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ELECTRONIC SPUTTERING : ANGULAR AND CHARGE-STATE DEPENDENCE OF THE YIELD
VIA SUPERPOSITION
R. Johnson
To cite this version:
R. Johnson. ELECTRONIC SPUTTERING : ANGULAR AND CHARGE-STATE DEPENDENCE
OF THE YIELD VIA SUPERPOSITION. Journal de Physique Colloques, 1989, 50 (C2), pp.C2-251-
C2-257. �10.1051/jphyscol:1989240�. �jpa-00229439�
ELECTRONIC SPUTTERING : ANGULAR AND CHARGE-STATE DEPENDENCE OF THE YIELD VIA SUPERPOSITION
R . E . JOHNSON
Department of Nuclear Engineering and Engineering Physics, University of Virginia, Charlottesville, V A 22901, U . S . A .
Resume : L a desorption Blectronique par ions rapides est traitee en utilisant la superposition d'effets h partir d e points s o u r c e s le long d e la trace d'un ion incident. L a comparaison est faite aver la dependance angulaire d u rendement d 9 C m i s s i o n s pour d e s gaz condens&s s o l i d e s h basse temperature. L'effet d'equilibre d'etats d e charge est considere. I1 est montrC q u e la dependance angulaire peut C t r e expliquee s a n s param&tres libres meme si le transport d'energie s'effectue s u r d e petites distances. Cependant ni l'angle d'incidence, ni I'Ctat d e charge n'induisent d e contraintes s@vOres s u r l@ mecanisme d'4mission.
Abstract
-
Fast-ion induced electronic sputtering (desorption) is treated using the superposition of effects from point sources along the track of an incident ion.Comparison is made with the angular dependence of the sputtering yield for low- temperature condensed-gas solids and the effect of charge-state equilibration is considered. It is shown that the measured angular dependence can be explained without free parameters if energy (momentum) transport occurs even over small distances. However, neither the incident
-
angle dependence nor the charge-state dependence place severe constraints on the ejection mechanism.l
-
IntroductionFast ions are known to stimulate the ejection (sputtering, desorption) of whole molecules, molecular ions, and fragments from molecular insulators. This process is of interest in astrophysics for surfaces consisting of low temperature condensed gases which are embedded in intense plasmas/l/ and as a means of ejecting large bio-molecules into the gas phase for analysis/2/. The ejection processes in both cases have been shown to be determined by the electronic stimulation of the material due to the passage of a fast ion and these processes are related to electron and photon stimulated desorption/3/. However, models for describing the measurements generally have a number of free parameters, so that the mechanisms for conversion of electronic energy into molecular momentum and the nature of the transport of this momentum have not been described quantitatively.
The dependence of the electronic sputtering yields on incident angle and incident ion charge state have been studied for a number of targets as these parameters can be used to vary the energy deposition near the surface. Therefore, aspects of this data set are explained here based, primarily, on the geometry of the excitation function. This is done using a framework in which point sources along the track of the incident ion contribute cooperatively and additively (superposition) to the ejection process at the surface and is an extension of an earlier paper/4/. Such a picture assumes a description of the transport of the disturbance and that the disturbances are additive, which are considerable assumptions for significant perturbations. However, these assumptions allow one to obtain useful analytic expressions and altering them is not expected to lead to major changes in the results presented.
2- Physical Model
P. fast ion passing through an insulating solid produces, primarily, electron-hole pairs. The cooling of the initial charge separation along the track, the cooling of the secondary electrons, and the recombination of electron-hole pairs all result in processes which can energize the molecules in the lattice/3/. Therefore, in the cylindrical region around the
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989240
C2-252 JOURNAL DE PHYSIQUE
path of the ion momentum (energy) impulses may originate which are transported both radially from the track and outward from the surface/5/ as in Fig. la. In this paper the conceptionally simple picture shown in Fig. lb is used to describe aspects of the ejection process. That is, from individual events along the 'track' impulses are generated and move out spherically reaching the surface according to a transport law. At any point in the material, and particularly at the surface, the effects from separate sources can be added to obtain the net effect on the molecules in the solid. It has been shown that small condensed- gas molecules can be ejected from a low temperature, condensed-gas solid by a single such impulse because of the low cohesive energy (e.g. -0.08 eV for Nq at 10K). For these materials the impulse is generated most likely, by a recombination process (e.g. N ~ +
+
e + N+
N in condensed N2)/6/. If the cohesive energy and/or the size of the molecule are increased then multiple impulses, closely spaced in time, may be required for ejection, so that the yields have been found to differ considerably for different materials at low excitation density/7,8/. As the excitation density increases the individual impulses act cooperatively forming a cylindrically energized region. In this region the ejection yields for different condensed-gas species are found to have very similar dependences on the excitation density/8/.It was expected that the angular dependence of the yield should also contain information on the nature of the ejection process. However, Johnson et a1./9/ showed that if the individual excitations are uniformlv distributed along the track at the time of decav and acted at their point of decav then the yield always varied as (cos8)-'. They showed that deviations from this incident angle dependence are caused by a depth dependence in the excitation density and they gave expressions for analyzing the measured angular dependence. In this paper the nature of the angular dependence predicted by a superposition of distributed spikes/4,5,10/
is analyzed in terms of the depth dependence of the excitation function.
Fig.l) (a) Schematic diagram of energy flow from a track in the solid. Also coordinates used in the text are given: z is length along ion's path (track), z' is depth into solid, p is radial distance from track, b is radial distance along surface measured from the intercept of the track with the surface, and Q is the angle of incidence to the surface normal
(all as in re£ ( g ) ) ,
(b) The impulses emanating spherically from four sources along track.
These add to give the net energy flow in Fig l(a).
(c) Spike with radial weighting given as ri2c(ri,t) vs distance from source, ri, at a number of times.
(d) The summed excitation function versus distance along track from Eq (4) obtained by adding spherical contributions in Fig (lb)
Statistically distributed impulses about the path of a fast ion have been used in order to describe the sputtering of condensed N2/10/ and have been used to describe the sputtering of Ar/ll/ due to diffusing excitons. The diffusion equation can be used to describe the transport of energy away from the point of initial deposition,
where e represents some energy density in the solid and r-I is a dissipation (trapping) rate. If the diffusivity n is assumed to be constant, the separate stimulations contributing to ejection at the surface can be treated additively. Cases for n not constant have been
where ri is the radial distance from the source. Here, the spatial integral over the energ density, E , is the initial value (AEo)i and the mean-square radius of the impulse is (3/2) f
S
with an initial value (3/2) fo2. (A time-averaged mean radial extent,
-
4nr+ro2, can be used to replace f2 giving a static estimate of the extent of the disturbance.) When discussing tracks, Eq (2), with r-I = o, is sometimes referred to as the Mozumder model/l4/.Although the function in Eq(2) usually describes diffusion, the form of (ri2E(ri,r)) versus time in Fig (lc) is similar to that of a pressure pulse or momentum transfer from a spherically symmetric impulse. Therefore, the angular dependence for ejection in a 'shock' model of sputtering/l5/ has been treated similarly but without spreading of the impulses. If the process of interest is the volume force at the surface then a better fundamental quantity is ( - Ve)/5/ which has a similar behavior to that in Fig (lc).
Distributing these contributions uniformly along an ion track of infinite extent, for constant average excitation density, gives the cylindrically symmetric solution to Eq. (l),
Here z is along the path of the ion, p is the radial distance measured from the track, and X is the average spacing between those excitations which lead to impulses (AEo) all of the same size. The quantity (dE/dx),ff = (AEo)/X is the effective energy per unit path length going into the impulses.
If the spikes are simply summed as above but the track (i.e., line of sources) is truncated at z=o as in Fig lb, then the energy density at a distance z into the material becomes
where z is measured alonv the track. In this expression the effect of the surface is ignored except as a starting point of the line of sources and erf(y) is the error function
erf (y) = 2
J
Yexp(-x2)dx/n1/20
Therefore, the presence of the surface combined with the transport of energy from depth (via f) produces a z dependence in the excitation function a as in Fig. Id. This z dependence varies in time, as determined by 2 , and can result in the yield having an angular dependence which differs from
cos^)-'.
In the limit that f -+ o, e(p,z, t) + c(p,t) for z # o. That is, no z dependence occurs, in which case the angular dependence of the yield would beassuming the absence of the other surface effects.
The sum of impulsive contributions at the surface, as in Fig lb, for an incident fast ion can be written in general as
cs(b,t) = C € ( P , z ~ ) surf
-
C[(g)eff
dz [+3,2exp(-i ) exp(-t/r) (nf i-.'l
where, as in ref /g/, z = zo X sin0 and p2 = b2
-
zo2, with X -b cos8. The distance from an impulse source to a point on the surface is r2 = (X - - zsin^)^ +
y2+
z2 cos20, where X and y describel?
on the surface with X in the plane of Fig. la. Here the constant c = 2 if the surface is primarily reflecting and c = 1 if no reflection of energy occurs as in Eq.(4). In Eq. (5) (dE/d~)~ff may have a dependence on z due to charge-state equilibration or, at low energies, due to the slowing of the ion/9/. One can also allow for a distribution of excitations about the 'track'.
Although the separate contributions to c at the surface are treated additively, the surface is expected to respond non-linearly. The surface response function, given here as a flux of molecules, i P , will depend on the total impulse €,(E, t) at a radial position l?
on
the surfaceC2-254 JOURNAL DE PHYSIQUE
at time t after the passage of the ion. Therefore, the number of ejected molecules of type j per incident ion is written
Here Pj is the probability of finding species j in the total ejecta from a region around
Ff
at time t/3/. In writing Q we have for convenience scaled c, to the target number density n and cohesive energy U (i.e. the cohesive energy density). In this paper we discuss the total ejecta, given as condensed molecules per ionIn this construction no assumptions have been made about Q except that the integrals exist.
We have discussed a variety of forms for Q/3,11,16/. At low excitation density a probability function is used, which for Ar, N2 and 02 becomes linear in es. At high excitation densities e is often the average energy for a Maxwellian distribution of energies in which case iP is an activated process given as an Arrenhius f ~ n c t i o n ( ~ ~ ~ ~ ~ ) ,
iP = A(es/nU) exp (-nU/cs) (7)
Also a delta function energy distribution has been used for which all molecules at (3,t) have the same value of e/10/. (Note that in ref /9/ SdtQ -t
S
dz' PS ( E , Z' ).
Also, although c is traditionally an energy symbol, it can represent other aspects of the impulse, as determiqed bythe
choice of 9.) The result for uniform distribution of excitations (i.e. (dE/dx),?f independent of z) is reviewed first and then the effect of charge-state equilibrium 1s considered.Uniform Distribution
Scaling all the length variables by f (e.g., b/f = 6, X/?&, etc.) and assuming (dE/dx),ff is inde~endent of z then
Y(0) =
1
d2 6S
dt i2 Q(cdnu) with= c dE
.S
7
(dx)efff(x,Y,O), f = di exp (-i2)exp(-t/r).2af
For a linear surface response function, Q a eS, the integrals are easily performed and Y(B)a cos0-l=oring the decay (,-l
-
o) and setting ro = o, the angular dependence of the yield as given by eqs (8a) and (Sb) can be obtained exactly for a 9 varying more rapidly with c,.Since the only remaining, time dependence in c, i s in the multiplicative factor (f2) the integrals can be rewritten (appendix)
2 - where
(dw/w3) @(W), W = <,/nu
and df f2(%,y)
This result is obtained using changes in the order of the integrations which can be justified as the function f decays rapidly for large values of the variables. For Eq. (9b) to be integrable Q -must grow faster than w2 at small W and grow slower than w2 at large W.
Note that the angular dependence is contained in I(0) which is a spatial integral. It is easily integrated over
f
and2
givingI(0) =
(2)
di' r d i exp(-i 2-+
sin 8(i 2+
2.3 /2)0 0
Changing variables I(0) can be written
Although this result was derived for ro = o it also applies if R, >> ro, where R, is an ' intrinsic' width of an impulse, = AE,/(~U~~/~) (i.e. e(o, t)-nu)
.
ANGLE ( R A D I A N S )
Fig. 2) Data for the relative yield vs. angle of incidence for (~e')~~ on 02 at 10K. Solid line drawn through data points (c0s8-l.~~) dashed llne result in Eq (14a)/4/.
Small Angle Analysis
Iri ref/8/ the deviations from (cost?)-l were examined at small values of [cos@'1-l]. The result Y(0) = Y(o)/cosR is obtained if e(p,z,t) is independent of z. This is not the case for the summed spherical contributions as seen in Eq (4). The result in Eq(l1a) at small
[ c o s ~ - ~ - l ] becomes
Defining Y(o) as
Y(0)
-
$dt $d2b [(r(~.o.t)l~)/n~lit was shown in re£ /8/ that Y(R) could be written quite generally as Y(R) Y(O)/COSR~+~
where for the model described here,
For the a given by Eq (4)
2 2 a 2 a
After some manipulation, using the forms in the appendix, this gives the result in Eq. (llb)
(c
= 2/* = 0.637) if the integral in Eq (9b) exists.C2-256 JOURNAL
DE
PHYSIQUEc
is seen to be a constant in this model, independent of n the details of the form for 0.This can be understood from the expressions in ref. /g/. When the sputtering function acts only in the surface layer (i.e. first term in Eq. (12b) is zero) the
c
w;ls shown to be proportional to the mean-squared radial extent of 6 divided by the square of the mean depth for attaining the bulk value of E . In the model described here both of these quantities are proportional to t2 at all times.If (dE/dx),ff in Eq (6b) depends on z (i.e., e(p,z,t) has an additional surface deficit) then Eq(l2b) can be used to determine an additive correction to the
c
above. However, the results of Gibbs et a1./4/ for ~ e + and charge-state equilibrated ~ e + on condensed 02 showed that the charge-state equilibration effect is small in this target. This is presumably the case also for CO so that its contribution to 5. was over estimated in ref/9/. Below charge equilibration is considered separately for 8=o.Charge-State Eauilibration: Normal Incidence
The form in Eq (5) or (8b) simplifies considerably for 8-0. If there is a depth dependence in (d~/dx),ff i n Eq (5) (i.e. + (dE/d~),~f fe(z)) then the excitation density can be written
(2&) where
Generally, fe(o)
-
1-
A where A is the fractional deficit at the surface/9/ and fe -t 1 for z>> i where i is the equilibration depth. If there is an excess in (dE/d~)~ff at the surface, compared to deeper in the solid, then A is negative. For simplicity we use
in which case the yield becomes
where wo = [0.5 ( d ~ / d x ) ~ ~ ~ / s t ~ ] / n ~ . It is seen from Eq (14) that the charge-state equilibration effect also is relatively insensitive to the form for @ /19/. Using the form
fpr @ in Eq.
( 7 )
with A a constant then C(wo)- (wo-l+l)exp(-wo-l). Writing A = 1-Zi2/Z 2, where Zi is the effective charge of the incoming ion/20/ and Zeq is the equilibrium value:qthen C depends only on t and U which can be obtained by fitting to the available data.
Conclusion
Writing the angular dependence of the yield at small [(cos@)-'-11 as
COS&)-(^+^)
values of 5.different from zero (positive or negative) can be caused by a depth dependence in the excitation function/9/. In the auadratic yield regime the measured angular dependence of the electronic sputtering for solid CO and 02 both give
c
= 0.6. This deviation fromc
= ofor CO was initially attributed to a z-dependence in (dE/dx),ff/9/. However, Gibbs et a1/4/
obtained a similar value for
c
for solid 02 for which the charge equilibrium effects were shown to be small. These measured angular dependences are very close to that obtained using a superposition of diffusive spikes from point sources. The principle requirement is that uniformly distributed events have an influence which propagates outward from the point of deposition so that the effective excieation function has a depth dependence in the near surface region. This can occur via diffusing species or via energy (momentum) transport.For the quadratic regime described here the value of
c
is indeoendent of the parameter n and is also insensitive to the detailed dependence of the sputter function 0. Consistent with the above it was also shown that charge-state equilibration effects are also insensitive to the nature of i P .The author wishes to acknowledge the support of NSF AST Grant-85-0047 and AT&T Bell Labs and Uppsala University while on visits.
The simplifications of the integrals for the yield are well known; we give them here for the convenience of the reader. One can write quite generally
where Yo = c2/(4nx) with C
-
(c/2 nu) (dE/dx&ff. In Eq (A.l) d26-dgd?,6
=b/t and q-l = c/(at2), with qo-l = C/l(aro ) . Because W is separable, W
-
£(C,?) f(q), simplifications can be made. If g = q-,
as in Eq (8b) with 7-l-0, then dq = (-f dw/w ) so that Eq (9a) is obtained if qo = o. For normal incidence f-
exp(-b2) as in Eq (13a) so that d26-
ndIS2 = K (-dw/w) with o<w<g. We can write for qo = o, after changing order of integration,where q(w) is the solution to w
-
g(q). For the case in Eq (13a), W-
q-l F(?), which leads to the result in Eq (14)References
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