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Angle and energy distributions of sputtered particles from molybdenum (110) surfaces
Nuclear Instruments and Methods North-Holland, Amsterdam
in Physics
Research
ANGLE AND ENERGY DIS~IBU~ONS OF SPIED FROM MOLYBDE~M (110) SURFACES * I.R. CHAKAROV, and R.G. VICHEV
V.T. CHEREPIN
81
B39 (1989) 81-8.5
‘) , D.S. KARPUZOV,
PARTICLES
A.A. KOSYACHKOV
‘)
‘)
Institute of Electronics, Bulgarian Acudemy of Sciences, Boul. Lenin 72, Sofin 1784, Bulgaria Ii Institute of Metal Physics, Academy of Sciences of UkSSR. 252142 Kieu, USSR
A secondary ion mass spectrometer with high energy, angle and mass resolution is used to study the energy and angular distributions of ions sputtered from molybdenum (110) surface under 4 keV argon beam bombardment. The sputtering at different beam orientations is also simulated by the MARLOWE computer code. The sputtering yields, in addition to the angular distribution of sputtered particles are assessed as a function of a given angle and energy.
1. Introduction Angle-resolved secondary ion mass spectroscopy has a number of advantages over other sputtering techniques. It allows the surface anisotropy effects to be studied and yields unique information on the top few layers of the crystal surface. Meanwhile, it is well recognized that single-crystal sputtering data are important in proving the sputtering mechanisms. A few early works were devoted specifically to studying processes which contribute to sputtering of crystals by ion beams: channelling, random and focused collisions, etc. [l-3]. The role of the different mechanisms depends on characteristics of the ion beam and crystal parameters and the theory is still far from complete. The depth of origin of the sputtered particles is still a matter of controversy [4]. Even in random targets, the anisotropy of the momentum density in atomic collision cascades proves that momentum conservation in the cascade leads to intrinsic deviations from the asymptotic behaviour E-’ of the energy distributions. Such behaviour of the energy distributions was recognized for isotropic targets following linear cascade theory [5]. Computer simulation studies are more promising since more comprehensive models can be handled. It should be noted, however, that computer data as well as experimental results on crystal sputtering are quite scarce. Most of the data concerns copper single crystals (6-111 and there are no data on bee crystals. “The dependence of sputtered atom energy spectra on the direction of ejection has not been investigated theoretically, although a considerable body of experimental data is available. Such investiga-
* Part of this research
is sponsored
by the Bulgarian
Science
Committee, Research Grant No. 107. 0168-583X/89/$03.50 Q Elsevier Science Publishers (North-Holland Physics ~blishing Division)
B.V.
tions must be made without strong assumptions concerning ejection mechanisms. Computer simulation models can be used for this work in principle, but such calculations may be prohibitively expensive, even in BCA.” (M.T. Robinson, [12]). In this paper we report experimental and computer simulation results on angle-resolved sputtering of MO (110) surface.
2. Experimental All the angular resolved measurements were carried out in a UHV system. The residual gas pressure in the main chamber was 5 X lOAx Pa. The specimen was cut from a mon~~stalline ingot grown by electron-beam zone melting without using a crucible. The surface was oriented within a few minutes to the (110) crystal plane and the misalignement was controlled by an X-ray technique. Following mechanical and electrochemical polishing the sample was cleaned in the vacuum chamber by cyclic heating in vacuum and oxygen atmosphere (at pressure 10e4 Pa and temperature 1700 K) and argon beam sputtering of the surface. Before the measurements, the surface was exposed to brief annealing at higher temperatures. During the sputtering experiments the crystal surface was bombarded by 4 keV argon ions of beam current ion source density 6 X 10P5 A cmm2. The duoplasmotron was differentially pumped in order to maintain the argon pressure in the main chamber below 8 x lo-’ Pa throughout the measurements. The angular resolution of the parabolic analyzer used was 8.6 x 10M3 sr while the energy and mass resolution were within 0.1 eV and 1 m respectively. I. BEAM-SOLID
~NTE~CT~ONS
82
IX. ~hakarov et al. f Angie and energy
3. The simulation model The calculations were performed using the BCA computer code MARLOWE which is described in detail elsewhere [8,12]. Only the aspects specific to the present simulations will be given The target was a molybdenum bee crystal with a perfect (110) surface. In order to save computer time, we used targets having a finite thickness (between 4 and 7 lattice spacings). Primary argon projectiles at 4 keV initiated cascades of binary collisions described by the Moliere approximation to the Thomas-Fermi potential [13] with a screening length suggested by Firsov [14]. To obtain reasonable results on angle dependent energy distributions, the impact parameters of incident primary ions were assumed to be distributed in the incidence plane perpendicular to the MO (110) surface only. Recoil atoms are generated if their energy exceeds a sharp threshold, Ed (36 eV for MO), and are added to the cascade with kinetic energy T- E,, where T denotes the nuclear energy transfer and E, the bulk binding energy (here, E, = 0.2 eV [12]). All atoms are followed in the cascade until their energy falls below a cutoff energy, EC. In general, Usa -K Ed; Us, is the surface binding energy. Because this leads to an underestimation of sputtering yields, a special provision is made in MARLOWE [18] to follow all atoms in the near surface region, independent of Ed, until they escape from the surface or their energy falls below iJs, or EC. However, this produces a sharp edge in the energy distributions of the sputtered atoms near Ed. To avoid this artifact, we choose the “free recoils” model [17,18] which in our case leads to Ed = EC = Us, = 6.82 eV. A planar barrier is adopted in all simulations. For the specific purposes of the present study, provision is made in the MARLOWE code for a sputtering analysis procedure to obtain additional statistical information. A subroutine was developed to give the energy distributions of sputtered atoms at selected angles of ejection. The simulations have been performed over a set of 1~-2~ cascades, except when angle-dependent energy distributions were analysed. In the latter case, first 6000 and later another 38000 cascades were simulated.
of stuttering from Mofl 10)
plained by the channelling of the incident beam in the crystal [ 151. A similar angle-of-incidence dependence was found in the measurements. At angles of incidence, LY,greater than - 70 O, the portion of reflected argon ions sharply increases to 100% which leads to the decrease of the sputtering yield to zero. All further results refer to incidence and analysis in the (110) plane. A general view of the computer simulated energy distributions for different polar angles of ejection 8 (measured from the surface normal), is presented in fig. 2 for angle of incidence (Y= 54.7 o (along a closelypacked atomic direction). The difference in energy spectra taken for a given angle of emission (a = 54.7 o ) is given in fig. 3. With 6 increasing the statistics deteriorates since the number of sputtered atoms decreases. The results are compared to the experimental data for the appropriate interval of 8. We consider the agreement satisfactory. All spectra peak at energies of a few eV and decrease at higher energies. The peaking in the measured spectra is more prominent mostly due to the low-energy particles. The chosen histogram width (2 eV) is not suitable to follow the sharp rise in the region O-5 eV. When the ejection angle 6 increases from zero, the most probable energy is first slightly reduced at 6 = 5” but then rises steadily. The observed shift of the peak of the measured energy spectra of ions leaving the solid surface seems quite important in view of the recent analysis of Oliva and Falcone 1161. According to these authors, the shift to higher energies with increasing 6 can be related to an
5 keV Ar -
MO (1101
4. Results and discussion Fig. 1 illustrates the dependence of the total sputtering yield Y on the angle of incidence obtained by computer sim~ations. The results refer to ions impinging on the (110) crystal surface with trajectories lying in the (100) and (110) planes. As expected, superimposed on the general trend of Y increasing with (Y to - 70 O, one can find broad minima near the closely-packed crystallographic directions. Such a behaviour is ex-
a,ANGLE
OF INCIDENCE
Fig. 1. Dependence of the computed sputteringyield, Y, on the angle of incidence. o, for 4 keV Ar bombardment. The bombarded surface is MO (llO), the plane of incidence being parallel to (110) plane (open circles) or (100) plane (full circles).
83 4 keV
.
AT---MoIllOI
4keV
d=54.73”
AreMo(llOI,
&=!%.73
I_
Fig. 4. Angular distribution of atoms sputtered from MO (110) surface showing anisotropic emission (computer simulation) at different energies of the emitted particles.
ENERGY,
eV
Fig. 2. Energy-polar angle distribution of sputtered particles in the (110) plane
of incidence at o( = 54.7O. Computer tion with 40000 incident Ar ions.
a
1.
b
+
10
20
30
E.e
simula-
ionization process which takes place outside the surface. For some exit angles (corresponding to the closelypacked directions) quite a substantial high-energy part of the distribution was present in the simulations but we have not examined these tails in more detail. For instance, in the 6 = 54-58.5 interval (containing the (112) direction) the number of particles ejected with E > 80 eV exceeded by a factor of 3 compared with those for which 9=0-4.5 and 31.5-36” (with the (110) and (111) directions) and by about a factor of 5 the high energy tails for most other directions. Fig. 4 compares the computed dependence of the ejection probability on the emission angle 6 at different ion energies: 2, 12 and 40 eV. The distribution depends on the energy with the peak corresponding to the closely-packed direction 19= 35.2 o evolving at higher energies. This is related to the fact that the most intense sputtering with atoms exiting near closely-packed directions (cf Wehner spots fl51) occurs at relatively high energies. In fig. 5 we have summarized (over the energy interval from 0 to 30 eV) the computed and measured distributions to obtain the dependence of the ejection probability on the angle of emission 6. The data refer to different incidence angles. For each angle, the experimental and simulated data are normalized to the same
Fig. 3. Energy dist~butions of sputtered MO atoms at different ejection angles. Closed circles and crosses are experimental SIMS data normalized to the maxima of the calculated histograms. a) QeXP= 0 O, tic,,,, = O-4.5 O; b) i&, = 5 O, Qcalc = 4.5-9O; c) i&,=20°, 4,,,,=18-22Sa; d) 8_= 25O, i$,,,, = 22.5-27”; e) 8eXexp = 30”, S,,,, = 27-31.5”; f) tic_+ = 40°, &.,,, = 36-40.5 O.
I. BEAM-SOLID
INTERACTIONS
I.R. Chakarov et al. / Angle and energy of sputtering from Mo(ll0)
84
9. POLAR
EJECTION
ANGLE
Fig. 5. Angular distributions of sputtered particles at different angles of incidence, a, in MO (110) plane bombarded with 4 keV Ar ions. The distributions are integrated over the energy range 0 to 30 eV only. Open circles are experimental points
normalized to the maxima of the calculated histograms.
maximum for the sake of convenience. At small angles of incidence, the geometry of the experimental apparatus prevented the measurements of secondary ions emitted near the normal (small values of 9) to be
Ecdc=2t~eV
carried out. Taking into account statistical errors, the agreement between simulation and experiment is not bad. Best agreement can be seen for the case (Y= 54.7 O, where the number of simulated trajectories is six times that for other angles. All the distributions are rather smooth and do not exhibit sharp maxima. Finally, fig. 6 shows the angular distribution of sputtered particles for different energy intervals as a function of particle energy. They all refer to an angle of incidence LY= 54.7 O. The measured and computed distributions are normalized to cover approximately the same area. For all energies considered, the agreement is quite good. The present computer simulations may also yield information about the depth of origin of sputtered atoms. No correlation between the angle of incidence, a, and the depth of origin distributions was observed. Kelly and Oliva [19] estimate the characteristic depth of sputtering, La/X = 0.80 + 0.10, where I,,, is the characteristic depth and h is the mean atomic spacing. In the present calculations, L,/A = 0.90, with 82% of the sputtered atoms originating from the first layer and 15% from the second.
5. Conclusion The present study demonstrates the power of computer simulation to predict detailed energy and angular distributions of the sputtered particles from single crystals. Several experimental results have been reproduced. Numerical and experimental differential distributions of the sputtered atoms (figs. 3, 5, 6) have been obtained. We consider the agreement to be satisfactory considering the inadequate statistics which so far accompany Monte Carlo methods of obtaining differential distributions [12], and the measurement of only the ionized portion of the sputtered atoms. The obtained energy-polar angle distribution (fig. 2) of the sputtered atoms strongly resembles the one obtained for amorphous targets [20], but peaks corresponding to closely-packed directions can also be identified in the present simulation. The characteristic depth and the depth of origin of the sputtered atoms have been evaluated.
References 9,
POLAR
EJECTION
ANGLE
Fig. 6. Angular distributions of sputtered particles for different energy intervals. Angle of incidence u = 54.7O on the (110) plane. Bombarding particles are Ar ions at 4 keV. Open circles
are experimental points normalized approximately to the area of the calculated histograms.
HI J.H. Fluit, P.K. Rol and J. Kistemaner,
J. Appl. Phys. 34 (1963) 690. Canad. J. Phys. 46 (1968) 739. 121 D. Onderdelinden, Philos. 131 R.S. Nelson, M.W. Thomson and H. Montgomery, Mag. 7 (1962) 1385. [41 P. Sigmund, Nucl. Instr. and Meth. B27 (1987) 1.
I.R. Chakarov et al. /Angle
and energy of sputtering
[5] H.E. Roosendaal and J.B. Sanders. Radiat. Eff. 52 (1980) 137. [6] V.M. Bukhanov, V.E. Yurasova, A.A. Sysoev, G.V. Samsonov and B.I. Nykolaev, Soviet Phys.-Solid State 12 (1970) 313. [7] E. Dennis and R.J. MacDonald, Radiat. Eff. 13 (1972) 243. [S] M. Hou and M.T. Robinson, Appl. Phys. 18 (1979) 381. [S] V.I. Shulga, Radiat. Eff. 70 (1983) 65; 82 (1984) 169; 85 (1985) 1. [IO] M. Hou and W. Eckstein, Nucl. Instr. and Meth. B13 (1986) 324. [ll] D.E. Harrison, W.L. Moore and H.T. Holcombe, Radiat. Eff. (1973) 167. [12] M.T. Robinson, in: Sputtering by Particle Bombardment I, cd. R. Behrisch (Springer, 1981) p. 73.
85
fromMo(Il0)
[13] G. Molihre, 2. Naturforsch, 2a (1947) 133. 1141 O.B. Firsov, J. Exp. Phys. 6 (1958) 534. [l5] H.E. Roosendaal, in: Sputtering by Particle Bombardment I, ed. R. Behrisch (Springer, 1981). [16] A. Oliva and G. Falcone, Nucl. Instr. and M&h. B13 (1986) 377. [17] W. Miiller and W. Eckstein, Nucl. Instr. and Meth. B2 (1984) 814. [18] M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008. [79] R. Kelly and A. Oliva, Nucl. Instr. and Meth. B13 (1986) 283. (201 J.P. Biersack and W. Eckstein, Appl. Phys. A34 (1984) 73.
I. BEAM-SOLID
INTE~~TIONS
in Physics
Research
ANGLE AND ENERGY DIS~IBU~ONS OF SPIED FROM MOLYBDE~M (110) SURFACES * I.R. CHAKAROV, and R.G. VICHEV
V.T. CHEREPIN
81
B39 (1989) 81-8.5
‘) , D.S. KARPUZOV,
PARTICLES
A.A. KOSYACHKOV
‘)
‘)
Institute of Electronics, Bulgarian Acudemy of Sciences, Boul. Lenin 72, Sofin 1784, Bulgaria Ii Institute of Metal Physics, Academy of Sciences of UkSSR. 252142 Kieu, USSR
A secondary ion mass spectrometer with high energy, angle and mass resolution is used to study the energy and angular distributions of ions sputtered from molybdenum (110) surface under 4 keV argon beam bombardment. The sputtering at different beam orientations is also simulated by the MARLOWE computer code. The sputtering yields, in addition to the angular distribution of sputtered particles are assessed as a function of a given angle and energy.
1. Introduction Angle-resolved secondary ion mass spectroscopy has a number of advantages over other sputtering techniques. It allows the surface anisotropy effects to be studied and yields unique information on the top few layers of the crystal surface. Meanwhile, it is well recognized that single-crystal sputtering data are important in proving the sputtering mechanisms. A few early works were devoted specifically to studying processes which contribute to sputtering of crystals by ion beams: channelling, random and focused collisions, etc. [l-3]. The role of the different mechanisms depends on characteristics of the ion beam and crystal parameters and the theory is still far from complete. The depth of origin of the sputtered particles is still a matter of controversy [4]. Even in random targets, the anisotropy of the momentum density in atomic collision cascades proves that momentum conservation in the cascade leads to intrinsic deviations from the asymptotic behaviour E-’ of the energy distributions. Such behaviour of the energy distributions was recognized for isotropic targets following linear cascade theory [5]. Computer simulation studies are more promising since more comprehensive models can be handled. It should be noted, however, that computer data as well as experimental results on crystal sputtering are quite scarce. Most of the data concerns copper single crystals (6-111 and there are no data on bee crystals. “The dependence of sputtered atom energy spectra on the direction of ejection has not been investigated theoretically, although a considerable body of experimental data is available. Such investiga-
* Part of this research
is sponsored
by the Bulgarian
Science
Committee, Research Grant No. 107. 0168-583X/89/$03.50 Q Elsevier Science Publishers (North-Holland Physics ~blishing Division)
B.V.
tions must be made without strong assumptions concerning ejection mechanisms. Computer simulation models can be used for this work in principle, but such calculations may be prohibitively expensive, even in BCA.” (M.T. Robinson, [12]). In this paper we report experimental and computer simulation results on angle-resolved sputtering of MO (110) surface.
2. Experimental All the angular resolved measurements were carried out in a UHV system. The residual gas pressure in the main chamber was 5 X lOAx Pa. The specimen was cut from a mon~~stalline ingot grown by electron-beam zone melting without using a crucible. The surface was oriented within a few minutes to the (110) crystal plane and the misalignement was controlled by an X-ray technique. Following mechanical and electrochemical polishing the sample was cleaned in the vacuum chamber by cyclic heating in vacuum and oxygen atmosphere (at pressure 10e4 Pa and temperature 1700 K) and argon beam sputtering of the surface. Before the measurements, the surface was exposed to brief annealing at higher temperatures. During the sputtering experiments the crystal surface was bombarded by 4 keV argon ions of beam current ion source density 6 X 10P5 A cmm2. The duoplasmotron was differentially pumped in order to maintain the argon pressure in the main chamber below 8 x lo-’ Pa throughout the measurements. The angular resolution of the parabolic analyzer used was 8.6 x 10M3 sr while the energy and mass resolution were within 0.1 eV and 1 m respectively. I. BEAM-SOLID
~NTE~CT~ONS
82
IX. ~hakarov et al. f Angie and energy
3. The simulation model The calculations were performed using the BCA computer code MARLOWE which is described in detail elsewhere [8,12]. Only the aspects specific to the present simulations will be given The target was a molybdenum bee crystal with a perfect (110) surface. In order to save computer time, we used targets having a finite thickness (between 4 and 7 lattice spacings). Primary argon projectiles at 4 keV initiated cascades of binary collisions described by the Moliere approximation to the Thomas-Fermi potential [13] with a screening length suggested by Firsov [14]. To obtain reasonable results on angle dependent energy distributions, the impact parameters of incident primary ions were assumed to be distributed in the incidence plane perpendicular to the MO (110) surface only. Recoil atoms are generated if their energy exceeds a sharp threshold, Ed (36 eV for MO), and are added to the cascade with kinetic energy T- E,, where T denotes the nuclear energy transfer and E, the bulk binding energy (here, E, = 0.2 eV [12]). All atoms are followed in the cascade until their energy falls below a cutoff energy, EC. In general, Usa -K Ed; Us, is the surface binding energy. Because this leads to an underestimation of sputtering yields, a special provision is made in MARLOWE [18] to follow all atoms in the near surface region, independent of Ed, until they escape from the surface or their energy falls below iJs, or EC. However, this produces a sharp edge in the energy distributions of the sputtered atoms near Ed. To avoid this artifact, we choose the “free recoils” model [17,18] which in our case leads to Ed = EC = Us, = 6.82 eV. A planar barrier is adopted in all simulations. For the specific purposes of the present study, provision is made in the MARLOWE code for a sputtering analysis procedure to obtain additional statistical information. A subroutine was developed to give the energy distributions of sputtered atoms at selected angles of ejection. The simulations have been performed over a set of 1~-2~ cascades, except when angle-dependent energy distributions were analysed. In the latter case, first 6000 and later another 38000 cascades were simulated.
of stuttering from Mofl 10)
plained by the channelling of the incident beam in the crystal [ 151. A similar angle-of-incidence dependence was found in the measurements. At angles of incidence, LY,greater than - 70 O, the portion of reflected argon ions sharply increases to 100% which leads to the decrease of the sputtering yield to zero. All further results refer to incidence and analysis in the (110) plane. A general view of the computer simulated energy distributions for different polar angles of ejection 8 (measured from the surface normal), is presented in fig. 2 for angle of incidence (Y= 54.7 o (along a closelypacked atomic direction). The difference in energy spectra taken for a given angle of emission (a = 54.7 o ) is given in fig. 3. With 6 increasing the statistics deteriorates since the number of sputtered atoms decreases. The results are compared to the experimental data for the appropriate interval of 8. We consider the agreement satisfactory. All spectra peak at energies of a few eV and decrease at higher energies. The peaking in the measured spectra is more prominent mostly due to the low-energy particles. The chosen histogram width (2 eV) is not suitable to follow the sharp rise in the region O-5 eV. When the ejection angle 6 increases from zero, the most probable energy is first slightly reduced at 6 = 5” but then rises steadily. The observed shift of the peak of the measured energy spectra of ions leaving the solid surface seems quite important in view of the recent analysis of Oliva and Falcone 1161. According to these authors, the shift to higher energies with increasing 6 can be related to an
5 keV Ar -
MO (1101
4. Results and discussion Fig. 1 illustrates the dependence of the total sputtering yield Y on the angle of incidence obtained by computer sim~ations. The results refer to ions impinging on the (110) crystal surface with trajectories lying in the (100) and (110) planes. As expected, superimposed on the general trend of Y increasing with (Y to - 70 O, one can find broad minima near the closely-packed crystallographic directions. Such a behaviour is ex-
a,ANGLE
OF INCIDENCE
Fig. 1. Dependence of the computed sputteringyield, Y, on the angle of incidence. o, for 4 keV Ar bombardment. The bombarded surface is MO (llO), the plane of incidence being parallel to (110) plane (open circles) or (100) plane (full circles).
83 4 keV
.
AT---MoIllOI
4keV
d=54.73”
AreMo(llOI,
&=!%.73
I_
Fig. 4. Angular distribution of atoms sputtered from MO (110) surface showing anisotropic emission (computer simulation) at different energies of the emitted particles.
ENERGY,
eV
Fig. 2. Energy-polar angle distribution of sputtered particles in the (110) plane
of incidence at o( = 54.7O. Computer tion with 40000 incident Ar ions.
a
1.
b
+
10
20
30
E.e
simula-
ionization process which takes place outside the surface. For some exit angles (corresponding to the closelypacked directions) quite a substantial high-energy part of the distribution was present in the simulations but we have not examined these tails in more detail. For instance, in the 6 = 54-58.5 interval (containing the (112) direction) the number of particles ejected with E > 80 eV exceeded by a factor of 3 compared with those for which 9=0-4.5 and 31.5-36” (with the (110) and (111) directions) and by about a factor of 5 the high energy tails for most other directions. Fig. 4 compares the computed dependence of the ejection probability on the emission angle 6 at different ion energies: 2, 12 and 40 eV. The distribution depends on the energy with the peak corresponding to the closely-packed direction 19= 35.2 o evolving at higher energies. This is related to the fact that the most intense sputtering with atoms exiting near closely-packed directions (cf Wehner spots fl51) occurs at relatively high energies. In fig. 5 we have summarized (over the energy interval from 0 to 30 eV) the computed and measured distributions to obtain the dependence of the ejection probability on the angle of emission 6. The data refer to different incidence angles. For each angle, the experimental and simulated data are normalized to the same
Fig. 3. Energy dist~butions of sputtered MO atoms at different ejection angles. Closed circles and crosses are experimental SIMS data normalized to the maxima of the calculated histograms. a) QeXP= 0 O, tic,,,, = O-4.5 O; b) i&, = 5 O, Qcalc = 4.5-9O; c) i&,=20°, 4,,,,=18-22Sa; d) 8_= 25O, i$,,,, = 22.5-27”; e) 8eXexp = 30”, S,,,, = 27-31.5”; f) tic_+ = 40°, &.,,, = 36-40.5 O.
I. BEAM-SOLID
INTERACTIONS
I.R. Chakarov et al. / Angle and energy of sputtering from Mo(ll0)
84
9. POLAR
EJECTION
ANGLE
Fig. 5. Angular distributions of sputtered particles at different angles of incidence, a, in MO (110) plane bombarded with 4 keV Ar ions. The distributions are integrated over the energy range 0 to 30 eV only. Open circles are experimental points
normalized to the maxima of the calculated histograms.
maximum for the sake of convenience. At small angles of incidence, the geometry of the experimental apparatus prevented the measurements of secondary ions emitted near the normal (small values of 9) to be
Ecdc=2t~eV
carried out. Taking into account statistical errors, the agreement between simulation and experiment is not bad. Best agreement can be seen for the case (Y= 54.7 O, where the number of simulated trajectories is six times that for other angles. All the distributions are rather smooth and do not exhibit sharp maxima. Finally, fig. 6 shows the angular distribution of sputtered particles for different energy intervals as a function of particle energy. They all refer to an angle of incidence LY= 54.7 O. The measured and computed distributions are normalized to cover approximately the same area. For all energies considered, the agreement is quite good. The present computer simulations may also yield information about the depth of origin of sputtered atoms. No correlation between the angle of incidence, a, and the depth of origin distributions was observed. Kelly and Oliva [19] estimate the characteristic depth of sputtering, La/X = 0.80 + 0.10, where I,,, is the characteristic depth and h is the mean atomic spacing. In the present calculations, L,/A = 0.90, with 82% of the sputtered atoms originating from the first layer and 15% from the second.
5. Conclusion The present study demonstrates the power of computer simulation to predict detailed energy and angular distributions of the sputtered particles from single crystals. Several experimental results have been reproduced. Numerical and experimental differential distributions of the sputtered atoms (figs. 3, 5, 6) have been obtained. We consider the agreement to be satisfactory considering the inadequate statistics which so far accompany Monte Carlo methods of obtaining differential distributions [12], and the measurement of only the ionized portion of the sputtered atoms. The obtained energy-polar angle distribution (fig. 2) of the sputtered atoms strongly resembles the one obtained for amorphous targets [20], but peaks corresponding to closely-packed directions can also be identified in the present simulation. The characteristic depth and the depth of origin of the sputtered atoms have been evaluated.
References 9,
POLAR
EJECTION
ANGLE
Fig. 6. Angular distributions of sputtered particles for different energy intervals. Angle of incidence u = 54.7O on the (110) plane. Bombarding particles are Ar ions at 4 keV. Open circles
are experimental points normalized approximately to the area of the calculated histograms.
HI J.H. Fluit, P.K. Rol and J. Kistemaner,
J. Appl. Phys. 34 (1963) 690. Canad. J. Phys. 46 (1968) 739. 121 D. Onderdelinden, Philos. 131 R.S. Nelson, M.W. Thomson and H. Montgomery, Mag. 7 (1962) 1385. [41 P. Sigmund, Nucl. Instr. and Meth. B27 (1987) 1.
I.R. Chakarov et al. /Angle
and energy of sputtering
[5] H.E. Roosendaal and J.B. Sanders. Radiat. Eff. 52 (1980) 137. [6] V.M. Bukhanov, V.E. Yurasova, A.A. Sysoev, G.V. Samsonov and B.I. Nykolaev, Soviet Phys.-Solid State 12 (1970) 313. [7] E. Dennis and R.J. MacDonald, Radiat. Eff. 13 (1972) 243. [S] M. Hou and M.T. Robinson, Appl. Phys. 18 (1979) 381. [S] V.I. Shulga, Radiat. Eff. 70 (1983) 65; 82 (1984) 169; 85 (1985) 1. [IO] M. Hou and W. Eckstein, Nucl. Instr. and Meth. B13 (1986) 324. [ll] D.E. Harrison, W.L. Moore and H.T. Holcombe, Radiat. Eff. (1973) 167. [12] M.T. Robinson, in: Sputtering by Particle Bombardment I, cd. R. Behrisch (Springer, 1981) p. 73.
85
fromMo(Il0)
[13] G. Molihre, 2. Naturforsch, 2a (1947) 133. 1141 O.B. Firsov, J. Exp. Phys. 6 (1958) 534. [l5] H.E. Roosendaal, in: Sputtering by Particle Bombardment I, ed. R. Behrisch (Springer, 1981). [16] A. Oliva and G. Falcone, Nucl. Instr. and M&h. B13 (1986) 377. [17] W. Miiller and W. Eckstein, Nucl. Instr. and Meth. B2 (1984) 814. [18] M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008. [79] R. Kelly and A. Oliva, Nucl. Instr. and Meth. B13 (1986) 283. (201 J.P. Biersack and W. Eckstein, Appl. Phys. A34 (1984) 73.
I. BEAM-SOLID
INTE~~TIONS