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Shape of the target region affected by the cascade recoils
Nuclear Instruments and Methods in Physics Research 218 (1983) 747-750 North-Holland, Amsterdam
747
S H A P E OF THE TARGET REGION AFFECTED BY THE CASCADE RECOILS T.D. ANDREADIS,
M.L. ROUSH,
F. D A V A R Y A
and G.P. CHAMBERS
Uhemwal and Nuclear ~ngineering Department, Uni~ersiO' of Maryland, College Park, Maryland 20742, USA
O.F. GOKTEPE Nat~al Surface Weapons Center, White Oak, Maryland 20910, USA
Joseph FINE Surface Science Division, National Bureau of Standards, Washington, D.C. 20234, USA
Ion bombardment of materials causes the sputtering, i.e., ejection into the vacuum, of target atoms from the near surface layers. Sputtered atoms leave the target in the vicinity of the point where the incident ion strikes the surface. In addition each incident beam ion and the recoil cascade it initiates dislodge target atoms in a volume of target situated about an extension into the solid of the path of the incident ion. The dependence of the above phenomena on the angle of incidence and the energy of the ion beam have been examined using the Monte Carlo computer program EVOLVE. In the EVOLVE simulation, incident ions as well as the cascade recoils produced within the medium are followed until they escape from the solid or their energy falls below a low-energy cut-off value. The target composition is treated in semi-infinite slab geometry. Relocation and movement of target atoms by the beam and cascade recoils are recorded in three dimensions. Scattering angles are calculated using a realistic atomic potential.
I. Introduction Most of the atoms ejected from a target under ion b o m b a r d m e n t originate from the first few atom layers [1]. Sputtered atoms are dislocated directly by the ion b o m b a r d m e n t as well as by recoil atoms set into motion by moving target atoms. In order to be sputtered, a dislocated atom must be near the surface and it must either be set in m o t i o n towards the surface or it must become directed towards the surface by subsequent collisions it experiences with other atoms. There is usually a chain of collision events from the first primary knock-on produced by an incident ion before a sputtered a t o m is produced. Thus the sputtered atom may be far removed from the i o n - t a r g e t atom collision which initiated the cascade. As the angle of incidence is increased from normal incidence towards more oblique angles, the sputtering yield rises to a peak and then decreases to zero as tangential incidence is approached [2]. The dependence of the sputtering yield on the angle of incidence of the ion b e a m is noteworthy since the sputtered atom is unlikely to have any " m e m o r y " of the direction of the incident ion. It is possible that, though a sputtered atom does not contain m u c h information about the incident ion's angle, the information is distributed in the cascade as a whole. If this is true, then such information may be 0 1 6 7 - 5 0 8 7 / 8 3 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
in part contained in the spatial distribution of recoil production in the target. The sputtering yield is also d e p e n d e n t on the energy of the incident ions. Such a dependence is to be expected as the n u m b e r of recoils produced in the nearsurface region is d e p e n d e n t upon the energy of the incident ion. Very little information is found in the literature a b o u t the shape of the recoil density distribution. Shimizu et al. [3] traced the trajectories of recoil atom motion through the target for various incident angles a n d energies. In addition there is some work on the angular and energy distribution [4,5] of sputtered atoms; these results carry information a b o u t interactions beneath the surface. E V O L V E [6], a computer program which simulates ion b o m b a r d m e n t of materials, was used to study the shape of the collision cascade's recoil density for a single ion (or a very thin beam) in the solid. Struck atoms which do not receive enough energy to be displaced from their site are not included. It is assumed the shape of the recoil density distribution can give an insight into the origin of the dependence of sputtering yield on the angle of incidence of the beam. As the regions with higher collision densities are brought closer to the surface the sputtering yield increases. C o m p u t e r
748
72D. Andreadis et al. / Shape of target region affected I~v cascade recoiA'
simulations were carried out for Si targets b o m b a r d e d by 5 keV a n d 15 keV Ar atoms. The incident angles used were 0 ° and 60 ° with respect to the surface normal. Simulations were made for all the c o m b i n a t i o n s of the two energies and two angles. The shape of the intensity of recoil p r o d u c t i o n in the target was obtained by outlining the disturbed region, from various perspectives, with contours of the recoil production density. Each c o n t o u r represents a locus of points of equal recoil density. The sputtered atoms generally leave the surface at exit points which are not far removed from the point of impact of the incident ion. We have also examined the distributions of exit locations of sputtered particles on the X Y plane of the surface, where the surface normal denotes the Z-axis.
L i n d h a r d a n d Scharff [12] was used to calculate electronic energy loss.
3. Shape of recoil c a s c a d e Fig. 1 displays four selected recoil track patterns, each for a single 15 keV A r ion incident upon silicon. The superposition of 20 such patterns is shown in fig. le, where the dark interior gives an indication of the average shape of the recoil cascade. The individual track p a t t e r n s show considerable variation from cascade to cascade. In the following we will deal with the average spatial behavior and with recoil p r o d u c t i o n density distributions. To obtain the average response, the spatial distribu-
15-keV Ar BEAM Si TARGET
laJ
2. C o d e description
The M o n t e Carlo Code, E V O L V E [6], is used to simulate atomic collision cascade effects in the ion b o m b a r d m e n t of solids. The cascade d e v e l o p m e n t is affected by the mass difference [7,8] and the different binding energies [9] (surface and bulk) of the constituents. E V O L V E treats the transport a n d scattering of ions ( a n d recoil atoms) in a solid as in a r a n d o m walk problem. The trajectories of individual particles are followed in the form of straight-line segments joining points of interaction. The target is treated in slab geometry with the elemental composition of each slab evolving in order to represent the system. A t o m s in the target are treated as r a n d o m l y located. A t o m - a t o m interactions are treated in the binary approximation. If the struck atom receives kinetic energy in excess of a displacement energy, E j , the atom leaves its site with a kinetic energy T - E d , where T is the energy loss of the incident atom. Beam atoms and recoiling target atoms are all tracked through the target until they leave the surface or lose sufficient energy to fall below 1.2 eV. A moving atom may escape from the target on reaching the surface by overcoming the surface b i n d i n g energy, E~, which was represented by using a p l a n a r model [10]. The scattering angle for individual interactions is d e p e n d e n t upon a r a n d o m l y selected impact p a r a m e t e r a n d is found by integration of the classical centralpotential scattering integral. The T h o m a s Fermi potential with the screening function of Moliere [11] was used as the interaction potential. A calculation of electronic energy loss was carried out for each segment of path length using the present material composition for that layer. Since the ion velocities involved here are less than the velocity of the electrons in the first Bohr orbit, the formulation of
!
!
{a) J
Ar~.~
(b)
/
Ar >.
.....
~
(c)
T-( Ar~ .
--*-
k _.
~-,~.-,, ~
..Jr
(d)
(e)
Fig. 1. Track patterns are shown in (a-d) for single 15 keV Ar ions incident normally upon St. The trajectories are shown for both incident ion and all recoil atoms. The lines emerging from the surface indicate reflecting ions or sputtered atoms. The combined tracks for 20 particles are shown in (e).
749
T.D. Andreadis et al. / Shape of target region affected by cascade recoils 5-keV Ar BEAM e=o o ~
5-keV Ar BEAM 8 6=60 o
!V A TAR
~';~!'/">~/~1,,,~£~//:;Y/,~//,' , )//)//)2))7 ,//////Z:j')/~'////)'S~,,,~ ~,~////////////,~jJ U~ (a) "~.., (b)
)
15-keV Ar BEAM
nrr
15-keV Ar BEAM
8=0° l
:~>;~?:~////b//////////2 (c)
,
Si TARGET
Fig. 2. Recoil density contours are shown for Ar bombardment of Si. The incident energy is 5 keV for (a) and (b) and 15 key for (c) and (d). The angle of incidence is 0 ° for (a) and (c) and 60 ° for (b) and (d).
tion of the number of recoils produced was recorded for the trajectories associated with 5000 incident particles. This was accomplished by dividing the target into a three dimensional rectangular mesh of small volumes with an integer assigned to each volume. The integer assigned to a volume was incremented whenever a recoil was created in that volume. After the simulation was complete, the data were processed to exhibit features of the recoil production density distribution. The perspectives used to illustrate the shapes are those an observer would see facing the X Y, X - Z , or Y - Z planes. In the case of the X - Y plane, all recoils within a given X - Y grid interval were summed (independent of Z ) to obtain a projection onto the X - Y plane. The contours represent lines along points of equal recoil density. In all the cases presented here the ion beam's impact point is the origin, the beam is in the X - Z plane, and the beam has a positive velocity component in the X direction for oblique angles. Fig. 2a shows the recoil density distribution produced by bombardment of a Si target by normally-incident 5 keV Ar atoms. The innermost contour represents the higher recoil production density. If the maximum recoil density is normalized to 6, the curves will represent densities of 5, 3, and 1. As expected, the distribution is reasonably symmetrical about the impact point. The innermost contour which represents the higher number density extends into the target along the direction of the incident ion. The succeeding contours appear to be increasingly spherical in shape. A study was made to determine the sensitivity to choice of displacement energy, E d. By reducing E,~ from 14 eV [13] to a very low value of 1.2 eV, a large increase was observed in the total number of recoils produced
a) RECOIL PRODUCTION DISTRIBUTION
b) DISTRIBUTION OF EXIT LOCATIONS OF SPUTTERED PARTICLES
Fig. 3. (a) Projected recoil density distribution for 15 keV Ar normally incident on a silicon target. The Ar ions strike the shown plane surface at the center. (b) Distribution of the exit locations of the sputtered Si atoms.
but no change was observed for the shape of the recoil production distribution. The outermost contour tended to be slightly larger but of the same shape as shown in fig. 2. Fig. 2c shows the recoil density distribution for normal incidence under 15 keV bombardment. Unlike the 5 keV case the latter two lower-density contours retain the cylindrical nature of the first contour. The higher energy ions are less likely to undergo large-angle scattering and tend to retain the inward directed momentum within the cascade (incident ion and recoiling atoms). Oblique incidence brings the regions of high recoil density closer to the surface of the target as may be seen in figs. 2b and 2d. As more recoils are produced closer to the surface the sputtering yield will increase. Fig. 3a shows the projection of the recoil density distribution onto the X Y plane for normally incident 15 keV Ar ions. The distribution peaks sharply at the axis along which the beam is incident, dropping to 1 / e of the peak intensity at 3.9 nm from the axis.
4. Distribution of exit locations for sputtered particles Fig. 3b displays the intensity of sputtered particles as a function of position of the exit location. This distribution is even more narrowly peaked than that in fig. 3a, reflecting the narrow nature of the recoil cascade at the point of entry on the surface. Here the intensity drops to 1 / e of the peak value at 2.1 nm from the point of incidence of the ion beam. The projection of recoil production density shown in fig. 3a reflects the broader nature of the recoil cascade at points well below the surface. Fig. 4 shows the distribution of the exit locations for
750
]2 D. A ndreadis et a L / Shape of target region affected l~y cascade recmlv
{t) I.U .J 0
A
/
B
(a) 5-keVAr BEAM
,oo
[ / ~
Lu .6
A
if)
0
~_.9a.'UJ
x (nm)
8
12
~
~:~ g
4
a
(b)
I-I.-60
-8
-4
0 y
4
8
(nm)
Fig. 4. (a) Number of sputtered particles as a function of the x coordinate on the surface for 5 keV Ar incident on Si. The Ar ions strike the target at x = 0. (b) Distribution of the sputtered particles in the y direction are shown for fixed x value at the points A and B. sputtered Si target atoms due to 5 keV Ar b o m b a r d ment at an angle of 60 ° . The distribution of sputtered particles as a function of the X-coordinate of exit locations is displayed in fig. 4a. Fig. 4b shows slices taken t h r o u g h the distribution at the points A a n d B in fig. 4a. A t o m s sputter preferentially from the portion of the target which lies a h e a d of the b e a m a n d past the impact p o i n t on the surface. This result is in agreement with previous calculations [6]. The distribution has a crest along the X axis, i.e., along the direction of the beam.
5. Summary E V O L V E simulations have been utilized to d e m o n strate the track p a t t e r n s formed by trajectories of single b o m b a r d i n g ions along with associated recoil particles.
These patterns are shown to vary greatly from particle to particle. The average behavior of recoil cascades was exhibited by s u m m i n g the recoil production distributions for 5000 incident particle histories. The contours of c o n s t a n t recoil production density are found to be ellipsoidal in nature, with the density concentrated very strongly along the line of the incident ion. As the angle of incidence moves away from the surface normal, a portion of this ellipsoidal recoil cascade is brought closer to the surface where recoils can escape, with corresponding increases in the sputtering yield. As the ion energy is decreased from 15 keV to 5 keV, the average scattering angle increases and a more spherical shape for the cascade is demonstrated. The c o m p u t e r time for this project was supported in full through the facilities of the C o m p u t e r Science Center of the University of Maryland. One of us, GPC, wishes to express his appreciation to the US National Bureau of S t a n d a r d s for the support under cooperative agreement NB 82 N A H A 2039.
References [l] G. Falcone and P. Sigmund, Appl. Phys. 25 (1981) 307. [2] H. Oechsner, Appl. Phys. 8 (1975) 185. [3] R. Shimizu, Proc. 7th Intn. Vac. Congr. and 3rd lntn. Conf. on Solid surfaces, Vienna (1977) p. 1417. [4] T. Okutani, M. Shikata, S. Ichimura and R. Shimizu, J. Appl. Phys. 51 (5) (1980). [5] H. Oechsner, Z. Phys. 238 (1970) 433. [6] M.L. Roush, T.D. Andreadis and O.F. Goktepe, Rad. Eft. 55 (1981) 119. [7] M.L. Roush, T.D. Andreadis, F. Davarya and O.F. Goktepe, Appl. Surf. Sci. 11/12 (1982) 235. [8] M.L. Roush, O.F. Goktepe, T.D. Andreadis and F. Davarya, Nucl. Instr. and Meth. 194 (1982) 611. [9] H.H. Andersen, in: Proc. 10th Yugoslavian Summer School and Symp. on Ionized Gases, ed., M. Matic (Boris Kidric Inst. Nucl. Sci., Belgrade, 1980) p. 421. [10] M. Hou and M.T. Robinson, Appl. Phys. 18 (1979) 381. [11] M.T. Robinson and I.M. Torrens, Phys. Rev. 9 (1974) 5008. [12] J. Eindhard and M. Scharff, Phys. Rev. 124 (1961) 128. [131 H.H. Andersen, Appl. Phys. 18 (1979) 131.
747
S H A P E OF THE TARGET REGION AFFECTED BY THE CASCADE RECOILS T.D. ANDREADIS,
M.L. ROUSH,
F. D A V A R Y A
and G.P. CHAMBERS
Uhemwal and Nuclear ~ngineering Department, Uni~ersiO' of Maryland, College Park, Maryland 20742, USA
O.F. GOKTEPE Nat~al Surface Weapons Center, White Oak, Maryland 20910, USA
Joseph FINE Surface Science Division, National Bureau of Standards, Washington, D.C. 20234, USA
Ion bombardment of materials causes the sputtering, i.e., ejection into the vacuum, of target atoms from the near surface layers. Sputtered atoms leave the target in the vicinity of the point where the incident ion strikes the surface. In addition each incident beam ion and the recoil cascade it initiates dislodge target atoms in a volume of target situated about an extension into the solid of the path of the incident ion. The dependence of the above phenomena on the angle of incidence and the energy of the ion beam have been examined using the Monte Carlo computer program EVOLVE. In the EVOLVE simulation, incident ions as well as the cascade recoils produced within the medium are followed until they escape from the solid or their energy falls below a low-energy cut-off value. The target composition is treated in semi-infinite slab geometry. Relocation and movement of target atoms by the beam and cascade recoils are recorded in three dimensions. Scattering angles are calculated using a realistic atomic potential.
I. Introduction Most of the atoms ejected from a target under ion b o m b a r d m e n t originate from the first few atom layers [1]. Sputtered atoms are dislocated directly by the ion b o m b a r d m e n t as well as by recoil atoms set into motion by moving target atoms. In order to be sputtered, a dislocated atom must be near the surface and it must either be set in m o t i o n towards the surface or it must become directed towards the surface by subsequent collisions it experiences with other atoms. There is usually a chain of collision events from the first primary knock-on produced by an incident ion before a sputtered a t o m is produced. Thus the sputtered atom may be far removed from the i o n - t a r g e t atom collision which initiated the cascade. As the angle of incidence is increased from normal incidence towards more oblique angles, the sputtering yield rises to a peak and then decreases to zero as tangential incidence is approached [2]. The dependence of the sputtering yield on the angle of incidence of the ion b e a m is noteworthy since the sputtered atom is unlikely to have any " m e m o r y " of the direction of the incident ion. It is possible that, though a sputtered atom does not contain m u c h information about the incident ion's angle, the information is distributed in the cascade as a whole. If this is true, then such information may be 0 1 6 7 - 5 0 8 7 / 8 3 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
in part contained in the spatial distribution of recoil production in the target. The sputtering yield is also d e p e n d e n t on the energy of the incident ions. Such a dependence is to be expected as the n u m b e r of recoils produced in the nearsurface region is d e p e n d e n t upon the energy of the incident ion. Very little information is found in the literature a b o u t the shape of the recoil density distribution. Shimizu et al. [3] traced the trajectories of recoil atom motion through the target for various incident angles a n d energies. In addition there is some work on the angular and energy distribution [4,5] of sputtered atoms; these results carry information a b o u t interactions beneath the surface. E V O L V E [6], a computer program which simulates ion b o m b a r d m e n t of materials, was used to study the shape of the collision cascade's recoil density for a single ion (or a very thin beam) in the solid. Struck atoms which do not receive enough energy to be displaced from their site are not included. It is assumed the shape of the recoil density distribution can give an insight into the origin of the dependence of sputtering yield on the angle of incidence of the beam. As the regions with higher collision densities are brought closer to the surface the sputtering yield increases. C o m p u t e r
748
72D. Andreadis et al. / Shape of target region affected I~v cascade recoiA'
simulations were carried out for Si targets b o m b a r d e d by 5 keV a n d 15 keV Ar atoms. The incident angles used were 0 ° and 60 ° with respect to the surface normal. Simulations were made for all the c o m b i n a t i o n s of the two energies and two angles. The shape of the intensity of recoil p r o d u c t i o n in the target was obtained by outlining the disturbed region, from various perspectives, with contours of the recoil production density. Each c o n t o u r represents a locus of points of equal recoil density. The sputtered atoms generally leave the surface at exit points which are not far removed from the point of impact of the incident ion. We have also examined the distributions of exit locations of sputtered particles on the X Y plane of the surface, where the surface normal denotes the Z-axis.
L i n d h a r d a n d Scharff [12] was used to calculate electronic energy loss.
3. Shape of recoil c a s c a d e Fig. 1 displays four selected recoil track patterns, each for a single 15 keV A r ion incident upon silicon. The superposition of 20 such patterns is shown in fig. le, where the dark interior gives an indication of the average shape of the recoil cascade. The individual track p a t t e r n s show considerable variation from cascade to cascade. In the following we will deal with the average spatial behavior and with recoil p r o d u c t i o n density distributions. To obtain the average response, the spatial distribu-
15-keV Ar BEAM Si TARGET
laJ
2. C o d e description
The M o n t e Carlo Code, E V O L V E [6], is used to simulate atomic collision cascade effects in the ion b o m b a r d m e n t of solids. The cascade d e v e l o p m e n t is affected by the mass difference [7,8] and the different binding energies [9] (surface and bulk) of the constituents. E V O L V E treats the transport a n d scattering of ions ( a n d recoil atoms) in a solid as in a r a n d o m walk problem. The trajectories of individual particles are followed in the form of straight-line segments joining points of interaction. The target is treated in slab geometry with the elemental composition of each slab evolving in order to represent the system. A t o m s in the target are treated as r a n d o m l y located. A t o m - a t o m interactions are treated in the binary approximation. If the struck atom receives kinetic energy in excess of a displacement energy, E j , the atom leaves its site with a kinetic energy T - E d , where T is the energy loss of the incident atom. Beam atoms and recoiling target atoms are all tracked through the target until they leave the surface or lose sufficient energy to fall below 1.2 eV. A moving atom may escape from the target on reaching the surface by overcoming the surface b i n d i n g energy, E~, which was represented by using a p l a n a r model [10]. The scattering angle for individual interactions is d e p e n d e n t upon a r a n d o m l y selected impact p a r a m e t e r a n d is found by integration of the classical centralpotential scattering integral. The T h o m a s Fermi potential with the screening function of Moliere [11] was used as the interaction potential. A calculation of electronic energy loss was carried out for each segment of path length using the present material composition for that layer. Since the ion velocities involved here are less than the velocity of the electrons in the first Bohr orbit, the formulation of
!
!
{a) J
Ar~.~
(b)
/
Ar >.
.....
~
(c)
T-( Ar~ .
--*-
k _.
~-,~.-,, ~
..Jr
(d)
(e)
Fig. 1. Track patterns are shown in (a-d) for single 15 keV Ar ions incident normally upon St. The trajectories are shown for both incident ion and all recoil atoms. The lines emerging from the surface indicate reflecting ions or sputtered atoms. The combined tracks for 20 particles are shown in (e).
749
T.D. Andreadis et al. / Shape of target region affected by cascade recoils 5-keV Ar BEAM e=o o ~
5-keV Ar BEAM 8 6=60 o
!V A TAR
~';~!'/">~/~1,,,~£~//:;Y/,~//,' , )//)//)2))7 ,//////Z:j')/~'////)'S~,,,~ ~,~////////////,~jJ U~ (a) "~.., (b)
)
15-keV Ar BEAM
nrr
15-keV Ar BEAM
8=0° l
:~>;~?:~////b//////////2 (c)
,
Si TARGET
Fig. 2. Recoil density contours are shown for Ar bombardment of Si. The incident energy is 5 keV for (a) and (b) and 15 key for (c) and (d). The angle of incidence is 0 ° for (a) and (c) and 60 ° for (b) and (d).
tion of the number of recoils produced was recorded for the trajectories associated with 5000 incident particles. This was accomplished by dividing the target into a three dimensional rectangular mesh of small volumes with an integer assigned to each volume. The integer assigned to a volume was incremented whenever a recoil was created in that volume. After the simulation was complete, the data were processed to exhibit features of the recoil production density distribution. The perspectives used to illustrate the shapes are those an observer would see facing the X Y, X - Z , or Y - Z planes. In the case of the X - Y plane, all recoils within a given X - Y grid interval were summed (independent of Z ) to obtain a projection onto the X - Y plane. The contours represent lines along points of equal recoil density. In all the cases presented here the ion beam's impact point is the origin, the beam is in the X - Z plane, and the beam has a positive velocity component in the X direction for oblique angles. Fig. 2a shows the recoil density distribution produced by bombardment of a Si target by normally-incident 5 keV Ar atoms. The innermost contour represents the higher recoil production density. If the maximum recoil density is normalized to 6, the curves will represent densities of 5, 3, and 1. As expected, the distribution is reasonably symmetrical about the impact point. The innermost contour which represents the higher number density extends into the target along the direction of the incident ion. The succeeding contours appear to be increasingly spherical in shape. A study was made to determine the sensitivity to choice of displacement energy, E d. By reducing E,~ from 14 eV [13] to a very low value of 1.2 eV, a large increase was observed in the total number of recoils produced
a) RECOIL PRODUCTION DISTRIBUTION
b) DISTRIBUTION OF EXIT LOCATIONS OF SPUTTERED PARTICLES
Fig. 3. (a) Projected recoil density distribution for 15 keV Ar normally incident on a silicon target. The Ar ions strike the shown plane surface at the center. (b) Distribution of the exit locations of the sputtered Si atoms.
but no change was observed for the shape of the recoil production distribution. The outermost contour tended to be slightly larger but of the same shape as shown in fig. 2. Fig. 2c shows the recoil density distribution for normal incidence under 15 keV bombardment. Unlike the 5 keV case the latter two lower-density contours retain the cylindrical nature of the first contour. The higher energy ions are less likely to undergo large-angle scattering and tend to retain the inward directed momentum within the cascade (incident ion and recoiling atoms). Oblique incidence brings the regions of high recoil density closer to the surface of the target as may be seen in figs. 2b and 2d. As more recoils are produced closer to the surface the sputtering yield will increase. Fig. 3a shows the projection of the recoil density distribution onto the X Y plane for normally incident 15 keV Ar ions. The distribution peaks sharply at the axis along which the beam is incident, dropping to 1 / e of the peak intensity at 3.9 nm from the axis.
4. Distribution of exit locations for sputtered particles Fig. 3b displays the intensity of sputtered particles as a function of position of the exit location. This distribution is even more narrowly peaked than that in fig. 3a, reflecting the narrow nature of the recoil cascade at the point of entry on the surface. Here the intensity drops to 1 / e of the peak value at 2.1 nm from the point of incidence of the ion beam. The projection of recoil production density shown in fig. 3a reflects the broader nature of the recoil cascade at points well below the surface. Fig. 4 shows the distribution of the exit locations for
750
]2 D. A ndreadis et a L / Shape of target region affected l~y cascade recmlv
{t) I.U .J 0
A
/
B
(a) 5-keVAr BEAM
,oo
[ / ~
Lu .6
A
if)
0
~_.9a.'UJ
x (nm)
8
12
~
~:~ g
4
a
(b)
I-I.-60
-8
-4
0 y
4
8
(nm)
Fig. 4. (a) Number of sputtered particles as a function of the x coordinate on the surface for 5 keV Ar incident on Si. The Ar ions strike the target at x = 0. (b) Distribution of the sputtered particles in the y direction are shown for fixed x value at the points A and B. sputtered Si target atoms due to 5 keV Ar b o m b a r d ment at an angle of 60 ° . The distribution of sputtered particles as a function of the X-coordinate of exit locations is displayed in fig. 4a. Fig. 4b shows slices taken t h r o u g h the distribution at the points A a n d B in fig. 4a. A t o m s sputter preferentially from the portion of the target which lies a h e a d of the b e a m a n d past the impact p o i n t on the surface. This result is in agreement with previous calculations [6]. The distribution has a crest along the X axis, i.e., along the direction of the beam.
5. Summary E V O L V E simulations have been utilized to d e m o n strate the track p a t t e r n s formed by trajectories of single b o m b a r d i n g ions along with associated recoil particles.
These patterns are shown to vary greatly from particle to particle. The average behavior of recoil cascades was exhibited by s u m m i n g the recoil production distributions for 5000 incident particle histories. The contours of c o n s t a n t recoil production density are found to be ellipsoidal in nature, with the density concentrated very strongly along the line of the incident ion. As the angle of incidence moves away from the surface normal, a portion of this ellipsoidal recoil cascade is brought closer to the surface where recoils can escape, with corresponding increases in the sputtering yield. As the ion energy is decreased from 15 keV to 5 keV, the average scattering angle increases and a more spherical shape for the cascade is demonstrated. The c o m p u t e r time for this project was supported in full through the facilities of the C o m p u t e r Science Center of the University of Maryland. One of us, GPC, wishes to express his appreciation to the US National Bureau of S t a n d a r d s for the support under cooperative agreement NB 82 N A H A 2039.
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