11]
(as shown before, in the Section 3.1, the total sputtering
yield of ice is nearly constant for temperatures <100 K),
Brown et al. at 60 K [28] and Rocard et al. at 60 K [29].
For Ar+ we used two very different ice film thicknesses
(100 and 3000 ML) to test any dependence with Y, but
for both cases the sputtering yields follow the same projectile energy dependence, within errors.
1.0
0.8
0
20
40
60
80
100
120
140
160
Ice Temperature (K)
Fig. 1. Normalized sputtering yield of ice for He+ and Ar+ at normal
incidence versus temperature. This work: d and m 2 keV Ar+ and He+,
respectively. Baragiola et al. [11]: s and n, 30 keV Ar+ and He+,
respectively. The solid line is a fit to the expression
Y =Y 0 ¼ 1 þ ðY 1 =Y 0 ÞeEa =kT , with Y1/Y0 = 220 and Ea = 0.06 eV.
M. Famá et al. / Surface Science 602 (2008) 156–161
Sputtering Yield (molecules/ion)
Y ¼ KF D ðE; h; xÞ
He
10
1
Y ¼
1
10
100
Energy (keV)
Fig. 3. Sputtering yield of ice versus He+ energy. This work: d (150 ML)
at 80 K. Christiansen et al. [18]: h at 78 K (the data were multiplied by
cos(45)1.45, see text). Baragiola et al. [11]: s at 60 K. Brown et al. [28]: n
at 60 K. Rocard et al. [29]: , at 60 K. The dotted line is proportional to
the elastic stopping cross section, whereas the dash-dotted line is
proportional to the square of the electronic stopping cross section. The
solid line represents the sum for both contributions (see text in Section 4).
100
+
Sputtering Yield (molecules/ion)
Ar
10
0.1
ð1Þ
where E is the projectile energy, h is the angle of incidence
of the projectile to the surface, FD(E, h, x) is the distribution
of deposited energy over depth x, and K depends only on
target parameters such as the surface-binding energy U0
and the molecular density N. A necessary condition for
the yield to be proportional to the deposited energy at
the surface is that E U0. This condition is satisfied in
our case since U0 = 0.45 eV for water and E was at least
350 eV. For sputtering at perpendicular incidence Eq. (1)
may be simplified into,
+
0.1
159
1
10
100
Energy (keV)
Fig. 4. Sputtering yield of ice versus Ar+ energy. This work: d (3000 ML)
and m (100 ML) at 80 K. Christiansen et al. [18]: h at 78 K (the data were
multiplied by cos(45)1.78, see text). Baragiola et al. [11]: s 60 K. The
dotted line is proportional to the elastic stopping cross section, whereas
the dash-dotted line is proportional to the square of the electronic
stopping cross section. The solid line represents the sum for both
contributions (see text in Section 4).
4. Model
3 aS n
4p2 C 0 U 0
ð2Þ
where Sn is the nuclear-stopping cross section, a is an energy-independent function of the ratio between the mass of
the target m2 and of the projectile m1 [30], and C0 is the constant of the differential cross section dr for elastic scattering
in the binary collision approximation, i.e., dr = C0dT/T,
with T the energy of the recoil [7]. Since the molecular dissociation energy of water is much larger than U0, we take m2 to
be the mass of H2O. To evaluate Sn, we followed the formalism from Ref. [31] using the ZBL ‘‘Universal Potential’’ (see
Appendix for a full description). For the particular case of
water as a target, we evaluate Sn for a compound constituted
of 2/3 atomic hydrogen and 1/3 atomic oxygen. An alternative, used by Chrisey et al. [32], is to multiply Eq. (2) by a factor of 1/3 converting the molecular Sn into an averaged
atomic value. In Figs. 3 and 4 we plot the elastic component
of the sputtering yield according to Eq. (2) where we used
a = 0.54 for He and a = 0.26 for Ar from Ref. [30], and
C0 = 1.3 Å2. Clearly, at very low energies, the sputtering
yield of water ice can be explained by the elastic collision theory for sputtering, but as the energy increases the electronic
processes become dominant.
The application of Sn in Eq. (2) is not necessarily straightforward since the molecular solids contain internal chemical
structure which can absorb some of the elastic energy transferred to the molecule into internal inelastic energy rather
than transforming it into collision cascades. For instance,
the internal O–H binding in water can absorb up to
5.12 eV before dissociation, an order of magnitude larger
than U0. However, results from a classical dynamical simulation of the bombardment of ice by 23, 59 and 115 eV O+
[33], can be fitted with Eq. (2) using values for Sn following
Eqs. (A.1)–(A.3) in the Appendix and a = 0.32 in agreement
the value adequate for monoatomic solids [30]. We should
also mention that for the fitting we do not consider the effect
of reflected projectiles (they contribute only partially to the
Sn) since an estimation using the TRIM code [31] gives us
5% for 0.35 keV He+ and <0.1% for 0.35 keV Ar+.
4.1. Elastic sputtering
4.2. Electronic sputtering
According to the standard linear collision cascade theory [7], the elastic sputtering yield for atomic targets can
be expressed as,
We also included in Figs. 3 and 4 curves proportional
to S 2e to fit the experimental data at higher energies.
Experimental Sputtering Yield (molecules/ion)
160
M. Famá et al. / Surface Science 602 (2008) 156–161
100
B B
B
AB
BBAB
A
B
A AA
A
B
C
CC
C B
CC
B
CD
BCCC C
ECC
10
D
C
A
CB C
CAC C
D
CC D
D E
CC D
C
C
C
C
CC
CC
CC
C
C
C
C
C
1
D
1
10
100
Calculated Sputtering Yield (molecules/ion)
Fig. 5. Experimental vs. calculated sputtering yield of ice. (A) Christiansen et al. [18]: Z1 = 2, 7, 10, and 18, E = 2–6 keV, T = 78 K, h = 45; (B)
Baragiola et al. [11]: Z1 = 2, 8, and 18, E = 10–50 keV, T = 60 K, h = 0;
(C) present measurements: Z1 = 2 and 18, E = 0.35–4 keV, T = 30–140 K,
h = 0–60; (D) Brown et al. [28]: Z1 = 1 and 2, E = 5–50 keV, T = 60 K,
h = 0; (E) Rocard et al. [29]: Z1 = 2, E = 15–25 keV, T = 60 K, h = 0.
Experimental results for Se of He+ and Ar+ in water at low
energies do not exist. Therefore, to evaluate Se, we used the
effective-charge theory by Yarlagadda et al. [34] for Se(Z1)
as a function of the projectile atomic number Z1, normalized to extrapolated experimental Se values for protons in
ice [35], and assumed a linear dependence of Se with projectile velocity at low energies (see the Appendix for a full
description).
Within the precision of our measurements and those in
previously published reports we could fit a complete analytical expression for the total sputtering yield of water
ice valid for temperatures up to 140 K and projectile energies below the maximum in Se, and incidence angle h (see
Appendix for a full description),
1
3
2
Y H2 O ðE; m1 ; Z 1 ; h; T Þ ¼
aS n þ gS e
U 0 4p2 C 0
Y 1 Ea =kT
1þ e
ð3Þ
cosf ðhÞ
Y0
where g is an oscillatory function of the atomic number of
the projectile (see Appendix) needed because the effectivecharge theory of stopping [34] does not include the known
shell effects that produce Z1 oscillations. In Fig. 5. we compare the validity of Eq. (3) with more than seventy experimental data points from several authors, including different
temperatures, incidence angles, energies and projectile type
(Z1 = 1, 2, 7, 8, 10, and 18), finding an excellent match.
5. Conclusions
We have measured the sputtering yield of water ice for
low-energy He+ and Ar+ as a function of the projectile en-
ergy, temperature and angle of incidence. Our results show
a clear transition from elastic to electronic sputtering regimes for both projectiles. At very low energies the sputtering yield is proportional to the Sn in agreement with the
standard linear cascade theory. As the energy increases,
and electronic processes become important, the sputtering
yield can be fitted to a S 2e dependence. We observe a temperature dependence of the sputtering yield that is the same
for elastic and electronic processes, likely attributed to
thermally activated processes leading to O2 and H2 production. Finally, we introduced a generalized formula to calculate the total sputtering yield of water ice relevant for the
astrophysical icy bodies in the outer solar system. This formula is valid for ice temperatures up to 140 K, ion energies
from few hundreds of eV up to energies below the maximum in Se, and it has only been tested with H+, He+,
N+, O+, Ne+, and Ar+ projectiles.
Acknowledgements
We thank R.E. Johnson for useful discussions. This
material is based upon work supported by the National
Science Foundation under Grant No. 0506565.
Appendix. Elastic stopping
In units of eV/ (1015 atoms/cm2) the nuclear-stopping
cross section Sn can be expressed [31],
Sn ¼
8:462Z 1 Z 2 m1 S red ðeÞ
ðm1 þ m2 ÞðZ 0:23
þ Z 0:23
1
2 Þ
ðA:1Þ
where Z1 and Z2 are the atomic numbers of the projectile
and the target atoms and e is the reduced energy expressed
in terms of the projectile energy E (keV units) as,
e¼
32:53m2 E
Z 1 Z 2 ðm1 þ m2 ÞðZ 0:23
þ Z 0:23
1
2 Þ
ðA:2Þ
The reduced nuclear-stopping Sred(e), valid for e < 30, is
fitted to an analytical expression, as shown in Ref. [31]:
S red ðeÞ ¼
lnð1 þ 1:1383eÞ
2ðe þ 0:01321e0:21226 þ 0:19593e0:5 Þ
ðA:3Þ
Function a
a can be interpolated from experimental sputtering
yields from Ref. [30] and fitted by a double exponential
function. Particularly for water (m2 = 18) we found,
a ¼ 0:25574 þ 1:25338 expð0:86971m1 Þ þ 0:3793
expð0:10508m1 Þ
ðA:4Þ
M. Famá et al. / Surface Science 602 (2008) 156–161
Electronic stopping
For projectile energies up to 50 keV/amu, we found the
electronic stopping cross section expressed in units of eV/
(1015 atoms/cm2) to be,
!2
2=3
1=2
0:2ðE=m1 Þ1=2 Z 1
2125ðE=m1 Þ
2 1e
Z1
Se ¼
ðA:5Þ
1=2
1 e0:2ðE=m1 Þ
ðE=m1 Þ3=2 þ 1500
Factor g
The variable g in Eq. (3) gives the proportionality between electronic sputtering and S 2e =U 0 . The following
empirical fit includes a sin2 term to take into account oscillations in Se with Z1 since they are not included in the effective-charge theory [34],
g ¼ 0:0002223 þ 0:0013326 sin2
ð2:72923ðZ 1 1Þ
0:31812
Þ eV1 Å
4
ðA:6Þ
Angular dependence – exponent f
The exponent f in the angular dependence term has been
approximated by fitting the few existing experimental data
as
ln m1
f ¼ 1:3 1 þ
ðA:7Þ
10
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