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Ultramicroscopy 110 (2010) 991–997
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Ultramicroscopy
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Basic questions related to electron-induced sputtering in the TEM
R.F. Egerton a,b,n, R. McLeod a,b, F. Wang b, M. Malac a,b
a
b
Department of Physics, University of Alberta, Edmonton, Canada T6G 2G7
National Institute for Nanotechnology, Edmonton, Alberta, Canada T6G 2M9
a r t i c l e in fo
Keywords:
TEM
Radiation damage
Sputtering
Knock-on displacement
abstract
Although the theory of high-angle elastic scattering of fast electrons is well developed, accurate
calculation of the incident-energy threshold and cross section for surface-atom sputtering is hampered
by uncertainties in the value of the surface-displacement energy Ed and its angular dependence. We
show that reasonable agreement with experiment is achieved by assuming a non-spherical escape
potential with Ed = (5/3) Esub, where Esub is the sublimation energy. Since field-emission sources and
aberration-corrected TEM lenses have become more widespread, sputtering has begun to impose a
practical limit to the spatial resolution of microanalysis for some specimens. Sputtering can be delayed
by coating the specimen with a thin layer of carbon, or prevented by reducing the incident energy;
60 keV should be sufficiently low for most materials.
& 2009 Elsevier B.V. All rights reserved.
1. Introduction
As problems associated with electron optics and stability are
overcome, radiation damage becomes the main physical limit to
imaging and spectroscopy in a transmission electron microscope.
This situation has long been appreciated for biological and organic
specimens, where the damage arises from relatively efficient
radiolysis mechanisms, triggered by the inelastic scattering of
electrons [1,2]. Radiolysis occurs also in inorganic specimens such
as halides and oxides but in the case of conducting materials
(metals, semiconductors) it is suppressed due to the high density
of delocalised electrons, leaving knock-on displacement (subsequent to elastic scattering; see Fig. 1) as the only damage
mechanism.
The situation is summarised in Table 1. In electron microscopy,
the radiation resistance of a sample is commonly represented by a
characteristic exposure or dose De required to reduce the
specimen thickness, EELS fine-structure or diffraction-spot
intensity by a factor of e= 2.718. In reality, these different types
of damage (representing mass loss, short-range and long-range
order, respectively) correspond to different De so the values in
Table 1 are only order-of-magnitude estimates.
A direct (rather than inverse) measure of radiation sensitivity
is the damage cross section sd = q/De where q is the electronic
charge (with De in Coulombs per unit area). These cross
sections are also given in Table 1, together with values of the
n
Corresponding author. University of Alberta, Department of Physics, Edmonton, Canada T6G 2G7
E-mail address: regerton@ualberta.ca (R.F. Egerton).
0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.ultramic.2009.11.003
K-shell ionization cross section sK of light elements for comparison. The situation sd 4 sK indicates that radiation damage
prevents detection of a single atom by K-shell EELS. If sd o sK,
single-atom detection is possible in principle but in practice
depends on many factors, including instrumental drift and
specimen thickness.
As seen in Table 1, knock-on displacement processes have
cross sections considerably below those for radiolysis, so although
displacement effects do occur in insulating and organic
specimens, they can usually be neglected. The low cross sections
also imply that radiation damage in conductors and semiconductors is relatively slow and in some circumstances negligible. But
with high-brightness electron sources and aberration correctors,
very large current density ( 4106 A/cm2) is possible within a
probe of small diameter ( o1 nm). Therefore displacement
damage is increasingly observed, especially in spectroscopy
applications using a probe that is stationary or scanned over a
limited area.
All knock-on processes depend on some energy transfer Ed that
is required for atomic displacement. Ed is generally above 10 eV
for atoms in a bulk crystal, where a Frenkel (vacancy+interstitial)
pair must be created, whereas removal of an atom from the
surface (electron-induced sputtering) requires considerably less
energy. Elastic scattering can also stimulate radiation-enhanced
diffusion of atoms at the surface [31] or vacancy migration in the
bulk; both processes require energy of the order of 1 eV or less
and have relatively high cross sections. Note that the vacancydiffusion cross section is per vacancy rather than per atom; the
vacancy concentration is very low in a single crystal at room
temperature but can be much higher at a grain boundary or at the
surface. While all of these knock-on effects could be significant in
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for very light elements, whereas a high-voltage microscope is
required in the case of heavy elements. On the other hand,
electron-induced sputtering (needing only a few eV per atom) is
possible for many elements at usual TEM voltages (100–300 kV).
3. Sputtering threshold
If Emax exceeds an appropriate displacement energy Ed, largeangle scattering can permanently displace atoms from their
lattice sites or from the surface of a solid. The minimum
that allows such a process is found
incident-electron energy Emin
0
by solving Eq. (2) with Emax =Ed, giving
¼ ½ðm0 c2 Ed =2Þ2 þ ð1þ m0 =MÞ2 Mc2 Ed =21=2 m0 c2 þEd =2
Emin
0
ð3Þ
2
Fig. 1. (a) Elastic scattering of electrons from an atomic nucleus, shown
schematically (particle model) for a large-angle collision (A) and a 1801 collision
(B). (b) Sputtering of atoms from the beam-exit surface (C) and the beam-entrance
surface (D).
Table 1
mechanisms of radiation damage in a TEM, together with typical values of
characteristic dose De, cross section s per atom (in barn= cm2 10 24) and
displacement energy Ed.
Mechanism
Radiolysis
Radiolysis
K-ionization
Bulk displacement
Bulk diffusion
Surface sputtering
Surface diffusion
Specimen
Organic
Inorganic
Any
Conducting
Conducting
Conducting
Conducting
De(C/cm2)
0.002–1
0.2–106
103–104
s (barn)
5
Ed(eV)
8
10 –10
0.1–106
102–105
10–100
102–104
102–103
4103
10–50
0.5–1.5
1–10
o1
some specimens, we concentrate in this study on the sputtering of
atoms from the surface. In order to avoid radiolysis effects, we
performed measurements on thin films of electrically conducting
elements (metals or semimetals).
Since m0c = 511 keVbEd and M/m0 E1823 A b1, where A is
the atomic mass number (atomic weight), the threshold energy
can be rewritten with negligible error (o10 4 for A =12) as
Emin
¼ m0 c2 f½1 þ ðM=2m0 ÞðEd =m0 c2 Þ1=2 1g
0
¼ ð511 keVÞf½1 þ AEd =ð561 eVÞ1=2 1g
ð4Þ
The threshold therefore increases with increasing displacement energy and increasing atomic number (Table 2).
In the case of electron-induced sputtering, Ed has often been
taken as the sublimation energy Esub, although values between
Esub and 2Esub have been contemplated [4]. In fact, thermal
sublimation is known to require only the half-crystal energy per
atom [5,6], which is equal to the energy of a surface atom at a kink
site: K in Fig. 3. If we consider a simple model in which each atom
is represented by a cube, each kink-site atom is bonded to three
nearest neighbours, whereas the majority of atoms on a flat
surface (F in Fig. 3) are joined to five neighbours. Therefore we
might estimate the average surface-binding energy as Ed =(5/
3)Esub, rather than Esub. This change has a substantial effect on the
threshold energy, as illustrated in Table 2.
To find out which approximation works best, the electron
beam in a TEM can be focused on a thin film of an element whose
predicted thresholds lie on both sides of the microscope operating
voltage. By timing the appearance of a hole in the film, the
sputtering rate R can be estimated and a sputtering cross section
2. Energy transfer in elastic scattering
Although elastic scattering (electrostatic deflection of electrons by atomic nuclei) is usually thought of as causing negligible
energy transfer, this is true only for small scattering angles y, such
as those involved in imaging or electron diffraction in the TEM. In
general, the energy E lost by an incident electron (rest mass m0)
and transferred to an atomic nucleus (mass M) is
E ¼ Emax sin2 ðy=2Þ ¼ Emax ð1 cos yÞ=2
ð1Þ
Emax is the maximum energy transfer, corresponding to
y = 1801, and exact relativistic kinematics gives [3]
Emax ¼ E0 ðE0 þ 2m0 c2 Þ=½E0 þ ð1 þ m0 =MÞ2 Mc2 =2Þ 2E0 ðE0 þ2m0 c2 Þ=ðMc2 Þ
ð2Þ
Clearly, Emax increases with increasing incident-electron
energy E0 but decreases as the nuclear mass M (i.e. atomic weight
or atomic number) increases. Fig. 2 gives values of Emax computed
using Eq. (2) and demonstrates that an energy transfer sufficient
to cause bulk displacement (10–50 eV) can occur at E0 =100 keV
Fig. 2. Maximum energy Emax transferred by 1801 elastic scattering in various
elements, as a function of the incident-electron kinetic energy E0.
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sd deduced by applying the formula
R ¼ ðJ=eÞsd ½uA=r1=3 ¼ ðJ=eÞsd monolayers=s
ð5Þ
where u is the atomic mass unit, r the density of the material and
J the current density at the centre of the probe. Our results, shown
Fig. 3. Simplified model of a crystal surface in which each atom is represented by
a cube. F represents an atom within the surface of a flat region of crystal, K is an
atom located at a kink site and S is an atom attached to an atomic-height step.
993
in Table 3, indicate that Ed = (5/3)Esub is the better approximation
for these metallic-bonded materials. The situation could be
different for covalent bonding, where the surface energy varies
significantly with orientation [7]. If Esub =8 eV for carbon, the
Ed = (5/3)Esub criterion predicts a threshold of 68 keV, whereas an
observed value of 86 keV has been reported for a carbon nanotube
[8].
Closely related to cross section is the sputtering yield: the
number of surface atoms sputtered per incident electron, given by
Y= sdNs where Ns is the number of surface atoms per unit area.
Since Ns is of the order of 1015 cm 2, a sputtering cross section of
100 barn (10 22 cm2) implies a sputtering yield of the order of
10 7.
The case of gold is illustrated further in Fig. 4, which includes
cross sections measured by Cherns et al. [9] from the time for hole
formation in (1 1 1) gold films. Again, assuming Ed = (5/3)Esub
rather than Ed = Esub gives a better fit to the dependence of cross
section on the incident-electron energy.
During observation in the TEM, the specimen surface is
sometimes observed to become rough on a near-atomic scale
[10]. Therefore the removal energy might start at (5/3)Esub and fall
towards Esub during further sputtering. However, if surface
diffusion is rapid compared to sputtering, it could act to maintain
a smooth surface with Ed E(5/3)Esub. Surface diffusion of silver
has been observed during hole-drilling in the TEM [11].
There is also evidence for preferential electron-beam etching
of grain boundaries [12], where atomic binding energies are
Table 2
Sputtering threshold energies evaluated for displacement energies of Esub and (5/3)Esub, using sublimation energies tabulated from various sources [15].
Element symbol
Atomic wt. A
Esub(eV)
Emin
0 (keV) for Ed = Esub
Emin
0 (keV) for Ed =(5/3)Esub
Li
C
Al
Si
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ge
Sr
Zr
Nb
Mo
Ag
Ta
W
Pt
Au
6.94
12.0
27.0
28.1
47.9
50.9
52.0
54.9
55.9
58.9
58.7
63.6
65.4
72.6
87.6
91.2
92.9
95.9
107.9
180.9
183.9
195.1
197.0
1.66
8
3.42
4.63
4.86
5.31
4.10
2.93
4.29
4.47
4.52
3.49
1.35
3.86
1.72
6.26
7.50
6.83
2.95
8.12
8.92
5.85
3.80
5.2
42
40
56
97
111
89
68
100
109
109
93
39
115
65
215
254
242
129
461
501
379
270
8.7
68
65
91
154
175
142
109
158
171
172
147
63
181
104
328
385
366
202
673
728
560
407
The sublimation energy of carbon depends upon its structure and may be as high as 11 eV in diamond.
Table 3
Sputtering cross sections (in barn) measured for four metals, compared with Mott values calculated using a spherical escape potential with two values of displacement
energy.
Element
E0(keV)
Measured sd
Calculated sd for Ed = Esub
Calculated sd for Ed =(5/3)Esub
Nb
Mo
Ag
Au
300
300
200
300
1.07 0.4
o 0.13
o5
o 0.08
64
95
735
250
0
0
0
0
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Fig. 4. Measured sputtering cross sections for gold, compared with Mott cross
sections calculated (for spherical escape potential) using two values of Ed.
lower. Likewise, small particles with highly convex surface will
have a high density of kink and step sites (S in Fig. 3), so particles
below about 10 nm diameter might be predicted to undergo
sputtering at incident energies below the threshold for bulk
material. This might provide an explanation for the small but
measurable sputtering observed from silver nanoparticles
(6–14 nm diameter) when exposed to 200 keV electrons [13],
the bulk threshold being 202 keV for Ed =(5/3)Esub.
4. Calculation of sputtering cross sections
Since the screening effect of the atomic electrons is unimportant for the high-angle elastic scattering that gives rise to
sputtering, the scattering per unit angle is given approximately by
the Rutherford differential cross section
ðds=dyÞR ¼ FðZ 2 r0 2 Þ½2p sin y=ð1cos yÞ2 ¼ FðZ 2 r0 2 =4Þ½2p sin y=sin4 ðy=2Þ
ð6Þ
where F = (1 v2/c2)/(v4/c4) is a relativistic term (v= incidentelectron speed) and r0 = (4pe0) 1(e2/m0c2)= 2.81794 fm, the ‘‘classical radius’’ of an electron.
This simple expression can be integrated analytically over
scattering angle y or equivalently, by using Eq.(1), over energy
loss E between Emin and Emax, to provide an estimate of the
displacement cross section
FZ 2 r02 ½ðEmax =Emin Þ1
sd ¼ p
¼ ð2:494 10
29
2
Once again, (ds/dy) can be integrated analytically to give [15]
sd ¼ ½4pa20 Z 2 R2 =ðm20 c4 Þ½ð1b2 Þ=b4 fX þ 2pabX 1=2
2
½1þ 2pab þ ðb þ pabÞ ln ðXÞg
ð9Þ
2
m ÞFZ ½ðEmax =Emin Þ1
ð7Þ
where Emax is obtained from Eq. (2) and Emin can be taken as Ed in
the simplest case (spherical potential, see later).
As illustrated in Fig. 5, the displacement cross section increases
from zero at the threshold incident energy (E0 =Emin
0 ) up to a
maximum value and then slowly decreases. This maximum occurs
at about twice the threshold energy for a light element such as
carbon and at just over three times the threshold for a heavy
element like gold.
In principle, greater accuracy is represented by Mott cross
sections that include the effects of electron spin. For lighter
elements (Z o21), the differential Mott cross section can be
obtained to a good approximation by multiplying (ds/dy)R by a
factor r(y) given by [14]
2
Fig. 5. Mott cross section, McKinley–Feshbach approximation and Rutherford
cross section for (a) carbon and (b) gold, as a function of primary-electron energy.
The values used here for Ed are close to the sublimation energies, rather than (5/
3)Esub.
rðyÞ ¼ 1b sin2 ðy=2Þ þ pab sinðy=2Þ½1sinðy=2Þ
ð8Þ
where a0 = 53 pm (the Bohr radius), R =13.6 eV, a = Z/137, b =v/c
and X= Emax/Emin with Emin =Ed. As shown by the triangular data
points in Fig.5a, the resulting cross section is lower (by up to 20%)
than the Rutherford cross section but matches the exact Mott
cross section very well in the case of a light element such as
carbon.
For heavier elements, a Mott cross section must be evaluated
by summing a slowly convergent series of terms. Values are
tabulated by Oen [16] and Bradley [7] for most elements and for
certain values of Ed. As illustrated for gold in Fig. 5b, the Mott
cross section now exceeds the Rutherford value but not greatly, so
Eq. (7) can still be used to give a reasonable estimate. The
McKinley–Feschbach cross section lies considerably lower, so
Eq. (8) should not be used for heavy elements.
It is possible for the momentum transferred to a subsurface
atom to be transmitted to a surface atom. In the case of a
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995
crystalline material, this process leads to focused collision
sequences in which energy is channeled in particular directions.
Such effects are known to be important in determining the
sputtering yield from a target bombarded with ions [17] but
molecular-dynamics modeling of electron-induced sputtering
from crystalline (1 1 1) gold foils has shown that subsurface
collisions only start to increase the sputtering yield for incident
energies more than twice the threshold value [9]. It is therefore
reasonable to neglect the contribution of subsurface collisions for
most single-element specimens and TEM incident energies.
5. Geometry of the escape potential
Taking the minimum energy required for sputtering as the
surface-binding energy Ed implies that escape of a surface atom
depends only on the transferred energy E and not on the angle f
(relative to the incident beam) of the transferred momentum; see
Fig. 1. This assumption implies that neighbouring atoms elastically reflect any component of momentum that is parallel to the
surface, i.e. that a surface atom has a radially symmetric
(spherical) escape potential. If the potential were spherical
beyond 1801, atoms could also be sputtered from the beamentrance surface (process D in Fig. 1). A spherical potential seems
a reasonable approximation for an adatom on a flat surface, less so
for an atom embedded in that surface. However, it accounts fairly
well for data obtained by ion-beam sputtering [17].
An alternative assumption is that there is a planar potential
step at the surface, in which case only the momentum component
(2ME)1/2 cos f perpendicular to the surface, corresponding to an
energy E cos2f, is used to overcome the surface-potential barrier
(height Ed) and escape of an atom requires E cos2f 4Ed. Because
y = p–2f, Eq. (1) implies
E ¼ Emax cos2 f
ð10Þ
and therefore escape from a planar potential barrier will occur if
Emax cos4f 4Ed. Escape now involves a maximum value of f
given by cos fmax = (Ed/Emax)1/4, rather than the condition cos
fmax = (Ed/Emax)1/2 that would apply if the direction of the
momentum were unimportant. The minimum energy transfer
for sputtering is then
Emin ¼ Ed cos2 fmax ¼ ðEd Emax Þ1=2
ð11Þ
and the displacement cross section is given by Eq. (7) or Eq. (9)
with Emin =(EdEmax)1/2 rather than Emin =Ed.
dependent
A planar potential makes the threshold energy Emin
0
on the angle g between the electron beam and the surface normal.
From Eq. (11), the energy required to cross the potential barrier
(at emission angle f = g) is now Ed = Emax cos2g, requiring an
energy transfer of Emax = Ed/cos2g and the threshold incident
is given by Eq. (4) with Ed replaced by Ed/cos2g. In
energy Emin
0
the case of a spherical particle or nanotube, this directiondependent Ed implies a higher threshold at the edges (where the
angle g approaches 901) and a larger rate of thinning in the centre
(g = 0). A round particle should eventually develop an oblate
shape.
In principle, the response of a solid to a given momentum
transfer can be predicted by molecular-dynamics (MD) calculations, which can also deal with the fact that the interatomic
bonding itself may be directional (e.g. within a covalent crystal).
In practice, the results have to be treated with caution, since they
depend on adequate knowledge of the interatomic potentials. MD
calculations for a carbon nanotube [18] have given Ed =23 eV for
= 113 keV,
perpendicular incidence (g =0), corresponding to Emin
0
increasing to over 40 eV at the edges (g = 901). Damage does in fact
Fig. 6. Dependence of surface-removal energy Ed on the angle g between the ebeam and the surface-normal, as predicted by molecular dynamics calculations
[19], for two values of azimuthal direction d, and as predicted by a planar escape
potential (small dots) with Ed(0) = 12.4 eV and by a spherical escape potential with
Ed = 12.4 eV (dashed line).
Table 4
Cross sections (in barn) for sputtering by 300 keV electrons, measured from hole
formation in thin films of carbon and aluminum, compared with Mott cross
sections calculated for two values of surface-binding energy and two approximations for the escape potential.
Material
Escape potential
Ed =Esub
Ed = (5/3)Esub
Carbon
Spherical
Planar
Spherical
Planar
73
14
339
67
38
9
173
41
Aluminum
Experiment
127 6
787 29
occur for 100 keV electrons and has been reported to be absent for
E0 =80 keV [8].
The results of other MD calculations for a single-wall nanotube
[19] are shown in Fig. 6, for two values of the in-plane component
d of the emission angle. The increase in Ed with g is less dramatic
than implied by the planar-potential approximation, suggesting
that (for typical d) the situation lies between the spherical- and
planar-potential approximations, as also concluded by Cherns
et al. [30] for the case of gold foils.
The choice of escape-potential geometry also affects the
sputtering cross section, even for normal incidence (g = 0). Values
tabulated by Oen [16] and Bradley [7] all assume a spherical
potential. For the planar-potential case, we must use Eq.(9) or
Eq.(11) with a lower limit given by Eq.(11), rather than taking
Emin =Ed. Measurements of sputtering cross section, made by
timing the appearance of holes in thin films of carbon and
aluminum, are shown in Table 4. Although hardly conclusive,
these results favour a displacement energy Ed that is higher than
Esub and an escape potential that is to some degree non-spherical.
A completely spherical potential would imply that atoms are
sputtered equally from both surfaces of a uniform thin specimen.
For atoms at the beam-entrance surface, the momentum
component in the incident-beam direction would be elastically
reversed by atoms lying deeper within the foil (D in Fig. 1b). If this
process is absent, sputtering is expected only from the beam-exit
surface, in accordance with observations from stereo microscopy
[10] that surface pits form only on the exit surface of a gold foil.
In fact, surface pits on the beam-entrance surface would not
necessarily indicate sputtering from that surface. Medlin and
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Howitt [20] developed a model for the combined effect of
sputtering and radiation-enhanced diffusion of vacancies, assuming no lateral surface diffusion. When vacancy-enhanced displacement is faster than surface sputtering, their model predicts
the beam-exit surface to remain flat (even though sputtering is
occurring from that surface) because the material above becomes
less dense. When this lower-density region reaches the entrance
surface, a crater should form there, deepening with time. On the
basis of estimated displacement and sputtering cross sections,
Medlin and Howitt [20] expected this situation to apply to
aluminum.
Bullough [21] examined sputtering in aluminum films (thickness 50–250 nm) due to a finely focused (2 nm diameter) probe of
100 keV electrons, tilting the specimen after irradiation to obtain
depth information. This work showed that a surface pit forms
initially at the electron-exit surface but as its depth increases,
sputtered atoms collect on the side walls, so the pit eventually
seals at a point near the pit opening, leaving a subsurface void
that moves under the influence of the electron irradiation towards
the electron-entrance surface. Pit growth and void formation then
resume at the electron-exit surface and this process may be
repeated many times in a thick specimen. Arrival of the voids at
the electron-entrance surface results in a pit at that surface (even
though no sputtering is occurring there) and eventually leads to a
hole extending through the entire sample thickness.
This description illustrates a potential problem in measuring
sputtering cross sections in the TEM. Although vacancy diffusion
does not affect the sputtering rate, redeposition of atoms on the
side walls of the exit-surface pit reduces the thinning rate, leading
to an artificially low cross section. This effect can be made small
by using a beam diameter larger than the specimen thickness, in
other words by using very thin specimens and a TEM with a
thermionic (rather than field-emission) electron source to achieve
the necessary beam current and current density.
6. Alloys and compounds
To put the present discussion into context, we consider briefly
some of the more complicated effects that can occur when the
specimen contains two or more different species of atom. As
illustrated in Fig. 2, more energy can be transferred to a light
for a given
atom, implying a lower threshold incident energy Emin
0
binding energy Ed. On the other hand, the equations for sputtering
cross section sd contain the term Z2, so the sputtering rate tends
to be higher for a heavy atom. The relative cross sections can be
estimated from Eq. (7), using the atomic number Z of each
element involved but a binding energy Ed characteristic of the
whole solid, although such a procedure will clearly fail in the case
of multi-element compounds with atoms in different chemical
environments.
In general, one element will sputter faster, leading to a
depletion of that element at the surface and thereby increasing
the sputtering rate of the other component(s). In ion-beam
sputtering, it is believed that a stable concentration gradient is
set up, such that (after an initial period of adjustment) the ratio of
sputtered atoms is the same as in the bulk of the sputtering target.
In the case of a compound or alloy TEM specimen, the
concentration gradient through the specimen can lead to radiation-enhanced diffusion, which could be the rate-limiting process
[22–24]. In some circumstances, there may be a compositional
change, reducing the accuracy of elemental analysis by X-ray
emission spectroscopy or electron energy-loss spectroscopy
[25,26].
Many compounds are non-conducting, in which case radiolysis
is likely to be the dominant process causing mass loss. Radiolysis
is particularly rapid in organic compounds and halides but also
believed to exist in oxides. To determine which mechanism is
dominant, the following factors are relevant.
(1) The surface-sputtering process itself is independent of specimen temperature, although in compounds diffusion processes
may limit the rate of mass loss at lower temperature [20].
Mass loss due to radiolysis is usually considerably less at
lower temperature, due to the much lower bulk-diffusion rate.
(2) Being a surface process, sputtering can be independent of
specimen thickness. Therefore a linear decrease in thickness
during irradiation may indicate sputtering [27]. By contrast,
radiolysis is a bulk process and mass loss is often exponential
with dose or irradiation time.
(3) Sputtering effects should disappear below some threshold
incident energy. On this basis, hole formation (above 120 keV)
in SiN was judged to involve sputtering [27]. Radiolysis results
in a characteristic dose that is roughly proportional to
incident energy, since inelastic cross sections are inversely
proportional to E0.
7. Control of sputtering
Because sputtering is a surface process, it can be delayed or
prevented by coating the specimen a suitable material. If
sputtering occurs entirely at the beam-exit surface, only that
surface need by coated. But to be practical in the TEM, the coating
should be:
(1) very thin, to minimise additional electron scattering that
reduces the contrast of a TEM image
(2) devoid of microstructure (e.g. amorphous) to avoid artifacts in
the TEM image
(3) permanent, for example using a material of high atomic
number whose sputtering threshold lies above the incidentbeam energy. Otherwise the layer will act only as a sacrificial
layer that delays sputtering but does not prevent it.
Requirements (1) and (3) are largely contradictory and attempts
to use 1 nm tungsten coatings as a sputtering barrier [11] were
unsuccessful, probably because the nanocrystalline film was
somewhat porous. However, the carbonaceous layer that builds
up on the irradiated region of a specimen in the presence of
hydrocarbon contamination can easily fulfill conditions (1) and
(2). In fact, electron microscopists have been known to irradiate
their specimens under ‘‘dirty’’ conditions prior to imaging or
microanalysis under high-dose conditions; a 5–10 nm polymerized layer (heated to 180 1C for 1 h to prevent further contamination) was reported to provide protection for up to one hour of
microanalysis [23], which is consistent with a carbon-sputtering
cross section of 100 barn and current density 10 A/cm2. An oxide
film on a metal also represents a sputtering barrier but is likely
removed fairly quickly by sputtering and/or radiolysis.
Protection could be made permanent by providing a local
source of carbon. Hydrocarbons are known to diffuse along the
specimen surface into the beam, where they become polymerized.
The polymerization dose has been measured as 1.6 mC/cm2 (cross
section 108 barn) and the surface diffusion coefficient as
55,000 nm2/s at 18 1C [28]. However, it is not obvious what
experimental conditions might allow a natural limit to the
contamination buildup, with sputtering balanced by in-diffusion.
Although carbon-metal bonds can be strong, C–C bonds are even
stronger and the prospect of retaining just a few monolayers of
carbon seems unlikely.
ARTICLE IN PRESS
R.F. Egerton et al. / Ultramicroscopy 110 (2010) 991–997
There remains the possibility of avoiding sputtering by using
an incident energy below the threshold of the surface atoms. As
seen from Table 2, this threshold exceeds 60 keV for most
common materials, so an accelerating voltage of 60 kV could be
low enough for most specimens. Higher TEM voltages have been
traditional largely because they reduce spherical and chromatic
aberration effects of the imaging lenses but further development
of aberration correctors should allow even atomic resolution at
60 kV or even 40 keV [29]. Lower voltages are also advantageous
in terms of achieving high energy stability (e.g. for EELS) and in
terms of overall cost.
Electrons of lower energy are more strongly scattered, meaning that a TEM sample must be very thin in order to provide
sufficient transmitted intensity and readily interpreted image
contrast. Some specimens (nanotubes, nanoparticles) easily
satisfy this requirement; in fact, some of the best images of
carbon nanotubes have been obtained using a 30 kV SEM fitted
with a STEM attachment. Strong scattering leads to higher
contrast, so voltages of 60 or 80 kV are often preferred for lowcontrast biological specimens. The situation is different in the case
of inorganic specimens, particularly those containing high-Z
elements, but ion-thinning techniques sometimes produce very
thin specimens that are free of surface layers. Such specimens
could give good images at 60 kV, especially with appropriate
energy filtering.
8. Conclusions
An accurate knowledge of the threshold energy for sputtering
would help in determining the safe operating range of a TEM for a
given material under high-dose conditions. We have shown that
taking a displacement energy Ed somewhat larger than the
sublimation energy Esub, for example Ed = (5/3)Esub, gives a better
threshold estimate for metallic solids.
Knowledge of the sputtering rate (or cross section) is also of
practical importance, for example when interpreting observations
on TEM specimens under conditions where sputtering cannot be
avoided. In the past, these cross sections have usually been
calculated by taking Ed = Esub and assuming a spherically symmetric escape potential for the surface atoms. Use of a planar
surface potential reduces the cross section by as much as a factor
of 5 and provides better agreement with our measured values for
aluminum and carbon. However, more accurate measurements
are clearly needed.
Even according to these lower cross sections, electron-beam
sputtering of a TEM specimen imposes a practical limit to the
spatial resolution of microanalysis. For example, a cross section of
100 barn, typical of many elements and 100–300 keV irradiation,
would give a thinning rate of 6 monolayers/s in a current density
of 104 A/cm2, easily attainable in a focused probe from a fieldemission source even without aberration correction.
997
Sputtering can be delayed by depositing a thin layer of
amorphous carbon on the beam-exit surface. However, its
elimination seems to require use of an incident energy below
the threshold value; 60 keV appears safe for most materials.
Acknowledgments
We thank the Natural Sciences and Engineering Research
Council of Canada for financial support and the National Institute
for Nanotechnology for the provision of laboratory facilities.
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