- Email: [email protected]
Computer simulation of preferential sputtering
Nuclear Instruments and Methods in Physics Research B7/8 North-Holland, Amsterdam
(1985) 727-734
727
Section IX. Sputtering and SIMS COMPUTER SIMULATION OF PREFERENTIAL SPWITERING W. ECKSTEIN and W. MOLLER Max- Plonck - Insrirut fur Plosmophysrk, EURA
TOM- Association,
D - 8046 Gorching, Fed. Rep. Germany
Static and dynamic TRIM Monte Carlo calculations are employed to study preferential sputtering. Results are restricted to two-component. amorphous, single phase materials. Total as well as partial sputtering yields, energy and angular distributions of the sputtered species, surface concentration and composition profiles are given. In addition, the fluence dependence of the surface composition and the partial sputtering yields is investigated. Recoil densities are compared with data from analytical calculations, and the isotropy of cascades is studied Comparisons with experimental data show good agreement for compounds like TaC, but for metallic alloys the computed results do not agree with all experimental findings.
1. IntrotIttcrIon Preferential sputtering has been investigated experimentally for a long time, as reviewed by Betz and Wehner [l]. In many applications one deals with compound targets, alloys or layered structures, where one has to take into account preferential sputtering until equilibrium conditions are achieved [2]. Analytical theory [3] of sputtering and static computer simulation [4,5] can only describe the starting conditions of an undisturbed target. The change of the sputtering yield, surface composition, depth distribution of composition and possible changes in angular as well as in energy distributions with bombarding time or fluence can only be determined in dynamic calculations, which take all the previous changes into account [6,7]. In this paper we will report on investigations of preferential sputtering with static as well as dynamic computer simulations. It will be shown that some features can well be studied with a static simulation. The targets are restricted to two component single phase materials which are in a randomized (amorphous) state. The results presented show how the recoil density and the cascade isotropy compares with results from analytical theory. Furthermore, results on partial sputtering yields and surface concentrations as a function of dose and angular and energy distributions at equilibrium are given. The targets chosen for the calculations are TaC and TiC which are examples of compound targets, AgPd as an example of a metallic alloy, and TiD, bombarded by D (because it can be treated by a static calculation). The results are compared to experimental data where available.
2. The simulation programs The program TRSPZC is used for the static calculations. This program is an extension of the sputtering
0168-583X/85/$03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
program TRIMSP, which was extensively described in ref. [5]. The new version, TRSP2C, allows a two-component target to be treated. The main features which are included are that the kind of target atoms is chosen randomly according to the target composition, which is uniform throughout the target, and that different surface binding energies for the two target atoms are possible. The inelastic energy loss is treated according to Braggs rule. The choice of the surface binding energies is discussed below for the specific examples. It should be kept in mind that the target has a randomized (amorphous) structure and that a planar surface binding is assumed. The program is based on the binary wllision model with a fixed mean free pathlength X = n-i13, n denoting the total atomic density of the target. However, additional soft collisions within distant cylinder rings around the free path, each representing one atomic volume, are taken into account [S]. For the present calculations, two additional soft collisions are employed. The program TRIDYN22 is applied for the dynamical calculations. Compared to the preceding version, which is described in ref. [7], the present one is wnsistent with the sputtering version TRSPZC, with the maximum number of different components extended to five. It should be mentioned that recoil implantation, cascade mixing and surface recession are covered by TRIDYN simultaneously. Thermal or radiation enhanced diffusion and segregation cannot be taken into account in a program like the present one. This means that only changes due to atomic wllisions are investigated. Time dependent changes due to changes in surface topography are not studied. The surface of the target in the program stays flat (however, rough on an atomic scale [5], i.e. the normal position of the first collision partner of the projectile is randomly chosen).
IX. SPU-fTERING/SIMS
W. Eckstein,
728
W. Miller
10 keV Nt x0
ofpreferentialsputtering
/ Simulation
TaC
: 100“In a x0’
L 5 2 lm
Nc -+ TaC x0 * 100 “In 0.100
06r
I t
a$ at
u1
07
01
r---*-.4
*_____d--=-----
___r_z_,____;___‘----.-w---y---_ IO kcV
_I--_s-=
I.
IO keV
__--
-1
stortmg
C
-05
0 cos V , DIRECTION
.os
partlclc
10
COSINE
Fig. 2. Isotropy of the cascades: The cascades are-started by 1 and 10 keV Ne atoms at a depth of 100 nm and an angle a = 0’ to the surface normal. The cutoff-energy E, is chosen to be equal to the surface binding energy Es = 8.1 eV.
E, RECOIL
ENERGY
f eV)
Fig. 1. Normalized recoil density F(E)/& versus the recoil energy E. The cascades of Ta and C are started by 10 keV NC atoms at a depth of 100 nm and an angle o= O* versus the surface normal. The cutoff-energy EF is chosen to be equal to the surface binding energy E, = 8.1 eV. For comparison the normalized recoil density for U and C [8] calculated by an analytical theory is shown (thick Iines for the energy range given in ref. [8], thin lines extrapolated).
3. Rest&s 3. I. Recoil density Firstly we want to check some predictions of the analytical transport theory [S]. The recoil density plays a central role in the analytical treatment, representing the distribution function of the cascade atoms as function of their start energy. The comparison of the nor-
malized recoil density versus energy is shown in fig. 1. The static computer simulation is done for TaC. The particle creating the Ta-C cascades is a Ne atom with an energy E, = 10 keV starting at a depth x0 = 100 nm, the starting direction is a = 0” (with respect to the
surface normal). The cutoff energy E, = 8.1 eV is chosen equal to the surface binding energy Es, because particles with lower energies do not contribute to sputtering. Comparison with results from an analytical calculation (predicting F(E) - ET2) for uranium carbide shows good agreement with our computer simulation. The choice between U and Ta should make only a small difference. In addition, the starting particle should not be important [8]. Whereas in the analytical calculation the two curves for U and C are parallel, in the computer simulation the slope of the C curve seems to be slightly steeper than the slope for the Ta curve. 3.2. Isotropy of cascades To our knowledge, any anisotropy of collision cascades has not been investigated by analytical treatments of multicomponent sputtering. The assumption
that the cascades are isotropic is checked for the same target and the same conditions as in fig. 1. In fig. 2 the number of recoils per solid angle normalized to the number and energy of starting particles is plotted versus the direction cosine with respect to the surface normal. Because of the normal starting conditions (a = 0’) the distribution has azimuthal symmetry around the surface normal. The recoil distribution is found to deviate from isotropy, favouring the forward direction according to the starting particle, but the anisotropy decreases with increasing energy of the starting particle. An opposite energy dependence would be expected for the highly anisotropic primary knockons. Their number, however,
W. Ecksrern. W. MiNer / Smulation o/pre/erenrial sputtermg D-TiD, a. :oo
.
ION
WI.
PKA
o
ION
m
SKA
.
ION
out.
PKA
A
ION
out.
SKA
10
729
!
TI
0
is
g---_r---_-g-S 0 102
,
& % 10-3 c: 5 %
la3 E,. INCIDENT ENERGY (19)
Fig. 3. Relative contributionsof the four indicated processes leading to sputtering for the bombardment of TiD, with D at normal incidence versus the incident energy &.
2
lo-‘ ’
0
I
I
05
10
,
1
15
20
25
DEPTH OF ORIGIN ( nm
I
30
)
Fig. 4. Probability of sputtered Ta and C atoms escaping from different depths. TaC is bombarded with 1 keV 4He at an angle of incidence Q = 70”.
is small compared to the number of essentially isotropic
low-energy recoils, which increases approximately linearly with the starting energy. Fig. 2 also shows that the anisotropy is larger for the heavier Ta atom that for C. Lowering the cutoff energy E, makes the cascade distribution more isotropic, but these low energies do not contribute to sputtering. 3.3. Processes contributing to sputtering
As described in ref. (51, four processes leading to sputtering are distinguished. A PKA (primary knock-on atom) is a sputtered atom which gets its energy from the incident ion, independently of whether it makes additional collisions before it leaves the surface or not. An SKA (second knock-on atom) gets its energy from another target atom. A further distinction is made if the incident ion moves into the bulk (Ion in) or towards the surface (Ion out), when it starts a subcascade leading to sputtering. As an example the sputtering of TiD, by D at normal incidence for several incident energies EO is chosen. The contribution of the four processes for sputtering of Ti and D is shown in fig. 3. Whereas for the sputtering of Ti the PKA’s and SKA’s by reflected ions are the dominant processes, the PKA’s for both reflected and penetrating ions are mainly responsible for the sputtering of D. It should be noted that the present example is repre-
sentative for the single-knockon regime [3] where common analytical treatments are not applicable. 3.4. Depth of origin As shown earlier [5] for monoatomic targets the sputtered particles originate to an overwhelming extent from the first two layers. In the example chosen here for the bombardment of TaC by 1 keV 4He at an angle of incidence Q = 70” the depth of origin ~st~bution of the two species Ta and C are shown in fig. 4. Because of the large mass difference between Ta (181) and C(12), carbon atoms can escape from a much larger depth than Ta atoms. Nevertheless contributions from deeper layers are still small. 3.5. Surface concentrations
It has been proven experimentally [1,9] that the partial surface concentrations of a polyatomic substance converge towards a stationary state with the relative partial sputtering yields given by the relative bulk compositions. Consequently, an approximate result for the stationary surface concentrations can be obtained with the static program by adjusting the bulk concentration so that stoichiometric sputtering is achieved. This proceIX. SPUTTERING/SIMS
W. Eckstein,
730
W. Miiller
/ Simulation
of preferential sputtering
$j 10 I=
‘He
2 ?i
-.ToC
----__--
s Y
05 1keV To& 0 = 30’
lr_4 12:
+
3
to
2
0
se
Ne
eAr
,‘
t=
4
y(C)/y(b).
lXP
6
6
0 10
ENERGY TRANKER
H 12
1L
RATIO
I
16
IkeV TIC a=M*
c
; OS-
Y 9
* .’
s+--+-
+
I= ^. t ”
Oo
1 y ICI I y ITi),
sxP
4Hs
XaArNe
heat of formation H, of the molecule:
H
3
2 ENERGY
TRANSFER
i 10’~ He I cm2 1
-Fig. 6. Change of the surface composition of Ta as a function of ion fluence. Comparison of the result of a dynamic calculation with experimental data [9]. TaC is bombarded with ‘He at four different energies Eo at an angie of incidence a = 30°.
z Y S
32
ION FLUENCE
I L RATIO
Fig. 5. Equilibrium surface concentrations of Ta and Ti due to bombardment by different incident ions at an angle of incidence Q= 30’. Results determined by a static and dynamic calculations are compared with experimentalresults. y is the
Es = Hs + H, (for compound AB).
Cl) If there is an enrichment of one compound the surface binding energy Es for the enriched element is de-
maximum transferrableenergy.
dure neglects the dependence of the concentration profile on depth. However,‘the results are found to be in good agreement with those obtained by the dynamic program as shown in fig. 5. The advantage in using the static program to calculate equilibrium surface concentrations is the much shorter computing time. The choice of the surface binding energies is as follows: For each element of the compound the surface binding energy Es is chosen as the sum of the heat of sublimation Ifs of the pure element plus the value of the
Xe -
AsoePdo2
1 I
I
I i I
\ I I i
1 5
I I I 10
5 keV OSkeV
OSkeV
Table 1 Heat of subhmation, Ii,, of elements and heat of formation, HF. of compounds used in this paper H, (eV) Ta
8.10 I
C
7.43
Ti
4.84 2.95 3.90
43 Pd
If, (eV/atom) 0.77 0.46
ION FLUENCE f1O’5 crr~-~) Fig. 7. Surface composition of a silver-palladium alloy versus the ion fluence. Ag,,Pd,, is bombarded with Xe at three different energies. The result of a dynamic calculation is compared with experimental results 1121.
731
W. Eckstem, W. Miiiler / Simuiaii~ o~pre~erentiu~sputtering
termined by a hnear interpolation between the above calculated value (1) and the value for the pure element, whereas the surface binding energy for the element with the lower concentration is taken from formula (1). The values for H, and H, are taken from ref. [lo] and shown in table 1. TaC was chosen because of the large mass difference between the two constituents and their similar surface binding energies. In this case a mass effect is expected to dominate the preferential sputtering of C. For the other case of Tic the lower mass constituent has a higher surface binding energy so that the mass effect should be canceiled to some extent by a surface binding effect. This is actuahy the case as shown in fig. 5. The enrichment of Ta is quite large for all ions lighter than Ar, whereas the enrichment of Ti is small for all ions investigated. Experimental data [ll] are in reasonable overall agreement with the calculated data. The experimental data show a tendency to lower enrichment of the heavy component than the calculated results, which might be due to surface topography influencing the experimental values or mechanisms additional to collisional ones [Z]. The larger surface enrichment of Ti due to H embedment in the experiment may be due to chemical effects [II]. The dynamic surface composition change is shown in fig. 6. Here the Ta surface composition due to bombardment of TaC with 4He at an angle of incidence (a = 30°, experimental conditions) and for different incident energies EO is plotted versus the ion fluence. Again the calculation demonstrates the same behaviour as the experiments [9], but the calculated equilibrium concentrations are somewhat higher than the experimental data. The computational results are in reasonable agreement with earlier TRIDYN calculations [7] neglecting soft collisions (see sect. 2). For the alloy Ag,,Pd,a, bombarded with Xe at two energies the result of a dynamic calculation is shown in fig. 7. The surface composition changes only slightly due to the bombardment, whereas in the experiment [12] transients can be seen, which cannot be reproduced in the calculation. It seems to us that these transients cannot be explained by collisional effects, rather segregation of diffusion may be responsible [2]. The surface binding energies used in these calculations are given in table 1. 3.6. Energy distributions The embedment of TiDz with D was chosen as an example for energy distributions of sputtered particles This ion-target combination can be treated with the static program, because the bombardment of Ti with D reproduces TiD, (y-phase) continuously, which grows in depth as long as the bombardment continues [13]. There is no concentration change in the depth from which the
1
10
lo2
E. ENERGY OF SPUTT.(REFLECTED)
103 PART. (eV)
Fig. 8. Energy distributions of sputtered Ti and D and of reflected D. TiD, is bombarded by 0.5 keV D at normai incidence, a = 0”.
sputtered particles originate. Fig. 8 shows the energy distributions of both sputtered species and the reflected D. In this case the surface binding energies were chosen to be Es(Ti) = 4.89 eV and Es(D) = 3.65 eV. The surface binding energy Es(D) is chosen as the sum of the enthalpy of solution in the y-hydride phase and the dissociation energy of the hydrogen molecule [14]. The energy distributions of both sputtered species look very similar, with the main difference that the maximum of the D-distribution is at a higher energy (- 2.5 eV). 3.7. Angular distributions
The bombardment of TaC by 1 keV 4He, at an angle of incidence a! = 70°, was chosen to demonstrate differences in the angular distributions of both sputtered species. The total angular distributions are shown in fig. 9 as a contour line plot. A contour line presents an intensity per solid angle. The highest intensities appear near the plane of incidence {azimuthal angle cp=O”) and medium polar angles. The angular dist~butions are shown for starting conditions (relative bulk concentration of the heavy component x = OS), for stoichiometric sputtering calculated with the static program (x = 0.78) and with the dynamic program. The main difference in the distributions of Ta and C is the high intensity ridge in the carbon distribution. This ridge can be attributed to PKA and sputtering in one binary collision [5,15]. IX. SPUTTERING,‘SIMS
W. Eckstein.
732
W. Miiller
/ Simulation
of prejerentiai
sputtering
Ta
6CP dyn. x = 0.5
30° (r IP30@60@90@
120s
lso@
o”
lw
Q, AZIMUTHAL
w
60@
900
120’
1500
lw
ANGLE
Fig. 9. Angular distributions of sputtered Ta and C in the form of contour line plots (lines represent equal intensities per solid angle). Results of three different calculations for the bombardment of TaC with 1 keV 4He at an incident angle (I = 70” are shown. The upper four plots are results of static calculations with a target composition x (Ta,C,_,). The lower two plots are calculated with the dynamic program.
The
change
in the angular
distributions
for one
con-
due to the three calculations is rather small. This also means that the angular distributions depend only weakly on the surface composition. stituent
3.8. Partial and total sputtering yields
Amongst the many examples of alloy sputtering in the literature [l] we have chosen Ag,Pd, _-x because this is an example where the masses are nearly equal but the binding energies differ by about 30%. Fig. 10 shows the relative and total sputtering yields for two choices of the surface binding energies. For the full points it was assumed that the surface binding energies for Ag and Pd are the same and varied linearly between the values for the pure metals. For this case it is clear that the points lie on a straight line. The second choice keeps the surface binding energies for both constituents equal to
the values of the pure elements independent of the composition. For this case the partial sputtering yield for Ag is larger than for Pd leading to an enrichment of Pd at the surface. This is in agreement with experimental data [16,17) but the component sputtering yield ratio defined in ref. [l] Y&/Y& = 1.32 resulting from fig. 10 is somewhat smaller than the experimental values which vary from 2.4 1161 to 1.5 1171. The calculated sputtering yield ratio of the pure elements Y,,/Y,, = 1.27 is not far from the experimental value 1.4 for 0.6 keV Ar [Et]. Finally, in fig. 11 the total sputtering yield for the bombardment of TaC with 1 keV 4He at normal incidence is compared with experimental results [19]. The inclusion of soft collisions (see section 2) leads to an increase of the sputtering yields compared to earlier calculations [7] by up to a factor of 2. The calculated and experimental results are in good agreement. The insert shows the fluence dependence of the partial yields.
W. Eckstem,
0.5 keVAr
-
W. Miller
/ Simulation
of preferential
733
sputtering
Stoichiometric sputtering or equilibrium conditions reached at a fluence of about 6 x 10” atoms/cm2.
Ag,Pd,_,
are
4. Conclusions
L
0 Pd
x
Ag
Fig. 10. Relative partial and total sputtering yields of Ag and is bombarded with 0.5 keV Ar at normal Pd. Ag,Pd,_, incidence. 0 - Surface binding energies of Ag and Pd equal but linearly interpolated between the values for the pure metals. 0 - Surface binding energies equal to those of the pure metals, but independent of composition.
This paper demonstrates that the static and dynamic binary collision Monte Carlo programs are well suited to describe two component sputtering phenomena as total and partial sputtering yields and their fluence dependence. Also the determination of surface concentrations at equilibrium or before reaching stationary conditions show good agreement with experimental results as for the case of TaC. Transients observed experimentally in metallic alloys due to a change in the bombarding energy have not been observed in calculated resulted. This may indicate the influence of other effects such as segregation and diffusion. The angular distributions of species with a large mass difference are quite different at non-normal incidence as was also shown earlier experimentally [20]. The change in the angular distributions due to different surface compositions is small. The energy distributions of the two constituents are shown in this paper for one example, but the change of energy distributions due to other parameters will be studied in future work. This paper further demonstrates that the light species such as C of a compound target can originate from greater depths than the usually assumed two surface layers. It also makes clear that for the different target species the relative contributions of processes leading to sputtering can be largely different. Finally it is shown that the assumption of the isotropy of cascades is not well justified at low energies, whereas the recoil density is in good agreement with results from analytical theory. It should be mentioned that the choice of binding energies for both components especially during a change of surface composition remains problematic.
References [I] G. Bets and G.K. Wehner, in: Sputtering
[2]
13) Fig. 11. Total sputtering yield at equilibrium of TaC due to bombardment with ‘He at normal incidence versus incident energy. Full points represent results from dynamic calculations. open points are experimental data [19). Also, a semiempirical fit function [19] is shown. The insert shows the partial sputtering yields of C and Ta versus the He fluence.
[4] [5] [6] (71
by Particle Bombardment II, ed., R. Behrisch (Springer-Verlag. Berlin, 1983) p. 11. H.H. Andersen, in: Ion Implantation and Beam Processing, eds., J.S. Williams and J.M. Poate (Academic Press Australia, Sydney, 1984) ch. 6, p. 128. P. Sigmund, in: Sputtering by Particle Bombardment I, ed., R. Behrisch (Springer-Verlag, Berlin, 1981) p. 9. M.T. Robinson, J. Appl. Phys. 54 (1983) 2650. J.P. Biersack and W. Eckstein. Appl. Phys. 34 (1984) 73. M.L. Roush, T.D. Andreadis and O.F. Goktepe, Radiat. Effects 55 (1981) 119. W. Moller and and W. Eckstein, Nucl. Instr. and Meth. B2 (1984) 814. IX. SPUTTERING/SIMS
734
W. Eckstein, W. Malier / Sirn~ari~
[S] N. Andersen and P. Sigmund, Kong. Dan. Vid. Selskab Mat.-Fys. Medd. 39 (1974) no. 3. [9] E. Taglatter and W. Heiland, Proc. Symp. on Sputtering, eds., P. Varga, G. Bets and F.P. Viehbock (Vienna, 1980) p. 423. (101 R. Hultgren. R.L. Orr, P.D. Anderson and K.K. Kelly, Selected Values for the Thermodynamic Properties of Metals and ABoys (Wiley, New York, 1963). (111 P. Varga and E. Taglauer, 3. Nucl. Mater. 111-112 (1982) 726. [12) G. Betz, M. Opitz and P. Braun, Nucl. Instr. and Meth. 182/183 (1981) 63. 1131 J. Roth, W. Eckstein and J. Bohdansky, Radiat. Effects 48 (1980) 231.
ofpre~ereenrial sputtering
1141 W.M. MuelIer, J.P. Blackledge and G.G.Libowita, eds., Metal Hydrides (Academic Press, New York, 1968). 1151 J. Roth, J. Bohdansky and W. Efkstein. Nucl. Instr. and Meth. 218 (1983) 751. (161 H.J. Mathieu and D. Landolt, Surface Sci. 53 (1975) 228. 1171 G.J. Slusser and N. Winograd, Surface Sci. 84 (1979) 211. 118) N. Lallreid and G.K. Wehner, J. Appl. Phys. 32 (l%l) 365. [19] J. Roth, J. ~dansky, and A.P. Martinelli, Radiat. Effects 48 (1980) 213. f20] J. Roth and J. Bohdansky, J. Nucl. Mater. 103 (1981) 339.
(1985) 727-734
727
Section IX. Sputtering and SIMS COMPUTER SIMULATION OF PREFERENTIAL SPWITERING W. ECKSTEIN and W. MOLLER Max- Plonck - Insrirut fur Plosmophysrk, EURA
TOM- Association,
D - 8046 Gorching, Fed. Rep. Germany
Static and dynamic TRIM Monte Carlo calculations are employed to study preferential sputtering. Results are restricted to two-component. amorphous, single phase materials. Total as well as partial sputtering yields, energy and angular distributions of the sputtered species, surface concentration and composition profiles are given. In addition, the fluence dependence of the surface composition and the partial sputtering yields is investigated. Recoil densities are compared with data from analytical calculations, and the isotropy of cascades is studied Comparisons with experimental data show good agreement for compounds like TaC, but for metallic alloys the computed results do not agree with all experimental findings.
1. IntrotIttcrIon Preferential sputtering has been investigated experimentally for a long time, as reviewed by Betz and Wehner [l]. In many applications one deals with compound targets, alloys or layered structures, where one has to take into account preferential sputtering until equilibrium conditions are achieved [2]. Analytical theory [3] of sputtering and static computer simulation [4,5] can only describe the starting conditions of an undisturbed target. The change of the sputtering yield, surface composition, depth distribution of composition and possible changes in angular as well as in energy distributions with bombarding time or fluence can only be determined in dynamic calculations, which take all the previous changes into account [6,7]. In this paper we will report on investigations of preferential sputtering with static as well as dynamic computer simulations. It will be shown that some features can well be studied with a static simulation. The targets are restricted to two component single phase materials which are in a randomized (amorphous) state. The results presented show how the recoil density and the cascade isotropy compares with results from analytical theory. Furthermore, results on partial sputtering yields and surface concentrations as a function of dose and angular and energy distributions at equilibrium are given. The targets chosen for the calculations are TaC and TiC which are examples of compound targets, AgPd as an example of a metallic alloy, and TiD, bombarded by D (because it can be treated by a static calculation). The results are compared to experimental data where available.
2. The simulation programs The program TRSPZC is used for the static calculations. This program is an extension of the sputtering
0168-583X/85/$03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
program TRIMSP, which was extensively described in ref. [5]. The new version, TRSP2C, allows a two-component target to be treated. The main features which are included are that the kind of target atoms is chosen randomly according to the target composition, which is uniform throughout the target, and that different surface binding energies for the two target atoms are possible. The inelastic energy loss is treated according to Braggs rule. The choice of the surface binding energies is discussed below for the specific examples. It should be kept in mind that the target has a randomized (amorphous) structure and that a planar surface binding is assumed. The program is based on the binary wllision model with a fixed mean free pathlength X = n-i13, n denoting the total atomic density of the target. However, additional soft collisions within distant cylinder rings around the free path, each representing one atomic volume, are taken into account [S]. For the present calculations, two additional soft collisions are employed. The program TRIDYN22 is applied for the dynamical calculations. Compared to the preceding version, which is described in ref. [7], the present one is wnsistent with the sputtering version TRSPZC, with the maximum number of different components extended to five. It should be mentioned that recoil implantation, cascade mixing and surface recession are covered by TRIDYN simultaneously. Thermal or radiation enhanced diffusion and segregation cannot be taken into account in a program like the present one. This means that only changes due to atomic wllisions are investigated. Time dependent changes due to changes in surface topography are not studied. The surface of the target in the program stays flat (however, rough on an atomic scale [5], i.e. the normal position of the first collision partner of the projectile is randomly chosen).
IX. SPU-fTERING/SIMS
W. Eckstein,
728
W. Miller
10 keV Nt x0
ofpreferentialsputtering
/ Simulation
TaC
: 100“In a x0’
L 5 2 lm
Nc -+ TaC x0 * 100 “In 0.100
06r
I t
a$ at
u1
07
01
r---*-.4
*_____d--=-----
___r_z_,____;___‘----.-w---y---_ IO kcV
_I--_s-=
I.
IO keV
__--
-1
stortmg
C
-05
0 cos V , DIRECTION
.os
partlclc
10
COSINE
Fig. 2. Isotropy of the cascades: The cascades are-started by 1 and 10 keV Ne atoms at a depth of 100 nm and an angle a = 0’ to the surface normal. The cutoff-energy E, is chosen to be equal to the surface binding energy Es = 8.1 eV.
E, RECOIL
ENERGY
f eV)
Fig. 1. Normalized recoil density F(E)/& versus the recoil energy E. The cascades of Ta and C are started by 10 keV NC atoms at a depth of 100 nm and an angle o= O* versus the surface normal. The cutoff-energy EF is chosen to be equal to the surface binding energy E, = 8.1 eV. For comparison the normalized recoil density for U and C [8] calculated by an analytical theory is shown (thick Iines for the energy range given in ref. [8], thin lines extrapolated).
3. Rest&s 3. I. Recoil density Firstly we want to check some predictions of the analytical transport theory [S]. The recoil density plays a central role in the analytical treatment, representing the distribution function of the cascade atoms as function of their start energy. The comparison of the nor-
malized recoil density versus energy is shown in fig. 1. The static computer simulation is done for TaC. The particle creating the Ta-C cascades is a Ne atom with an energy E, = 10 keV starting at a depth x0 = 100 nm, the starting direction is a = 0” (with respect to the
surface normal). The cutoff energy E, = 8.1 eV is chosen equal to the surface binding energy Es, because particles with lower energies do not contribute to sputtering. Comparison with results from an analytical calculation (predicting F(E) - ET2) for uranium carbide shows good agreement with our computer simulation. The choice between U and Ta should make only a small difference. In addition, the starting particle should not be important [8]. Whereas in the analytical calculation the two curves for U and C are parallel, in the computer simulation the slope of the C curve seems to be slightly steeper than the slope for the Ta curve. 3.2. Isotropy of cascades To our knowledge, any anisotropy of collision cascades has not been investigated by analytical treatments of multicomponent sputtering. The assumption
that the cascades are isotropic is checked for the same target and the same conditions as in fig. 1. In fig. 2 the number of recoils per solid angle normalized to the number and energy of starting particles is plotted versus the direction cosine with respect to the surface normal. Because of the normal starting conditions (a = 0’) the distribution has azimuthal symmetry around the surface normal. The recoil distribution is found to deviate from isotropy, favouring the forward direction according to the starting particle, but the anisotropy decreases with increasing energy of the starting particle. An opposite energy dependence would be expected for the highly anisotropic primary knockons. Their number, however,
W. Ecksrern. W. MiNer / Smulation o/pre/erenrial sputtermg D-TiD, a. :oo
.
ION
WI.
PKA
o
ION
m
SKA
.
ION
out.
PKA
A
ION
out.
SKA
10
729
!
TI
0
is
g---_r---_-g-S 0 102
,
& % 10-3 c: 5 %
la3 E,. INCIDENT ENERGY (19)
Fig. 3. Relative contributionsof the four indicated processes leading to sputtering for the bombardment of TiD, with D at normal incidence versus the incident energy &.
2
lo-‘ ’
0
I
I
05
10
,
1
15
20
25
DEPTH OF ORIGIN ( nm
I
30
)
Fig. 4. Probability of sputtered Ta and C atoms escaping from different depths. TaC is bombarded with 1 keV 4He at an angle of incidence Q = 70”.
is small compared to the number of essentially isotropic
low-energy recoils, which increases approximately linearly with the starting energy. Fig. 2 also shows that the anisotropy is larger for the heavier Ta atom that for C. Lowering the cutoff energy E, makes the cascade distribution more isotropic, but these low energies do not contribute to sputtering. 3.3. Processes contributing to sputtering
As described in ref. (51, four processes leading to sputtering are distinguished. A PKA (primary knock-on atom) is a sputtered atom which gets its energy from the incident ion, independently of whether it makes additional collisions before it leaves the surface or not. An SKA (second knock-on atom) gets its energy from another target atom. A further distinction is made if the incident ion moves into the bulk (Ion in) or towards the surface (Ion out), when it starts a subcascade leading to sputtering. As an example the sputtering of TiD, by D at normal incidence for several incident energies EO is chosen. The contribution of the four processes for sputtering of Ti and D is shown in fig. 3. Whereas for the sputtering of Ti the PKA’s and SKA’s by reflected ions are the dominant processes, the PKA’s for both reflected and penetrating ions are mainly responsible for the sputtering of D. It should be noted that the present example is repre-
sentative for the single-knockon regime [3] where common analytical treatments are not applicable. 3.4. Depth of origin As shown earlier [5] for monoatomic targets the sputtered particles originate to an overwhelming extent from the first two layers. In the example chosen here for the bombardment of TaC by 1 keV 4He at an angle of incidence Q = 70” the depth of origin ~st~bution of the two species Ta and C are shown in fig. 4. Because of the large mass difference between Ta (181) and C(12), carbon atoms can escape from a much larger depth than Ta atoms. Nevertheless contributions from deeper layers are still small. 3.5. Surface concentrations
It has been proven experimentally [1,9] that the partial surface concentrations of a polyatomic substance converge towards a stationary state with the relative partial sputtering yields given by the relative bulk compositions. Consequently, an approximate result for the stationary surface concentrations can be obtained with the static program by adjusting the bulk concentration so that stoichiometric sputtering is achieved. This proceIX. SPUTTERING/SIMS
W. Eckstein,
730
W. Miiller
/ Simulation
of preferential sputtering
$j 10 I=
‘He
2 ?i
-.ToC
----__--
s Y
05 1keV To& 0 = 30’
lr_4 12:
+
3
to
2
0
se
Ne
eAr
,‘
t=
4
y(C)/y(b).
lXP
6
6
0 10
ENERGY TRANKER
H 12
1L
RATIO
I
16
IkeV TIC a=M*
c
; OS-
Y 9
* .’
s+--+-
+
I= ^. t ”
Oo
1 y ICI I y ITi),
sxP
4Hs
XaArNe
heat of formation H, of the molecule:
H
3
2 ENERGY
TRANSFER
i 10’~ He I cm2 1
-Fig. 6. Change of the surface composition of Ta as a function of ion fluence. Comparison of the result of a dynamic calculation with experimental data [9]. TaC is bombarded with ‘He at four different energies Eo at an angie of incidence a = 30°.
z Y S
32
ION FLUENCE
I L RATIO
Fig. 5. Equilibrium surface concentrations of Ta and Ti due to bombardment by different incident ions at an angle of incidence Q= 30’. Results determined by a static and dynamic calculations are compared with experimentalresults. y is the
Es = Hs + H, (for compound AB).
Cl) If there is an enrichment of one compound the surface binding energy Es for the enriched element is de-
maximum transferrableenergy.
dure neglects the dependence of the concentration profile on depth. However,‘the results are found to be in good agreement with those obtained by the dynamic program as shown in fig. 5. The advantage in using the static program to calculate equilibrium surface concentrations is the much shorter computing time. The choice of the surface binding energies is as follows: For each element of the compound the surface binding energy Es is chosen as the sum of the heat of sublimation Ifs of the pure element plus the value of the
Xe -
AsoePdo2
1 I
I
I i I
\ I I i
1 5
I I I 10
5 keV OSkeV
OSkeV
Table 1 Heat of subhmation, Ii,, of elements and heat of formation, HF. of compounds used in this paper H, (eV) Ta
8.10 I
C
7.43
Ti
4.84 2.95 3.90
43 Pd
If, (eV/atom) 0.77 0.46
ION FLUENCE f1O’5 crr~-~) Fig. 7. Surface composition of a silver-palladium alloy versus the ion fluence. Ag,,Pd,, is bombarded with Xe at three different energies. The result of a dynamic calculation is compared with experimental results 1121.
731
W. Eckstem, W. Miiiler / Simuiaii~ o~pre~erentiu~sputtering
termined by a hnear interpolation between the above calculated value (1) and the value for the pure element, whereas the surface binding energy for the element with the lower concentration is taken from formula (1). The values for H, and H, are taken from ref. [lo] and shown in table 1. TaC was chosen because of the large mass difference between the two constituents and their similar surface binding energies. In this case a mass effect is expected to dominate the preferential sputtering of C. For the other case of Tic the lower mass constituent has a higher surface binding energy so that the mass effect should be canceiled to some extent by a surface binding effect. This is actuahy the case as shown in fig. 5. The enrichment of Ta is quite large for all ions lighter than Ar, whereas the enrichment of Ti is small for all ions investigated. Experimental data [ll] are in reasonable overall agreement with the calculated data. The experimental data show a tendency to lower enrichment of the heavy component than the calculated results, which might be due to surface topography influencing the experimental values or mechanisms additional to collisional ones [Z]. The larger surface enrichment of Ti due to H embedment in the experiment may be due to chemical effects [II]. The dynamic surface composition change is shown in fig. 6. Here the Ta surface composition due to bombardment of TaC with 4He at an angle of incidence (a = 30°, experimental conditions) and for different incident energies EO is plotted versus the ion fluence. Again the calculation demonstrates the same behaviour as the experiments [9], but the calculated equilibrium concentrations are somewhat higher than the experimental data. The computational results are in reasonable agreement with earlier TRIDYN calculations [7] neglecting soft collisions (see sect. 2). For the alloy Ag,,Pd,a, bombarded with Xe at two energies the result of a dynamic calculation is shown in fig. 7. The surface composition changes only slightly due to the bombardment, whereas in the experiment [12] transients can be seen, which cannot be reproduced in the calculation. It seems to us that these transients cannot be explained by collisional effects, rather segregation of diffusion may be responsible [2]. The surface binding energies used in these calculations are given in table 1. 3.6. Energy distributions The embedment of TiDz with D was chosen as an example for energy distributions of sputtered particles This ion-target combination can be treated with the static program, because the bombardment of Ti with D reproduces TiD, (y-phase) continuously, which grows in depth as long as the bombardment continues [13]. There is no concentration change in the depth from which the
1
10
lo2
E. ENERGY OF SPUTT.(REFLECTED)
103 PART. (eV)
Fig. 8. Energy distributions of sputtered Ti and D and of reflected D. TiD, is bombarded by 0.5 keV D at normai incidence, a = 0”.
sputtered particles originate. Fig. 8 shows the energy distributions of both sputtered species and the reflected D. In this case the surface binding energies were chosen to be Es(Ti) = 4.89 eV and Es(D) = 3.65 eV. The surface binding energy Es(D) is chosen as the sum of the enthalpy of solution in the y-hydride phase and the dissociation energy of the hydrogen molecule [14]. The energy distributions of both sputtered species look very similar, with the main difference that the maximum of the D-distribution is at a higher energy (- 2.5 eV). 3.7. Angular distributions
The bombardment of TaC by 1 keV 4He, at an angle of incidence a! = 70°, was chosen to demonstrate differences in the angular distributions of both sputtered species. The total angular distributions are shown in fig. 9 as a contour line plot. A contour line presents an intensity per solid angle. The highest intensities appear near the plane of incidence {azimuthal angle cp=O”) and medium polar angles. The angular dist~butions are shown for starting conditions (relative bulk concentration of the heavy component x = OS), for stoichiometric sputtering calculated with the static program (x = 0.78) and with the dynamic program. The main difference in the distributions of Ta and C is the high intensity ridge in the carbon distribution. This ridge can be attributed to PKA and sputtering in one binary collision [5,15]. IX. SPUTTERING,‘SIMS
W. Eckstein.
732
W. Miiller
/ Simulation
of prejerentiai
sputtering
Ta
6CP dyn. x = 0.5
30° (r IP30@60@90@
120s
lso@
o”
lw
Q, AZIMUTHAL
w
60@
900
120’
1500
lw
ANGLE
Fig. 9. Angular distributions of sputtered Ta and C in the form of contour line plots (lines represent equal intensities per solid angle). Results of three different calculations for the bombardment of TaC with 1 keV 4He at an incident angle (I = 70” are shown. The upper four plots are results of static calculations with a target composition x (Ta,C,_,). The lower two plots are calculated with the dynamic program.
The
change
in the angular
distributions
for one
con-
due to the three calculations is rather small. This also means that the angular distributions depend only weakly on the surface composition. stituent
3.8. Partial and total sputtering yields
Amongst the many examples of alloy sputtering in the literature [l] we have chosen Ag,Pd, _-x because this is an example where the masses are nearly equal but the binding energies differ by about 30%. Fig. 10 shows the relative and total sputtering yields for two choices of the surface binding energies. For the full points it was assumed that the surface binding energies for Ag and Pd are the same and varied linearly between the values for the pure metals. For this case it is clear that the points lie on a straight line. The second choice keeps the surface binding energies for both constituents equal to
the values of the pure elements independent of the composition. For this case the partial sputtering yield for Ag is larger than for Pd leading to an enrichment of Pd at the surface. This is in agreement with experimental data [16,17) but the component sputtering yield ratio defined in ref. [l] Y&/Y& = 1.32 resulting from fig. 10 is somewhat smaller than the experimental values which vary from 2.4 1161 to 1.5 1171. The calculated sputtering yield ratio of the pure elements Y,,/Y,, = 1.27 is not far from the experimental value 1.4 for 0.6 keV Ar [Et]. Finally, in fig. 11 the total sputtering yield for the bombardment of TaC with 1 keV 4He at normal incidence is compared with experimental results [19]. The inclusion of soft collisions (see section 2) leads to an increase of the sputtering yields compared to earlier calculations [7] by up to a factor of 2. The calculated and experimental results are in good agreement. The insert shows the fluence dependence of the partial yields.
W. Eckstem,
0.5 keVAr
-
W. Miller
/ Simulation
of preferential
733
sputtering
Stoichiometric sputtering or equilibrium conditions reached at a fluence of about 6 x 10” atoms/cm2.
Ag,Pd,_,
are
4. Conclusions
L
0 Pd
x
Ag
Fig. 10. Relative partial and total sputtering yields of Ag and is bombarded with 0.5 keV Ar at normal Pd. Ag,Pd,_, incidence. 0 - Surface binding energies of Ag and Pd equal but linearly interpolated between the values for the pure metals. 0 - Surface binding energies equal to those of the pure metals, but independent of composition.
This paper demonstrates that the static and dynamic binary collision Monte Carlo programs are well suited to describe two component sputtering phenomena as total and partial sputtering yields and their fluence dependence. Also the determination of surface concentrations at equilibrium or before reaching stationary conditions show good agreement with experimental results as for the case of TaC. Transients observed experimentally in metallic alloys due to a change in the bombarding energy have not been observed in calculated resulted. This may indicate the influence of other effects such as segregation and diffusion. The angular distributions of species with a large mass difference are quite different at non-normal incidence as was also shown earlier experimentally [20]. The change in the angular distributions due to different surface compositions is small. The energy distributions of the two constituents are shown in this paper for one example, but the change of energy distributions due to other parameters will be studied in future work. This paper further demonstrates that the light species such as C of a compound target can originate from greater depths than the usually assumed two surface layers. It also makes clear that for the different target species the relative contributions of processes leading to sputtering can be largely different. Finally it is shown that the assumption of the isotropy of cascades is not well justified at low energies, whereas the recoil density is in good agreement with results from analytical theory. It should be mentioned that the choice of binding energies for both components especially during a change of surface composition remains problematic.
References [I] G. Bets and G.K. Wehner, in: Sputtering
[2]
13) Fig. 11. Total sputtering yield at equilibrium of TaC due to bombardment with ‘He at normal incidence versus incident energy. Full points represent results from dynamic calculations. open points are experimental data [19). Also, a semiempirical fit function [19] is shown. The insert shows the partial sputtering yields of C and Ta versus the He fluence.
[4] [5] [6] (71
by Particle Bombardment II, ed., R. Behrisch (Springer-Verlag. Berlin, 1983) p. 11. H.H. Andersen, in: Ion Implantation and Beam Processing, eds., J.S. Williams and J.M. Poate (Academic Press Australia, Sydney, 1984) ch. 6, p. 128. P. Sigmund, in: Sputtering by Particle Bombardment I, ed., R. Behrisch (Springer-Verlag, Berlin, 1981) p. 9. M.T. Robinson, J. Appl. Phys. 54 (1983) 2650. J.P. Biersack and W. Eckstein. Appl. Phys. 34 (1984) 73. M.L. Roush, T.D. Andreadis and O.F. Goktepe, Radiat. Effects 55 (1981) 119. W. Moller and and W. Eckstein, Nucl. Instr. and Meth. B2 (1984) 814. IX. SPUTTERING/SIMS
734
W. Eckstein, W. Malier / Sirn~ari~
[S] N. Andersen and P. Sigmund, Kong. Dan. Vid. Selskab Mat.-Fys. Medd. 39 (1974) no. 3. [9] E. Taglatter and W. Heiland, Proc. Symp. on Sputtering, eds., P. Varga, G. Bets and F.P. Viehbock (Vienna, 1980) p. 423. (101 R. Hultgren. R.L. Orr, P.D. Anderson and K.K. Kelly, Selected Values for the Thermodynamic Properties of Metals and ABoys (Wiley, New York, 1963). (111 P. Varga and E. Taglauer, 3. Nucl. Mater. 111-112 (1982) 726. [12) G. Betz, M. Opitz and P. Braun, Nucl. Instr. and Meth. 182/183 (1981) 63. 1131 J. Roth, W. Eckstein and J. Bohdansky, Radiat. Effects 48 (1980) 231.
ofpre~ereenrial sputtering
1141 W.M. MuelIer, J.P. Blackledge and G.G.Libowita, eds., Metal Hydrides (Academic Press, New York, 1968). 1151 J. Roth, J. Bohdansky and W. Efkstein. Nucl. Instr. and Meth. 218 (1983) 751. (161 H.J. Mathieu and D. Landolt, Surface Sci. 53 (1975) 228. 1171 G.J. Slusser and N. Winograd, Surface Sci. 84 (1979) 211. 118) N. Lallreid and G.K. Wehner, J. Appl. Phys. 32 (l%l) 365. [19] J. Roth, J. ~dansky, and A.P. Martinelli, Radiat. Effects 48 (1980) 213. f20] J. Roth and J. Bohdansky, J. Nucl. Mater. 103 (1981) 339.