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Track damage and erosion of insulators by ion-induced electronic processes
Nuclear Instruments and Methods North-Holland. Amsterdam
in Physics
Research
TRACK DAMAGE AND EROSION OF INSULATORS PROCESSES * T.A.
555
B2 (1984) 555-563
BY ION-INDUCED
ELECTRONIC
TO~BRELLO
Division of Physics, Mathemarics,
and Astronomy,
Caiijarnio Insriture of Technology. Pasadena, CA 91125 USA
Track damage and the associated ejection of atoms and molecules from insulators, which occur as a result of ion-induced electronic excitation, are of interest both in their own right and because of the mechanisms through which the energy in the excited etectrons is transformed into atomic motion. In this paper an overview is given of the phenomena that are observed. We show that there is a remarkable similarity between the damage profile along the ion’s track in the solid and the yield of ejected atoms at the energy that corresponds to each point on the track. It is also seen that the density of extended defects (or, correspondingly, the ejected form that is weakly dependent on the type of material. In the model presented this is a particle yield) appears to have a “universal” consequence of the inner-shell ionization of light elements in the solid by the incident ion; the resulting Auger decay produces an intense ionization spike that locally triggers the track formation/erosion process. This model allows the estimation of erosion yields/damage profiles for different ions and materials.
1. Introduction The observation
of damage
tracks
in dielectric
solids
from MeV/amu ions indicates that energy deposited in the electrons of the material can lead to atomic displacements [I]. Whatever mechanism is involved in this transfer of energy, if displacement can occur then atoms can also be ejected from the surface of the material [2]. This powerful erosion mechanism has been observed in a variety of materials: condensed gases [3-S]; large organic molecules [6-81; alkali halides [9,10]; and other dielectric solids [ll-131. Since there has been extensive review of the first three of these, in this paper I shall mainly concentrate on the fourth. In general, the erosion yields observed are quite large - comparable to those observed in the low energy sputtering of the same materials. In table 1 are summarized examples of the yields obtained for typical materials when bombarded by 20 MeV 35C1 ions. (Unfortunately, no data are available yet for metallic targets under these bombardment conditions). Usually, the yield tends to increase with the energy loss of the ion to the electrons of the solid. Of the examples shown, only UO, and InP depart from that behavior, and those two materials had a low resistivity in the experiments performed. Thus, the exceptions may indicate the presence of other erosion mechanisms that can be seen better when the electronic mechanism is reduced in size. Since the erosion reflects excitation by the ion near the surface of the material, it is not particularly surpris* Supported 81-13273)
in part by the NSF (PHY82-15500 and NASA (NAGW-202).
and
0168-583X/84/$03.00 0 Elsevier Science Publishers ~North-Holland Physics ~blishing Division)
CHE
ing that the yield depends strongly on the charge state of the incident ion. This has been shown in detail for a number of condensed gas targets [4,5], for large organic molecules [8], and for the dielectric solid, UF, [14]. This dependence is quite dramatic; the yield increases by an order of magnitude between 19F+5 and ‘9F+9 incident on UF, [14]. Velocity spectra for the neutral atoms or molecules emitted are known for only a few cases. For the case of UF,, the spectra are softer than from low energy sputtering and have a Maxwell-Bolt~ann shape corresponding to high temperatures (3-5 X lo3 K) that increase
with
d E/dx
(14,151.
Table 1 The erosion yields for materials bombarded by 20 MeV 35C1 ions in charge state equilib~um unless otherwise noted. (Unfortunately, no data for metallic targets are available yet for comparison.) Material SiO,(gIass) SiO,(crystaI) Si3N, Al 203 LiNbO, CaF, UF, InP InP
uo,a’ Si a) 5’ charge
B.V.
increasing
Atom detected
Erosion yield (detected at./incid.
Si Si Si AI Nb Ca U In P U Si
2.9 2.7 0.27 0.22 0.16 1.0 205. 0.06 0.12 0.06 < 0.01
Ref. ion) [I31 1131 D31 ]131 1131 1361 1141 (211
1211 1141 I131
state of 35C1. VIII. SPUTTERING
T.A. Tombrello / Track damage and erosion of insulators
U
.I
.2
.3 E
.4 (
.5
.6
7
.8
.9
!deV/amu)
Fig. 1. The yield of 235U eroded from a UF, target by 35Cl ions in charge state equilibrium. The solid curve shown is calculated using eq. (1) of the text with I* = 76 eV (see table 3). These data are taken from ref. [14].
The erosion yield in a material has a complicated dependence on dE/dx. Attempts to characterize this behavior as a power of d E/dx (or some selected part of d E/dx, like the ionization density) are moderately successful, but are not correct in detail [16]. Parametrized fits to the yield versus bombarding energy are better, but at the expense of introducing at least one additional free parameter. One of the most convenient of these has the Bethe-Bloch form to the fourth power: Yield = S = [A, ( Z&/r)ln(4&/Z*)]4.
(I)
Here the beam has equilibrium charge state Zes at an energy per atomic mass unit E (MeV/amu). M, is the electron mass in amu. The parameter A, is the normalization; Z* is a free parameter whose value is significantly greater that the ionization potential that would appear in the energy loss formula. For UF, it was found that approximately the same value of A, and Z* described the yields for i60, 19F and 35Cl ions in charge state equilibrium [14]. (Because of the strong dependence on the charge state of the incident ion, one must compare only experiments done under similar bombardment conditions.) In fig. 1 is shown the erosion yield for UF, by 35C1 ions with a fit using (1) [14]. The fact that such parameterizations work so well is a consequence of the “universal” shape observed for erosion yields of different substances in this bombarding energy range. For example, fig. 2 shows erosion yields for UF,, Hz0 and SO, due to MeV 19F ions, which all have virtually identical behavior with the bombarding energy [17]. In the following section we shall discuss in more detail the models of the erosion/ track damage process and the relevant data. We shall see that the track data show the existence of a triggering mechanism for the
x
0.0
I
0
5
I
IO Fluorine
I
15
I
I
20 25 Energy ( MeV
I
30
I
)
Fig. 2. The erosion yields for SO,, Ha0 and UF, (per incident ‘sF ion) are given versus 19F bombarding energy. At each energy the same charge state was used for each substance, but the charge state used changed with energy. These data are taken from ref. [17].
process that is provided by the decay of vacancies in inner electronic shells of light element atoms in target. In the third section we use this mechanism to make estimates that can be compared with the existing erosion and track data.
2. Models of the track formation/erosion
process
At the bombarding energies where tracks form and electronic erosion occurs, virtually all the energy lost by the ion is to the electrons of the solid. The models of track formation/erosion deal with the mechanisms by which this energy stored in the electronic system is transformed into atomic motion. The most plausible mechanism involves a modification of the interatomic potential of the solid due to the change in the electronic states. At one extreme (the ion explosion spike [l]) some electrons are considered to have been removed from each of the atoms along the track; the resulting repulsion of the charged atoms leads directly to damage in some models [l] and indirectly after quasi-thermalization in another 1151. Basically, both are contained within a recent model in which the atoms are accelerated in the modified lattice potential, which may involve ionization, but that is not a necessary condition for atomic motion to occur [18]. The lifetime of the excited electronic state is the controlling factor in all track models. It is thought that only in dielectrics will this lifetime be sufficiently long (Z lo-i3 s) that appreciable coupling to atomic motion
557
T.A. Tombrello / Track damage and erosion of insulators
can occur [I]. Estimates of the lifetime involve the dielectric relaxation time of the material. Thus, in agreement with most observations, metals and other low resistivity materials are not expected to exhibit track formation or electronic erosion [13,19,20]. As mentioned in the previous section, it has, however, been observed that InP (0.02 8. cm, n-type, (100)) shows both track damage and enhanced erosion [21]. This requires a modification of the accepted ideas to include other mechanisms that may become more easily visible in low resistivity materials where the standard track mechanism has been suppressed. The fact that in agreement with most track models, many materials (e.g. Si or metals) do not show enhanced erosion or tracks, gives some confidence that the exceptions, though interesting, may not compromise the utility of the models. In the model description there are three stages to track formation/erosion. The ion passes through the solid, slowing down by its interaction with the bound electrons of the material. Since the energy loss can be very high (keV/A for a 1 hIeV/amu fission fragment) many electrons are excited, and along the ion’s track the electrons can be described as a hot plasma (> lo4 K). This extended region of high electronic excitation is the main difference between ion bombardment and that due to individual photon or electron induced excitation. In the Iatter case the excitations produced are isolated and the subsequent behavior of the system is linear in the deposited energy of the projectile. This is also true for most low energy sputtering phenomena where the atoms in the collision cascade do not interact with one another. (Of course, this can be made to break down for sputtering by using heavy molecular ions as projectiles.) However, for MeV/amu ions the extended region of excitation tends to generate non-linear phenomena - as can be seen, for example, by the fact that the yield of emitted atoms varies approximately as a power (2 to 4) of the energy deposited by the ion [l&16]. One has a nearly continuous excited volume where the mutual/ collective interactions of the excited atoms are predominant. Because of this, one should not necessarily assume that the ground state properties of the material control the evolution of the system [18]. In the model of Watson and Tombrello the hot plasma along the ion track is much like a confined electron gas that cools mainly by collisions with the cold (bound) electrons on the boundary of the track [18]. Such collisions are allowed only if the cold electron can be promoted to a state above the band gap. Thus, the presence of an electronic band gap is essential in slowing down the cooling to times of the order of lo-” s. During this period the lattice potential is modified by the changed electronic configurations, and the nuclei are accelerated by the change in potential. These moving atoms collide with one another and after a few collisions are thought to achieve a quasi-equilibrium at
a high temperature (2 lo3 K), which agrees with the data in refs. (141 and [IS]. This produces displacements and/or a strain field aiong the track, and atoms evaporate from the surfaces of the material intersected by the track. The model has no adjustable parameters and manages to describe with reasonable accuracy the erosion yields of a number of dielectric solids and frozen gases, for which the erosion yields vary in magnitude by lo5 [18]. Note that in this model there is no need to invoke the idea of charge separation that is implicit in the ion explosion model [I,lS]. In fact, the electrons are not likely to diffuse away from the track core because they would be strongly attracted to any net positive charge there. Models of this type are based on collective mechanisms that depend on the existence of a coherent solid, and thus would not be expected to occur for free atoms. The only data that bear on this point come from Qiu et al. where the high energy erosion of thin layers of SiO, on carbon substrates by 20 MeV 35C1 ions was studied [13]. For thicknesses5 5 3 atomic layers the erosion yield (Si atoms/incident ion) was < 0.01; for thicknesses > 3 atomic layers the erosion yield increased to 2.8. Within the uncertainties associated with the uniformity of the deposited layer, these data clearly show that there is a point at which there is not enough material to support the existence of the collective erosion/ track formation mechanism. This is an area where further research may give important insights into the relation of the process to the nature of the material. An especially important contribution to our knowledge of tracks has come from the work of Dartyge et al. [22]. They determined the radial dimension of tracks with smali angle X-ray scattering for several materials. The defect density along the track was determined both
Table 2 The size of extended
defect regions in various minerals. These data were taken from Dartyge et al. [22]. These authors did not provide the energies at which many of the ~mbardments were performed. The d and h refer the average diameter and length of an extended defect region, respectively. Mineral
Ion
Mica
Ne ArtI MeV/amu) Ar( 10 MeV/amu) Fe Kr
Labradorite
Fe Kr
Olivine
Ar Fe Kr
‘) Extrapolated
d
84[Al
[Al
15 22 20 26 z 26 (33) a)
-700 -900 - 270 - 350
32 38
-60
>40
value used in the calculations
shown in fig. 4.
VIII. SPUTTERING
T.A Tombrello / Track damage and erosion of insulators
558 loot?~
300 T250 s E >200 d E = 150 c
‘0
2
4
6
E ( MeV/a~u
8
IO
)
Fig. 3. The density of extended defect regions determined from small angle X-ray scattering is given as a function of incident energy for Fe ions on mica. The solid curve is calculated using eq. (1) of the text with I* =159 eV (see table 3). The data are taken from ref. [22]. The dashed curve is the product of (dE/dx)‘/3 [23] and the cross section for K-shell ionization given by the binary encounter model 1261.
by looking with small angle X-ray scattering at the density of atomic displacements in this samples as a function of the ion bombarding energy and also by studying the preferential etching behavior of tracks in thicker samples. They determined that the diameter of a track (d) increased roughly linearly) with the Z of the projectile and had a weak variation with the bombarding energy of a given ion. (Hence there was little variation with the dE/dx of the ion!) Hard materials (i.e. those that register “continuous” tracks only from high 2 ions) had larger track diameters than those of soft materials (which register tracks of a greater range of ion types). (Some of their results are summarized in table 2). An unexpected result of their work was the observation that there were regions of extended defects, which were separated by portions of track that consisted only of point defects. The density of these extended defect regions was given as N(R), i.e. the number of these regions per unit length of residual track range. This is shown for mica in fig. 3 as N(c), i.e. the density measured at different bombarding energies on thin samples. (N(R) is easily converted to N(t) using the relationship between the range of the ion and its energy [23]. Since Dartyge et al. have determined ranges of the ions at several energies in mica, this conversion can be done quite accurately.) Although the density of point defects along a track varies approximately as dE/dx, the density of extended defects has a much steeper slope - much more like that of eq. (I), as shown by the solid curve in fig. 3. A measure of the length of an extended defect region was obtained by Dartyge et al. by observing the etching
‘0
i
2
3
4 5 6 E (MeV/amu)
7
8
3
Fig. 4. The solid curves give the density of extended defect regions (in number of regions per micron) determined from small angle X-ray scattering and etching rates for Kr and Fe ions incident on mica [22]. The open dots are calculated using eq. (1) with I* = 236 eV; the solid dots have I* = 159 eV (see table 3). As shown, the calculations are normalized separately to the Fe and Kr data; if the normalization of the calculations for Fe was determined from the Kr data, the solid dots would have to be lowered by 9.5%. The dashed curves are the product of (dE/dx)“’ (normalized) [23] and the cross section for K-shell ionization given by the binary encounter model [26]. Only the dashed curve for Kr was normalized to the data; the Fe curve was then completely determined.
rate along a track [22]. Some of these data are summarized in table 2. Like the track diameter, these lengths (h) increase with 2, but unlike the diameters these lengths are longer for soft materials than for hard materiafs. As the 2 of the ion increases the extended defect regions run together - becoming a more nearly continuous track. Putting these results together, Dartyge et al. were able to deduce the behavior of N(c) (or N(R) along a given track) for mica bombarded by Fe and Kr ions. These results are shown by the solid curves in fig. 4. They state that a dependence of this type might by typical of most silicate materials. Their results are remarkable and it is important that more data of this sort be obtained. It would, of course, be very interesting to see the pattern of extended defect regions in TEM where they do not overlap. The fission fragment tracks seen by Yada et al. corresponds to such a high Z that the tracks seem completely continuous ]241. In addition to the Dartyge et al. data there are track etching rate versus bombarding energy data for I60 on thin polycarbonate (Makrofol) targets by Diamond [25]. These data are shown in fig. 5. The peak in the ratio of track to bulk etching rates is quite sharply peaked very similar to the erosion data of fig. 2. The existence of discrete regions of extended defects
T.A. Tombrello / Track damage and erosion of insulators
0
-
VT/VG
‘60
I”
2ym
Mokrofol
dE/dx
559
[26].) Lighter elements have even higher cross sections, but the energy release from the Auger decay of their K-shell vacancies is too small to matter. It is also likely that the production of vacancies in higher shells of the heavier target constituents will also contribute. In the next section we shall compare the predictions of this model with the data discussed in the first two sections of this paper.
3. Connecting tracks to erosion
E/A
( t4eV
1 ~cleon)
Fig. 5. The ratio of the track etching rate to that of the bulk material for Makrofol (a polycarbonate track detecting material) bombarded by I60 ions. The solid curve is the electronic part of the energy loss of the ions in the material. These data are taken from ref. [25].
in the Dartyge et al. data implies the operation of either fluctuations in the energy loss process or an occasional triggering event of another type [22]. For these ion beams the energy loss near the peak of the curve in fig. 4 is greater than 500 eV/A. This means that there are tens of electronic collisions per A, so that even on an atomic length scale the fluctuations in the number of collisions are negligible. We may use the peak values of N(e) in fig. 4 to calculate a cross section for a triggering event. From fig. 4 we find that the density of extended defect regions implies a cross section of 6 X lo-l7 cm2 and 5 x lo-i7 cm2 for the oxygen atoms in the mica under irradiation by Kr and Fe ions, respectively. In order to make a crude estimate of the K-shell ionization cross section, we use the binary encounter model [26]. We assume that the charge of the projectile is that of the nucleus minus that due to electrons in shells comparably bound and more tightly bound that the K-shell of oxygen [27]. This calculation gives cross sections of lo-l6 and 8 X lo-l7 cm2 for Kr and Fe, respectively. The close agreement is probably fortuitous, but it does confirm that this is a reasonable mechanism for the process. The position of the peaks near 1 MeV/amu is also in agreement with the binary encounter model [27]. We thus see that the “universal” shape observed for the erosion curves (see fig. 2) probably reflects the fact that similar events initiate the track formation/ electronic erosion process in most materials, i.e. the K-shell ionization of light elements (e.g. C,O,F) at discrete points along the ion’s path through the material. These elements control the process because they have large K-shell ionization cross sections. (The cross section goes inversely as the K-shell binding energy squared
As discussed in the Introduction, eq. (1) provides a parameterization of the erosion yield that allows us the extrapolate from one ion to another on the same material. We can also use what we know of K-shell ionization cross sections in the same way. In this section we use the model of Dartyge et al. and show that we can tie together the erosion yield and their track data and also establish a method for extrapolation to other materials. As discussed by Dartyge et al., the probability of finding a region of extended defects at a position x along a track is: P(x)
= [1-exp(-AN(x))],
where both h and N have the same meanings as given in section 2. (One should note that N(x) is proportional to the cross section for producing an inner shell vacancy at x), i.e. N(x) a uKI(x).) We assume that particle will be ejected whenever the central portion of an extended defect region intersects the surface. Thus, the erosion yield for a track of diameter d is: S(r)ad2[1-exp(-AN(r))]. We shall assume that only a small central portion (whose length is proportional to X) of the extended defect region contributes to the erosion, i.e. the etching is much more sensitive to the tail of the defect distribution than the erosion process is. Thus, we can expand the exponential: S(c)ad2XN(c).
(2)
(If XN becomes too large, this expansion is not valid, and S(E) becomes proportional to d’. This will be discussed again later.) If we use the values (or reasonable extrapolations of the values) obtained for d and h (see table 1) and use the parametrized form for S(E) we obtain the open and closed dots shown in fig. 4. Only the value of I* was changed between Fe and Kr; the correct relative magnitude of the two curves was determined to within 10%. The small differences in the N(r) curves at the lowest energies (where they are least well determined) cause the difference in the I * values. At higher energies the N(Q) VIII. SPUTTERING
TA.
560
Tombrello / Track damage and erosion of insularors
and in the absence
of measurements
we assume that:
If we denote: Vr/Vo=“. then: N(x)
‘0
.I
.2
.3
4
5
6
7
.8
E (MeVhmu)
Fig. 6. The etching rate data of fig. 5 have been converted to a density of extended defect regions [N(c)] using eq. (3) of the text. The curves for N(e) correspond to three different values of a (defined in the text). The solid and open dots were calculated using eq. (1) for I* = 30 and 37 eV (see table 3). respectively.
curves
and the calculated
showing
points
have the same
that eq. (1) does very well for the higher
shape
-
values
of E. To use the etching data of Diamond [25] we must use the method of Dartyge et al. to convert to N(c). This can be done using an equation from their paper [22]:
VT ( x ) = the mean etching rate at x v, = [l+(K_s-l)exp(-AN(x))]
= - (l/h)ln(l//?
(3)
In fig. 6 we show a family of N(E) curves for various values of (Y.(Note that we must have cx> &,,,,.) We also show points corresponding to fits to N(c) using eq (1) for two values of I*. In table 3 we summarize the values of I* obtained from erosion yield and track data for several materials. One should note that within the rather large uncertainties given by the fits in the region of the peak of N(C) or S(E), the softer materials have lower values of I* - as one might expect. Having found a way to predict approximate yields for different ions on the same substance, we now need a method to make estimates for other materials. Fleischer et al. in characterizing the track registration properties of various materials defined the “stress ratio”, a quantity that involved the mechanical properties of the material [l]. Here we define a similar quantity that is similar to (but not identical to) the “stress ratio”. Like Fleischer et al. we assume that the breaking stress of a material is a constant fraction (l/q) of Young’s modulus (Y) and that the stress in a region of extended defects is electrostatic. In cylindrical geometry:
’ (area) -i X electrostatic
where VG, V, and VP are the etching rates of the bulk material, the extended defect regions, and the point defects, respectively. We note that: a=
- l/a).
V,/VsUl,
or (ndX))‘Z$$$
force = Y/n, = Y/q,
where QQ’ is a product of a charge and a linear charge density and x is the dielectric constant of the medium.
Table 3 Values of I* deduced from various measurements. (1963) 1240
Eq. (1) of the text was used with Zb, from H.H. Heckman et al., Phys. Rev. 129
Substance
Beam
Observed
1’ (ev)
Ref
Mica
Rr Fe
track damage profile
236 159
data [22] analysis [this paper]
UF,
0 F Cl
uc
69 76 76
data [14] analysis [this paper]
CSI
Makrofol (polycarbonate)
0 S cu I 0
cs+
track etching rate
51 57 62 55 30-37
data [16] analysis [14]
data [25] analysis [this paper]
561
T.A. Tombrello / Track damuge and erosion of insulntors
Table 4 Comparisons of d2X or the erosion yield (S) to (Yx)-‘. (Y is Young’s modulus and x is the dielectric constant of the target material.) Unless otherwise noted the values of Y and X were taken from ref. [26]. The values shown in parentheses were the points to which the others were normalized. The values of Sc, were taken from table 1. Target
Y [lo”
X
(Yx)-“’
SC, (eroded atoms (per ion)
dyne/cm21
Mica Olivine
17.8 32.4
8 20
(4.7X105) 1.0x 10s
A’ 20, SiO,(gIass) SiO,(crystal) CaF, LiNbO, Si,N,
49.4 7 11 16.4 20.4 30.7 =)
12.2 9 3.5 5.8 99.5 9-15 b,
0.16 1.5 2.5 (1.0) 0.05 0.21-0.34
(d’X)r, (A, 4.7x10’ 0.87 x lo5
0.22 2.9 2.1 1.0 0.16 0.27
a) F.F. Lange, J. Am. Ceram. Sot. 56 (1973) 445. b, G. Ramarao et al., Ceram. Bull. 57 (1978) 591.
(We use x for the dielectric constant because we have already used E for the energy per atomic mass unit.) Thus, d2X aQ'(YX)-' and for a given ion the erosion yield S is proportional to (Yx)-‘, if we ignore the small differences produced by the variation in I* or Q'. We can check this in two ways: compare erosion yields for various materials for a given ion; and compare the values of d2X from ref. [22]. We have summarized these data and the comparisons in table 4. (Most values of x and Y are from ref. [28].) Generally, the results look quite reasonable, and one should be able to estimate both the erosion yield and the damage distribution for a new material with a fair degree of confidence. This model is, in fact, consistent with the inner-shell ionization process that I suggest as the initiator of the formation of a given region of extended defects. In light eiements the decay of a K-shell vacancy is almost entirely by Auger processes [26]. Thus, an intense ionization spike is created that is localized by the short range of the Auger electrons; this is the charge Q in our calculation. One can, of course, consider this region of high electron density as the source of photolysis that changes the chemical or crystal nature of the surrounding material. Such models have been proposed for the decomposition that follows pulsed laser irradiation of compounds [29] and this effect may cause the change in local chemical form that produces the preferential etching of ion damage tracks [30]. The linear charge density Q’ is that due the ordinary energy loss processes. Although the total charge from these processes is much larger than Q, it is less well
localized because its extent is mainly determined by the range of the &rays from collisions with the least bound electrons of the target atoms and the larger impact parameters that contribute to these collisions. Although in future calculations we shall treat the evolution of the excited electronic system in the neighborhood of the K-shell vacancy in a manner similar to that of ref. [18], in order to obtain some instructive estimates here we shall continue in the spirit of the ion explosion spike model [l]. Although the limitations of this model are well known for light ions, for the energetic heavy ions considered here this model may not be unreasonable. We thus calculate the volume over which the electrostatic pressure exceeds the breaking stress of the material and the average energy given to each atom in this volume:
and by integrating the electrostatic the potential energy, we obtain E
=
a”
force equation
to get
1 QQ’e*ln(Va)
n
x(ad2X/4)
’
where n is number of atoms per unit volume and a is a typical interatomic spacing. If we put in reasonable values for the quantities in the first equation (Fe on olivine), we find n = 59, which is in fair agreement with the value of 10 used in ref. [l]. We can use the equation for Y/q to simplify the equation for E,,:
E,,=(2/n)(Y/9)ln(d/2a). Thus
the effective
“temperature”
depends
mainly
on
VIII. SPU’ITERING
562
T.A. Tombrello / Track damage and erosion of insulators
the material through Y. If we use the temperature for UF, [14] to determine E,,, we obtain n =i 43. Returning to the relation:
data
the emission of heavy molecular heavy projectiles [34].
ions caused
by very
d2h a Q’( Yx)-l,
4. Conclusions
we note that this implies that d and X are proportional to ( Q’)1’3. If we replace Q’ by dE/dx we see the reason for the slow variation of d with ion energy and atomic number. Using this relation we reproduce quite well the variation in d with 6 for Ar on mica (see tabie 2) and the variation of d and X for mica, labradorite and olivine. The change in the average energy per particle ejected (effective temperature) with dE/dx observed by ref. [14] is less well described by this model, We note that the dependence on dE/dx arises only from the ln(d/2a) term; since d varies as (dE/dx)rj3, the variation is in the right direction but produces only about half the change observed experimentally. We note that this model also describes the behavior of the erosion yield with incident charge state, 4. For less highly charged ions the variation with 4 is controlled by Q’, i.e. q2_ N(c) is determined by the most tightly bound electrons of the projectile and does not depend on q until q becomes sufficiently high that there are vacancies in the inner electron shells of the projectile ion. At this point N(e) increases very rapidly - as shown in the K-shell ionization data of Cocke et al. [31]. The S versus q data in refs. [8] and 1141 exhibit this behaviour. It should be noted that Dartyge et al. assumed that A did not depend on 6 when N(e) was extracted from their data [22]. Thus, since we find that X is proportional to we should compare (dE,/dx)1/3 am(e) with (Q’)“3, their N(t). This is done in figs. 3 and 4 as dashed lines. We see from this comparison that although the relative magnitudes of the curves are excellent, the shapes are not correct. Because of electron capture processes that grow very rapidly with the 2 of the projectile, it is obvious that the binary encounter model is inadequate for most K-shell ionization processes - see for example refs. [32] and [33]. However, there are neither data nor detailed models for energies significantly above the peak m ox, or for such systems where a light target atom is bombarded by a much heavier projectile. (It seems clear that the presence of excited projectile ions and L (and bier)-shell vacancy formation in heavier target constituents may play a significant role that cannot be easily dealt with theoretically.) Thus, measurements of inner shell ionization cross sections at high energies and for very asymmetric systems are an essential ingredient in extensions of the work shown here. Finally, as mentions earlier, when hN( e) becomes sufficiently large (i.e. for very heavy ions) the erosion yield will vary approximately as d* [i.e. as (dE/dx)2/3]. This saturation behavior has in fact been observed in
From what we have summarized here it is clear that the erosion of insulators by MeV/amu ions is a common phenomenon whose systematic behavior is linked to the ion’s exitation of electrons in the material. We have attempted to provided a simple framework with which a variety of related observations are linked and estimates made for new experimental situations. Although the scaling methods given are not yet as strongly anchored to theory as we would like, the obvious success of the simple model given here may provide a guide for more elaborate versions that treat the evolution of the excited electronic system more exactly. It is also clear that the inner-shell ionization mechanism should be incorporated into more detailed models like that of ref.
WI. It is especially important that the methods suggested be checked in greater detail. This will require more small angle X-ray scattering data of the sort given in ref. [22] as well as track etching rate measurements in a wider variety of materials. Measurements of ion erosion yields and inner vacancy production should also be extended to materials whose properties give a more definitive test of the extrapolation procedures and models. The observation that SiO, shows the enhanced erosion effect only for targets whose thicknesses are greater than three atomic layers deserves greater attention. This phenomenon may give as many new insights into the target material as it provides for the mechanism itself. If one could make sufficiently well characterized, uniform targets, studying the variation in the erosion yield with target thickness should be quite interesting. Although a detailed quantitative theory does not really exist, the overall systematic phenomenology of electronic excitation erosion is sufficiently well known that it can be applied. Generally, we can probably predict the high energy erosion of insulators about as well as we can predict their low energy sputtering yields, and that is certainly good enough for many purposes of application, e.g. to planetary science [35] or technology
[1,3a. One should be aware that the triggering mechanism proposed here may also be important in other contexts. For example, the observation that the adhesion of a thin film to a substrate can be enhanced by fast heavy ion bombardment may also involve inner-shell vacancy formation in initiating atomic processes that lead to increased binding [37-39,361. The fact that low energy electrons (- 2 keV, i.e. near the peak of ukr) can also produce this effect is certainly consistent with the model described here [40].
563
T.A. Tombrello / Track damage and erosion of insulators
I would like to acknowledge discussions with my colleagues {Peter Haff and Charles Watson) and students (Kelly Cherrey) that have helped me to organize and refine the ideas contained in this paper. Special thanks are also owed to Robert Fleischer who has provided a number of references that were otherwise unknown to the author. I am, in this regard, indebted to Keith Jones and Patrick Richard who helped me to find references to relevant data on K-shell ionization processes. Both Noriaki Itoh and Bo Sundqvist provided essential ideas during the development of this model. Finally, I express my appreciation to Allan Bromley for his hospitality at Yale University, where I have found a peaceful spot to write this paper.
References [l] R.L. Fleischer, P.B. Price and R.M. Walker, Nuclear tracks in solids (University of California Press, Berkeley, 1975). [2] P.K. Haff, Appl. Phys. Lett. 29 (1976) 443. [3] W.L. Brown, L.J. Lanzerotti, J.M. Poate and W.M. Augustyniak. Phys. Rev. Lett. 40 (1979) 1027. [4] F. Besenbacher, J. Bottiger, 0. Graversen and J.L. Hansen, Nucl. Instr. and Meth. 191 (1981) 221. [S] B.H. Cooper and T.A. Tombrello, Rad. Eff. (1983) in press. [6] R.D. McFarliane and D.F. Torgerson, Int. J. Mass Spectrom. Ion Phys. 21 (1976) 81. [7] P. Duck, W. Treu, W. Gaister, H. FrohIich and H. Voit, Nucl. Instr. and Meth. 168 (1980) 601. [8] P. Hakansson, E. Jayasinge, A. J8hansson. I. Kamensky and B. Sundqvist, Phys. Rev. Lett. 47 (1981) 1227. [9] J.P. Biersack and E. Santer, Nucl. Instr. and meth. 132 (1976) 229. [lo] M. Szymonski, H. Overeijnder and A.E. de Vries, Rad, Eff. 36 (1978) 189. [ll] J.E. Griffith, R.A. Weiler, L.E. Seiberling and T.A. Tombrello, Rad. Eff. 51 (1980) 223. [12] Y. Qiu, J.E. Griffith and T.A. Tombrello, Rad. Eff. 64 (1982) 111. ]13] Y. Qiu, J.E. Griffith, W.J. Meng and T.A. Tombreilo, Rad. Eff. 70 (1983) 231. [14] C.K. Meins, J.E. Griffith, Y. Qiu. M.H. Mendenhall, L.E. Seiberling and T.A. Tombrello, Rad. Eff. 71 (1983) 13.
1151 L.E. Seiberling,
J.E. Griffith and T.A. Tombrello, Eff. 52 (1980) 201. P. Hakansson and B. Sundqvist, Rad. Eff. 61 (1982) 1161 B.H. Cooper, C.L. Meicher and P71 D.J. LePoire, Tombrello, Rad. Eff. 71 (1983) 245. Rad Eff. (1983) (181 C.C. Watson and T.A. Tombrello, mitted.
Rad. 179. T.A. sub-
v91 J.E. Griffith, Ph.D. Thesis, California Institute of Technology (1979). Phys. Rev. Lett. 33 PO1 J.E. Robinson and D.A. Thompson, (1974) 1569. WI As quoted by T.A. Tombrello, Int. J. Mass Spectrom. Ion Phys. 53 (1983) 307. WI E. Dartyge, J.P. Duraud, Y. Langevin and M. Maurette, Phys. Rev. B 23 (1981) 5213. and R.F. Schilling, Range and stopping [231 L.C. Northcliffe power tabtes for heavy ions, Nuclear data tables 7, no. 3-4 (Academic Press, New York, 1970). ~241 K. Yada, T. Tanji and I. Sunagawa, Phys. Chem. Miner. 7 (1981) 47. manuscript. v51 W.T. Diamond, unpublished WI J.D. Garcia, R.J. Fortner and T.M. Kavanagb, Rev. Mod. Phys. 45 (1973) 111. 1271 J.C. Slater. Phys. Rev. 98 (1955) 1039. WI A. Sigrist and R. Bailer, Hdv. Phys. Acta 50 (1977) 49. K. Morita and N. Itoh, Phys. 1291 M. Okigawa, T. Nakayama, Rev. Lett. (1983), submitted. and T.A. Tombrello, N. 1301 N. Itoh, Private communication Itoh and T. Nakayama, Phys. Lett. (1983) in press. 1311 C.L. Cocke, R.R. Randall and 8. Cumutte, Electronic and atomic collisions, vol. 2, eds., J.S. Risley and R. Gebalfe (Univ. of Washington Press, Seattle, 1975) p. 933. IEEE Trans. 1321 G. Basbas, R. Rice and F.D. McDaniel, Nucl. Sci. NS-26 (1979) 1177. 1331 G. Brandt, IEEE Trans. Nucl. Sci. NS-26 (1979) 1179. I. Kamensky, J. 1341 B. Sundqvist, A. Hedin, P. Hakansson, Kjelfberg, M. Salehpour, G. Sawe and S. Widdiyasekera, Int. J. Mass. Spectrom. Ion Phys. (1983), in press. I351 T.A. Tombrello, Rad. Eff. 65 (1982) 149. 1361 T.A. Tombrello, Nucl. Instr. and Meth. 218 (1983) 679. [371 J.E. Griffith, Y. Qiu and T.A. Tombrello, Nucl. Instr. and Meth. 198 (1982) 607. Y. Qiu [381 B.T. Werner, T. Vreeland, Jr., M.H. Mendenhall, and T.A. Tombrello, Thin Solid Films 104 (1983) 163. Ph.D. Thesis, California Institute of I391 M.H. Mendenhall. Technology (1983). WI J.S. Williams, private communication.
VIII. SPLJT’IERING
in Physics
Research
TRACK DAMAGE AND EROSION OF INSULATORS PROCESSES * T.A.
555
B2 (1984) 555-563
BY ION-INDUCED
ELECTRONIC
TO~BRELLO
Division of Physics, Mathemarics,
and Astronomy,
Caiijarnio Insriture of Technology. Pasadena, CA 91125 USA
Track damage and the associated ejection of atoms and molecules from insulators, which occur as a result of ion-induced electronic excitation, are of interest both in their own right and because of the mechanisms through which the energy in the excited etectrons is transformed into atomic motion. In this paper an overview is given of the phenomena that are observed. We show that there is a remarkable similarity between the damage profile along the ion’s track in the solid and the yield of ejected atoms at the energy that corresponds to each point on the track. It is also seen that the density of extended defects (or, correspondingly, the ejected form that is weakly dependent on the type of material. In the model presented this is a particle yield) appears to have a “universal” consequence of the inner-shell ionization of light elements in the solid by the incident ion; the resulting Auger decay produces an intense ionization spike that locally triggers the track formation/erosion process. This model allows the estimation of erosion yields/damage profiles for different ions and materials.
1. Introduction The observation
of damage
tracks
in dielectric
solids
from MeV/amu ions indicates that energy deposited in the electrons of the material can lead to atomic displacements [I]. Whatever mechanism is involved in this transfer of energy, if displacement can occur then atoms can also be ejected from the surface of the material [2]. This powerful erosion mechanism has been observed in a variety of materials: condensed gases [3-S]; large organic molecules [6-81; alkali halides [9,10]; and other dielectric solids [ll-131. Since there has been extensive review of the first three of these, in this paper I shall mainly concentrate on the fourth. In general, the erosion yields observed are quite large - comparable to those observed in the low energy sputtering of the same materials. In table 1 are summarized examples of the yields obtained for typical materials when bombarded by 20 MeV 35C1 ions. (Unfortunately, no data are available yet for metallic targets under these bombardment conditions). Usually, the yield tends to increase with the energy loss of the ion to the electrons of the solid. Of the examples shown, only UO, and InP depart from that behavior, and those two materials had a low resistivity in the experiments performed. Thus, the exceptions may indicate the presence of other erosion mechanisms that can be seen better when the electronic mechanism is reduced in size. Since the erosion reflects excitation by the ion near the surface of the material, it is not particularly surpris* Supported 81-13273)
in part by the NSF (PHY82-15500 and NASA (NAGW-202).
and
0168-583X/84/$03.00 0 Elsevier Science Publishers ~North-Holland Physics ~blishing Division)
CHE
ing that the yield depends strongly on the charge state of the incident ion. This has been shown in detail for a number of condensed gas targets [4,5], for large organic molecules [8], and for the dielectric solid, UF, [14]. This dependence is quite dramatic; the yield increases by an order of magnitude between 19F+5 and ‘9F+9 incident on UF, [14]. Velocity spectra for the neutral atoms or molecules emitted are known for only a few cases. For the case of UF,, the spectra are softer than from low energy sputtering and have a Maxwell-Bolt~ann shape corresponding to high temperatures (3-5 X lo3 K) that increase
with
d E/dx
(14,151.
Table 1 The erosion yields for materials bombarded by 20 MeV 35C1 ions in charge state equilib~um unless otherwise noted. (Unfortunately, no data for metallic targets are available yet for comparison.) Material SiO,(gIass) SiO,(crystaI) Si3N, Al 203 LiNbO, CaF, UF, InP InP
uo,a’ Si a) 5’ charge
B.V.
increasing
Atom detected
Erosion yield (detected at./incid.
Si Si Si AI Nb Ca U In P U Si
2.9 2.7 0.27 0.22 0.16 1.0 205. 0.06 0.12 0.06 < 0.01
Ref. ion) [I31 1131 D31 ]131 1131 1361 1141 (211
1211 1141 I131
state of 35C1. VIII. SPUTTERING
T.A. Tombrello / Track damage and erosion of insulators
U
.I
.2
.3 E
.4 (
.5
.6
7
.8
.9
!deV/amu)
Fig. 1. The yield of 235U eroded from a UF, target by 35Cl ions in charge state equilibrium. The solid curve shown is calculated using eq. (1) of the text with I* = 76 eV (see table 3). These data are taken from ref. [14].
The erosion yield in a material has a complicated dependence on dE/dx. Attempts to characterize this behavior as a power of d E/dx (or some selected part of d E/dx, like the ionization density) are moderately successful, but are not correct in detail [16]. Parametrized fits to the yield versus bombarding energy are better, but at the expense of introducing at least one additional free parameter. One of the most convenient of these has the Bethe-Bloch form to the fourth power: Yield = S = [A, ( Z&/r)ln(4&/Z*)]4.
(I)
Here the beam has equilibrium charge state Zes at an energy per atomic mass unit E (MeV/amu). M, is the electron mass in amu. The parameter A, is the normalization; Z* is a free parameter whose value is significantly greater that the ionization potential that would appear in the energy loss formula. For UF, it was found that approximately the same value of A, and Z* described the yields for i60, 19F and 35Cl ions in charge state equilibrium [14]. (Because of the strong dependence on the charge state of the incident ion, one must compare only experiments done under similar bombardment conditions.) In fig. 1 is shown the erosion yield for UF, by 35C1 ions with a fit using (1) [14]. The fact that such parameterizations work so well is a consequence of the “universal” shape observed for erosion yields of different substances in this bombarding energy range. For example, fig. 2 shows erosion yields for UF,, Hz0 and SO, due to MeV 19F ions, which all have virtually identical behavior with the bombarding energy [17]. In the following section we shall discuss in more detail the models of the erosion/ track damage process and the relevant data. We shall see that the track data show the existence of a triggering mechanism for the
x
0.0
I
0
5
I
IO Fluorine
I
15
I
I
20 25 Energy ( MeV
I
30
I
)
Fig. 2. The erosion yields for SO,, Ha0 and UF, (per incident ‘sF ion) are given versus 19F bombarding energy. At each energy the same charge state was used for each substance, but the charge state used changed with energy. These data are taken from ref. [17].
process that is provided by the decay of vacancies in inner electronic shells of light element atoms in target. In the third section we use this mechanism to make estimates that can be compared with the existing erosion and track data.
2. Models of the track formation/erosion
process
At the bombarding energies where tracks form and electronic erosion occurs, virtually all the energy lost by the ion is to the electrons of the solid. The models of track formation/erosion deal with the mechanisms by which this energy stored in the electronic system is transformed into atomic motion. The most plausible mechanism involves a modification of the interatomic potential of the solid due to the change in the electronic states. At one extreme (the ion explosion spike [l]) some electrons are considered to have been removed from each of the atoms along the track; the resulting repulsion of the charged atoms leads directly to damage in some models [l] and indirectly after quasi-thermalization in another 1151. Basically, both are contained within a recent model in which the atoms are accelerated in the modified lattice potential, which may involve ionization, but that is not a necessary condition for atomic motion to occur [18]. The lifetime of the excited electronic state is the controlling factor in all track models. It is thought that only in dielectrics will this lifetime be sufficiently long (Z lo-i3 s) that appreciable coupling to atomic motion
557
T.A. Tombrello / Track damage and erosion of insulators
can occur [I]. Estimates of the lifetime involve the dielectric relaxation time of the material. Thus, in agreement with most observations, metals and other low resistivity materials are not expected to exhibit track formation or electronic erosion [13,19,20]. As mentioned in the previous section, it has, however, been observed that InP (0.02 8. cm, n-type, (100)) shows both track damage and enhanced erosion [21]. This requires a modification of the accepted ideas to include other mechanisms that may become more easily visible in low resistivity materials where the standard track mechanism has been suppressed. The fact that in agreement with most track models, many materials (e.g. Si or metals) do not show enhanced erosion or tracks, gives some confidence that the exceptions, though interesting, may not compromise the utility of the models. In the model description there are three stages to track formation/erosion. The ion passes through the solid, slowing down by its interaction with the bound electrons of the material. Since the energy loss can be very high (keV/A for a 1 hIeV/amu fission fragment) many electrons are excited, and along the ion’s track the electrons can be described as a hot plasma (> lo4 K). This extended region of high electronic excitation is the main difference between ion bombardment and that due to individual photon or electron induced excitation. In the Iatter case the excitations produced are isolated and the subsequent behavior of the system is linear in the deposited energy of the projectile. This is also true for most low energy sputtering phenomena where the atoms in the collision cascade do not interact with one another. (Of course, this can be made to break down for sputtering by using heavy molecular ions as projectiles.) However, for MeV/amu ions the extended region of excitation tends to generate non-linear phenomena - as can be seen, for example, by the fact that the yield of emitted atoms varies approximately as a power (2 to 4) of the energy deposited by the ion [l&16]. One has a nearly continuous excited volume where the mutual/ collective interactions of the excited atoms are predominant. Because of this, one should not necessarily assume that the ground state properties of the material control the evolution of the system [18]. In the model of Watson and Tombrello the hot plasma along the ion track is much like a confined electron gas that cools mainly by collisions with the cold (bound) electrons on the boundary of the track [18]. Such collisions are allowed only if the cold electron can be promoted to a state above the band gap. Thus, the presence of an electronic band gap is essential in slowing down the cooling to times of the order of lo-” s. During this period the lattice potential is modified by the changed electronic configurations, and the nuclei are accelerated by the change in potential. These moving atoms collide with one another and after a few collisions are thought to achieve a quasi-equilibrium at
a high temperature (2 lo3 K), which agrees with the data in refs. (141 and [IS]. This produces displacements and/or a strain field aiong the track, and atoms evaporate from the surfaces of the material intersected by the track. The model has no adjustable parameters and manages to describe with reasonable accuracy the erosion yields of a number of dielectric solids and frozen gases, for which the erosion yields vary in magnitude by lo5 [18]. Note that in this model there is no need to invoke the idea of charge separation that is implicit in the ion explosion model [I,lS]. In fact, the electrons are not likely to diffuse away from the track core because they would be strongly attracted to any net positive charge there. Models of this type are based on collective mechanisms that depend on the existence of a coherent solid, and thus would not be expected to occur for free atoms. The only data that bear on this point come from Qiu et al. where the high energy erosion of thin layers of SiO, on carbon substrates by 20 MeV 35C1 ions was studied [13]. For thicknesses5 5 3 atomic layers the erosion yield (Si atoms/incident ion) was < 0.01; for thicknesses > 3 atomic layers the erosion yield increased to 2.8. Within the uncertainties associated with the uniformity of the deposited layer, these data clearly show that there is a point at which there is not enough material to support the existence of the collective erosion/ track formation mechanism. This is an area where further research may give important insights into the relation of the process to the nature of the material. An especially important contribution to our knowledge of tracks has come from the work of Dartyge et al. [22]. They determined the radial dimension of tracks with smali angle X-ray scattering for several materials. The defect density along the track was determined both
Table 2 The size of extended
defect regions in various minerals. These data were taken from Dartyge et al. [22]. These authors did not provide the energies at which many of the ~mbardments were performed. The d and h refer the average diameter and length of an extended defect region, respectively. Mineral
Ion
Mica
Ne ArtI MeV/amu) Ar( 10 MeV/amu) Fe Kr
Labradorite
Fe Kr
Olivine
Ar Fe Kr
‘) Extrapolated
d
84[Al
[Al
15 22 20 26 z 26 (33) a)
-700 -900 - 270 - 350
32 38
-60
>40
value used in the calculations
shown in fig. 4.
VIII. SPUTTERING
T.A Tombrello / Track damage and erosion of insulators
558 loot?~
300 T250 s E >200 d E = 150 c
‘0
2
4
6
E ( MeV/a~u
8
IO
)
Fig. 3. The density of extended defect regions determined from small angle X-ray scattering is given as a function of incident energy for Fe ions on mica. The solid curve is calculated using eq. (1) of the text with I* =159 eV (see table 3). The data are taken from ref. [22]. The dashed curve is the product of (dE/dx)‘/3 [23] and the cross section for K-shell ionization given by the binary encounter model 1261.
by looking with small angle X-ray scattering at the density of atomic displacements in this samples as a function of the ion bombarding energy and also by studying the preferential etching behavior of tracks in thicker samples. They determined that the diameter of a track (d) increased roughly linearly) with the Z of the projectile and had a weak variation with the bombarding energy of a given ion. (Hence there was little variation with the dE/dx of the ion!) Hard materials (i.e. those that register “continuous” tracks only from high 2 ions) had larger track diameters than those of soft materials (which register tracks of a greater range of ion types). (Some of their results are summarized in table 2). An unexpected result of their work was the observation that there were regions of extended defects, which were separated by portions of track that consisted only of point defects. The density of these extended defect regions was given as N(R), i.e. the number of these regions per unit length of residual track range. This is shown for mica in fig. 3 as N(c), i.e. the density measured at different bombarding energies on thin samples. (N(R) is easily converted to N(t) using the relationship between the range of the ion and its energy [23]. Since Dartyge et al. have determined ranges of the ions at several energies in mica, this conversion can be done quite accurately.) Although the density of point defects along a track varies approximately as dE/dx, the density of extended defects has a much steeper slope - much more like that of eq. (I), as shown by the solid curve in fig. 3. A measure of the length of an extended defect region was obtained by Dartyge et al. by observing the etching
‘0
i
2
3
4 5 6 E (MeV/amu)
7
8
3
Fig. 4. The solid curves give the density of extended defect regions (in number of regions per micron) determined from small angle X-ray scattering and etching rates for Kr and Fe ions incident on mica [22]. The open dots are calculated using eq. (1) with I* = 236 eV; the solid dots have I* = 159 eV (see table 3). As shown, the calculations are normalized separately to the Fe and Kr data; if the normalization of the calculations for Fe was determined from the Kr data, the solid dots would have to be lowered by 9.5%. The dashed curves are the product of (dE/dx)“’ (normalized) [23] and the cross section for K-shell ionization given by the binary encounter model [26]. Only the dashed curve for Kr was normalized to the data; the Fe curve was then completely determined.
rate along a track [22]. Some of these data are summarized in table 2. Like the track diameter, these lengths (h) increase with 2, but unlike the diameters these lengths are longer for soft materials than for hard materiafs. As the 2 of the ion increases the extended defect regions run together - becoming a more nearly continuous track. Putting these results together, Dartyge et al. were able to deduce the behavior of N(c) (or N(R) along a given track) for mica bombarded by Fe and Kr ions. These results are shown by the solid curves in fig. 4. They state that a dependence of this type might by typical of most silicate materials. Their results are remarkable and it is important that more data of this sort be obtained. It would, of course, be very interesting to see the pattern of extended defect regions in TEM where they do not overlap. The fission fragment tracks seen by Yada et al. corresponds to such a high Z that the tracks seem completely continuous ]241. In addition to the Dartyge et al. data there are track etching rate versus bombarding energy data for I60 on thin polycarbonate (Makrofol) targets by Diamond [25]. These data are shown in fig. 5. The peak in the ratio of track to bulk etching rates is quite sharply peaked very similar to the erosion data of fig. 2. The existence of discrete regions of extended defects
T.A. Tombrello / Track damage and erosion of insulators
0
-
VT/VG
‘60
I”
2ym
Mokrofol
dE/dx
559
[26].) Lighter elements have even higher cross sections, but the energy release from the Auger decay of their K-shell vacancies is too small to matter. It is also likely that the production of vacancies in higher shells of the heavier target constituents will also contribute. In the next section we shall compare the predictions of this model with the data discussed in the first two sections of this paper.
3. Connecting tracks to erosion
E/A
( t4eV
1 ~cleon)
Fig. 5. The ratio of the track etching rate to that of the bulk material for Makrofol (a polycarbonate track detecting material) bombarded by I60 ions. The solid curve is the electronic part of the energy loss of the ions in the material. These data are taken from ref. [25].
in the Dartyge et al. data implies the operation of either fluctuations in the energy loss process or an occasional triggering event of another type [22]. For these ion beams the energy loss near the peak of the curve in fig. 4 is greater than 500 eV/A. This means that there are tens of electronic collisions per A, so that even on an atomic length scale the fluctuations in the number of collisions are negligible. We may use the peak values of N(e) in fig. 4 to calculate a cross section for a triggering event. From fig. 4 we find that the density of extended defect regions implies a cross section of 6 X lo-l7 cm2 and 5 x lo-i7 cm2 for the oxygen atoms in the mica under irradiation by Kr and Fe ions, respectively. In order to make a crude estimate of the K-shell ionization cross section, we use the binary encounter model [26]. We assume that the charge of the projectile is that of the nucleus minus that due to electrons in shells comparably bound and more tightly bound that the K-shell of oxygen [27]. This calculation gives cross sections of lo-l6 and 8 X lo-l7 cm2 for Kr and Fe, respectively. The close agreement is probably fortuitous, but it does confirm that this is a reasonable mechanism for the process. The position of the peaks near 1 MeV/amu is also in agreement with the binary encounter model [27]. We thus see that the “universal” shape observed for the erosion curves (see fig. 2) probably reflects the fact that similar events initiate the track formation/ electronic erosion process in most materials, i.e. the K-shell ionization of light elements (e.g. C,O,F) at discrete points along the ion’s path through the material. These elements control the process because they have large K-shell ionization cross sections. (The cross section goes inversely as the K-shell binding energy squared
As discussed in the Introduction, eq. (1) provides a parameterization of the erosion yield that allows us the extrapolate from one ion to another on the same material. We can also use what we know of K-shell ionization cross sections in the same way. In this section we use the model of Dartyge et al. and show that we can tie together the erosion yield and their track data and also establish a method for extrapolation to other materials. As discussed by Dartyge et al., the probability of finding a region of extended defects at a position x along a track is: P(x)
= [1-exp(-AN(x))],
where both h and N have the same meanings as given in section 2. (One should note that N(x) is proportional to the cross section for producing an inner shell vacancy at x), i.e. N(x) a uKI(x).) We assume that particle will be ejected whenever the central portion of an extended defect region intersects the surface. Thus, the erosion yield for a track of diameter d is: S(r)ad2[1-exp(-AN(r))]. We shall assume that only a small central portion (whose length is proportional to X) of the extended defect region contributes to the erosion, i.e. the etching is much more sensitive to the tail of the defect distribution than the erosion process is. Thus, we can expand the exponential: S(c)ad2XN(c).
(2)
(If XN becomes too large, this expansion is not valid, and S(E) becomes proportional to d’. This will be discussed again later.) If we use the values (or reasonable extrapolations of the values) obtained for d and h (see table 1) and use the parametrized form for S(E) we obtain the open and closed dots shown in fig. 4. Only the value of I* was changed between Fe and Kr; the correct relative magnitude of the two curves was determined to within 10%. The small differences in the N(r) curves at the lowest energies (where they are least well determined) cause the difference in the I * values. At higher energies the N(Q) VIII. SPUTTERING
TA.
560
Tombrello / Track damage and erosion of insularors
and in the absence
of measurements
we assume that:
If we denote: Vr/Vo=“. then: N(x)
‘0
.I
.2
.3
4
5
6
7
.8
E (MeVhmu)
Fig. 6. The etching rate data of fig. 5 have been converted to a density of extended defect regions [N(c)] using eq. (3) of the text. The curves for N(e) correspond to three different values of a (defined in the text). The solid and open dots were calculated using eq. (1) for I* = 30 and 37 eV (see table 3). respectively.
curves
and the calculated
showing
points
have the same
that eq. (1) does very well for the higher
shape
-
values
of E. To use the etching data of Diamond [25] we must use the method of Dartyge et al. to convert to N(c). This can be done using an equation from their paper [22]:
VT ( x ) = the mean etching rate at x v, = [l+(K_s-l)exp(-AN(x))]
= - (l/h)ln(l//?
(3)
In fig. 6 we show a family of N(E) curves for various values of (Y.(Note that we must have cx> &,,,,.) We also show points corresponding to fits to N(c) using eq (1) for two values of I*. In table 3 we summarize the values of I* obtained from erosion yield and track data for several materials. One should note that within the rather large uncertainties given by the fits in the region of the peak of N(C) or S(E), the softer materials have lower values of I* - as one might expect. Having found a way to predict approximate yields for different ions on the same substance, we now need a method to make estimates for other materials. Fleischer et al. in characterizing the track registration properties of various materials defined the “stress ratio”, a quantity that involved the mechanical properties of the material [l]. Here we define a similar quantity that is similar to (but not identical to) the “stress ratio”. Like Fleischer et al. we assume that the breaking stress of a material is a constant fraction (l/q) of Young’s modulus (Y) and that the stress in a region of extended defects is electrostatic. In cylindrical geometry:
’ (area) -i X electrostatic
where VG, V, and VP are the etching rates of the bulk material, the extended defect regions, and the point defects, respectively. We note that: a=
- l/a).
V,/VsUl,
or (ndX))‘Z$$$
force = Y/n, = Y/q,
where QQ’ is a product of a charge and a linear charge density and x is the dielectric constant of the medium.
Table 3 Values of I* deduced from various measurements. (1963) 1240
Eq. (1) of the text was used with Zb, from H.H. Heckman et al., Phys. Rev. 129
Substance
Beam
Observed
1’ (ev)
Ref
Mica
Rr Fe
track damage profile
236 159
data [22] analysis [this paper]
UF,
0 F Cl
uc
69 76 76
data [14] analysis [this paper]
CSI
Makrofol (polycarbonate)
0 S cu I 0
cs+
track etching rate
51 57 62 55 30-37
data [16] analysis [14]
data [25] analysis [this paper]
561
T.A. Tombrello / Track damuge and erosion of insulntors
Table 4 Comparisons of d2X or the erosion yield (S) to (Yx)-‘. (Y is Young’s modulus and x is the dielectric constant of the target material.) Unless otherwise noted the values of Y and X were taken from ref. [26]. The values shown in parentheses were the points to which the others were normalized. The values of Sc, were taken from table 1. Target
Y [lo”
X
(Yx)-“’
SC, (eroded atoms (per ion)
dyne/cm21
Mica Olivine
17.8 32.4
8 20
(4.7X105) 1.0x 10s
A’ 20, SiO,(gIass) SiO,(crystal) CaF, LiNbO, Si,N,
49.4 7 11 16.4 20.4 30.7 =)
12.2 9 3.5 5.8 99.5 9-15 b,
0.16 1.5 2.5 (1.0) 0.05 0.21-0.34
(d’X)r, (A, 4.7x10’ 0.87 x lo5
0.22 2.9 2.1 1.0 0.16 0.27
a) F.F. Lange, J. Am. Ceram. Sot. 56 (1973) 445. b, G. Ramarao et al., Ceram. Bull. 57 (1978) 591.
(We use x for the dielectric constant because we have already used E for the energy per atomic mass unit.) Thus, d2X aQ'(YX)-' and for a given ion the erosion yield S is proportional to (Yx)-‘, if we ignore the small differences produced by the variation in I* or Q'. We can check this in two ways: compare erosion yields for various materials for a given ion; and compare the values of d2X from ref. [22]. We have summarized these data and the comparisons in table 4. (Most values of x and Y are from ref. [28].) Generally, the results look quite reasonable, and one should be able to estimate both the erosion yield and the damage distribution for a new material with a fair degree of confidence. This model is, in fact, consistent with the inner-shell ionization process that I suggest as the initiator of the formation of a given region of extended defects. In light eiements the decay of a K-shell vacancy is almost entirely by Auger processes [26]. Thus, an intense ionization spike is created that is localized by the short range of the Auger electrons; this is the charge Q in our calculation. One can, of course, consider this region of high electron density as the source of photolysis that changes the chemical or crystal nature of the surrounding material. Such models have been proposed for the decomposition that follows pulsed laser irradiation of compounds [29] and this effect may cause the change in local chemical form that produces the preferential etching of ion damage tracks [30]. The linear charge density Q’ is that due the ordinary energy loss processes. Although the total charge from these processes is much larger than Q, it is less well
localized because its extent is mainly determined by the range of the &rays from collisions with the least bound electrons of the target atoms and the larger impact parameters that contribute to these collisions. Although in future calculations we shall treat the evolution of the excited electronic system in the neighborhood of the K-shell vacancy in a manner similar to that of ref. [18], in order to obtain some instructive estimates here we shall continue in the spirit of the ion explosion spike model [l]. Although the limitations of this model are well known for light ions, for the energetic heavy ions considered here this model may not be unreasonable. We thus calculate the volume over which the electrostatic pressure exceeds the breaking stress of the material and the average energy given to each atom in this volume:
and by integrating the electrostatic the potential energy, we obtain E
=
a”
force equation
to get
1 QQ’e*ln(Va)
n
x(ad2X/4)
’
where n is number of atoms per unit volume and a is a typical interatomic spacing. If we put in reasonable values for the quantities in the first equation (Fe on olivine), we find n = 59, which is in fair agreement with the value of 10 used in ref. [l]. We can use the equation for Y/q to simplify the equation for E,,:
E,,=(2/n)(Y/9)ln(d/2a). Thus
the effective
“temperature”
depends
mainly
on
VIII. SPU’ITERING
562
T.A. Tombrello / Track damage and erosion of insulators
the material through Y. If we use the temperature for UF, [14] to determine E,,, we obtain n =i 43. Returning to the relation:
data
the emission of heavy molecular heavy projectiles [34].
ions caused
by very
d2h a Q’( Yx)-l,
4. Conclusions
we note that this implies that d and X are proportional to ( Q’)1’3. If we replace Q’ by dE/dx we see the reason for the slow variation of d with ion energy and atomic number. Using this relation we reproduce quite well the variation in d with 6 for Ar on mica (see tabie 2) and the variation of d and X for mica, labradorite and olivine. The change in the average energy per particle ejected (effective temperature) with dE/dx observed by ref. [14] is less well described by this model, We note that the dependence on dE/dx arises only from the ln(d/2a) term; since d varies as (dE/dx)rj3, the variation is in the right direction but produces only about half the change observed experimentally. We note that this model also describes the behavior of the erosion yield with incident charge state, 4. For less highly charged ions the variation with 4 is controlled by Q’, i.e. q2_ N(c) is determined by the most tightly bound electrons of the projectile and does not depend on q until q becomes sufficiently high that there are vacancies in the inner electron shells of the projectile ion. At this point N(e) increases very rapidly - as shown in the K-shell ionization data of Cocke et al. [31]. The S versus q data in refs. [8] and 1141 exhibit this behaviour. It should be noted that Dartyge et al. assumed that A did not depend on 6 when N(e) was extracted from their data [22]. Thus, since we find that X is proportional to we should compare (dE,/dx)1/3 am(e) with (Q’)“3, their N(t). This is done in figs. 3 and 4 as dashed lines. We see from this comparison that although the relative magnitudes of the curves are excellent, the shapes are not correct. Because of electron capture processes that grow very rapidly with the 2 of the projectile, it is obvious that the binary encounter model is inadequate for most K-shell ionization processes - see for example refs. [32] and [33]. However, there are neither data nor detailed models for energies significantly above the peak m ox, or for such systems where a light target atom is bombarded by a much heavier projectile. (It seems clear that the presence of excited projectile ions and L (and bier)-shell vacancy formation in heavier target constituents may play a significant role that cannot be easily dealt with theoretically.) Thus, measurements of inner shell ionization cross sections at high energies and for very asymmetric systems are an essential ingredient in extensions of the work shown here. Finally, as mentions earlier, when hN( e) becomes sufficiently large (i.e. for very heavy ions) the erosion yield will vary approximately as d* [i.e. as (dE/dx)2/3]. This saturation behavior has in fact been observed in
From what we have summarized here it is clear that the erosion of insulators by MeV/amu ions is a common phenomenon whose systematic behavior is linked to the ion’s exitation of electrons in the material. We have attempted to provided a simple framework with which a variety of related observations are linked and estimates made for new experimental situations. Although the scaling methods given are not yet as strongly anchored to theory as we would like, the obvious success of the simple model given here may provide a guide for more elaborate versions that treat the evolution of the excited electronic system more exactly. It is also clear that the inner-shell ionization mechanism should be incorporated into more detailed models like that of ref.
WI. It is especially important that the methods suggested be checked in greater detail. This will require more small angle X-ray scattering data of the sort given in ref. [22] as well as track etching rate measurements in a wider variety of materials. Measurements of ion erosion yields and inner vacancy production should also be extended to materials whose properties give a more definitive test of the extrapolation procedures and models. The observation that SiO, shows the enhanced erosion effect only for targets whose thicknesses are greater than three atomic layers deserves greater attention. This phenomenon may give as many new insights into the target material as it provides for the mechanism itself. If one could make sufficiently well characterized, uniform targets, studying the variation in the erosion yield with target thickness should be quite interesting. Although a detailed quantitative theory does not really exist, the overall systematic phenomenology of electronic excitation erosion is sufficiently well known that it can be applied. Generally, we can probably predict the high energy erosion of insulators about as well as we can predict their low energy sputtering yields, and that is certainly good enough for many purposes of application, e.g. to planetary science [35] or technology
[1,3a. One should be aware that the triggering mechanism proposed here may also be important in other contexts. For example, the observation that the adhesion of a thin film to a substrate can be enhanced by fast heavy ion bombardment may also involve inner-shell vacancy formation in initiating atomic processes that lead to increased binding [37-39,361. The fact that low energy electrons (- 2 keV, i.e. near the peak of ukr) can also produce this effect is certainly consistent with the model described here [40].
563
T.A. Tombrello / Track damage and erosion of insulators
I would like to acknowledge discussions with my colleagues {Peter Haff and Charles Watson) and students (Kelly Cherrey) that have helped me to organize and refine the ideas contained in this paper. Special thanks are also owed to Robert Fleischer who has provided a number of references that were otherwise unknown to the author. I am, in this regard, indebted to Keith Jones and Patrick Richard who helped me to find references to relevant data on K-shell ionization processes. Both Noriaki Itoh and Bo Sundqvist provided essential ideas during the development of this model. Finally, I express my appreciation to Allan Bromley for his hospitality at Yale University, where I have found a peaceful spot to write this paper.
References [l] R.L. Fleischer, P.B. Price and R.M. Walker, Nuclear tracks in solids (University of California Press, Berkeley, 1975). [2] P.K. Haff, Appl. Phys. Lett. 29 (1976) 443. [3] W.L. Brown, L.J. Lanzerotti, J.M. Poate and W.M. Augustyniak. Phys. Rev. Lett. 40 (1979) 1027. [4] F. Besenbacher, J. Bottiger, 0. Graversen and J.L. Hansen, Nucl. Instr. and Meth. 191 (1981) 221. [S] B.H. Cooper and T.A. Tombrello, Rad. Eff. (1983) in press. [6] R.D. McFarliane and D.F. Torgerson, Int. J. Mass Spectrom. Ion Phys. 21 (1976) 81. [7] P. Duck, W. Treu, W. Gaister, H. FrohIich and H. Voit, Nucl. Instr. and Meth. 168 (1980) 601. [8] P. Hakansson, E. Jayasinge, A. J8hansson. I. Kamensky and B. Sundqvist, Phys. Rev. Lett. 47 (1981) 1227. [9] J.P. Biersack and E. Santer, Nucl. Instr. and meth. 132 (1976) 229. [lo] M. Szymonski, H. Overeijnder and A.E. de Vries, Rad, Eff. 36 (1978) 189. [ll] J.E. Griffith, R.A. Weiler, L.E. Seiberling and T.A. Tombrello, Rad. Eff. 51 (1980) 223. [12] Y. Qiu, J.E. Griffith and T.A. Tombrello, Rad. Eff. 64 (1982) 111. ]13] Y. Qiu, J.E. Griffith, W.J. Meng and T.A. Tombreilo, Rad. Eff. 70 (1983) 231. [14] C.K. Meins, J.E. Griffith, Y. Qiu. M.H. Mendenhall, L.E. Seiberling and T.A. Tombrello, Rad. Eff. 71 (1983) 13.
1151 L.E. Seiberling,
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Rad. 179. T.A. sub-
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VIII. SPLJT’IERING