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The energy distributions of atoms sputtered from HfC
Volume 82A, number 4
PHYSICS LETTERS
23 March 1981
THE ENERGY DISTRIBUTIONS OF ATOMS SPUTI’ERED FROM HfC ~ Marek SZYMONSKI Institute ofPhysics, Jagiellonian University, Reymonta 4, FL 30-059 Krakow, Poland
Received 22 October 1980 Revised manuscript received 18 November 1980 The energy spectra of Hf and C atoms sputtered from an HfC target with a 6 keV Xe+ beam have been measured. It was found that the target constituents of widely different masses were sputtered with energy distributions of the same form. The results are compared with the collision cascade theory for compound targets.
In order to describe the sputtering process of cornpound targets at least three effects which may lead to nonstoichiometry in the fluxes of sputtered particles
the lower eV-region, which corresponds to Thomas— Fermi scattering [1]. For heavier particles, however, m2 ~O.O55 should be more appropriate. The ratio of
must be taken into consideration. A basic problem concerns the sharing of the projectile energy between the different atomic constituents of a sample. This process may not only depend on the actual composition of the solid, but also on the atomic masses of its constituents. The effect of different binding energies and mobiities of the atomic components additionally complicate the picture, making investigations of preferential sputtering very difficult. A theoretical treatment of the collision cascade process in a homogeneous compound was given by Andersen and Sigmund [1] According to their theory a pronounced nonstoichiometric effect in sputtering from random collision cascades is expected for cornpounds containing atoms of very different masses. The particle flux of i-atoms in binary targets depends on the spectral2(mi_l) energy E in the following way [1]:
fluxes of the light and the heavy constituent, therefore, should depend 2mon energy E: ~ 1(E)I~2 (E) E 1—m2) (2)
.
~
i’~ -‘ -~ E
‘
~‘
where 0 ~ m~~ 1 is the parameter of the simplified power cross section describing the scattering of i-atoms over a limited range of energy [2]. For low-mass atoms, up to about oxygen, m 1 ~0.333 is expected, even in ‘~
The experiment has been performed at the FOM-Instituut voorNetherlands. The Atoom- en Molecuulfysica, Kruislaan 407, Amsterdam,
This result must not be generalized, however, for highfluence bombardment, i.e. under steady-state conditions. According to eq. (2) the fraction of moving atoms of the lighter species increases in the upper parts of the energy spectrum. This means that the light atoms can be ejected from a broader range in depth. Thus the deeper layers are more depleted in the light component than the heavy one. This depletion goes until it balances the increased sputtering yield of fast atoms. The same effect alters the spectrum of the heavy component in quite opposite way. The steadystate energy spectra of both components, therefore, shouldone be would much more perhaps identical,calculathan what expectsimilar, from the zero-fluence tions. Furthermore these spectra should have an intermediate form between those at zero-fluence. In this letter we will present the results of the first experimental test of this prediction. In this regard, the mass selected energy distributions of sputtered Hf and C atoms were measured during bombardment of an HfC target with 6 keY 2. The Xe~measurements ions. The ion current were perdensity formed wasusing 0.5 mA/cm the time of flight spectrometer of the
0 03 1—9163/81/0000—0000/s 02.50 © North-Holland Publishing Company
203
Volume 82A, number 4
PHYSICS LETTERS
are described by eq. (3) with nearly the same param-
Xe4-’ HfC
etersa
1~ua2~0.1.
100 Hf >. t_10
/.
•.......&•
C ,—;~
\. •“.,
\\
~ x
1
\ \
\.
\
\
\
23 March 1981
I
1 10 100 ENERGY (eV) • 1. Hf and C atoms sputtered from an HfC target with Fig. 6 keV Xe~ions. The theoretical energy distributions (solid lines) are presented together with the experimental points. FOM Institute of Atomic and Molecular Physics in Amsterdam described in detail elsewhere [3]. The mass ratio of constituents of this compound is M 2/M1 14.9. energy distributions ed The in fig.experimental 1. In order to analyse the spectraare wepresentextended well known Thompson’s formula [3,4]. Thus the differential flux of i-type sputtered atoms reads as: E/(E + E )(3_t) (3)
Contrary to what was usually expected [5] the steady-state energy distributions of the heavy and the light constituents of the compound are nearly identi. cal except the small difference of binding energies. As was discussed above, this is most likely due to composition gradients induced by nonstoichiometric sputtering of the surface layers. Alternatively the following reasoning can be made. The values of a1 are equal or nearly equal zero. Since 2m2 ~ a~•~<2m1it seems plausible to say that m1 m2 ~ 0.5. Thus the scattering law with m near zero would be appropriate for describing the slowing-down atoms of this compound. Consequently, the possible preferential sputtering due to energy sharing would not be significant, since the ratio of the fluxes for m1 m~ mmaybe written [1]: ~ — (~Ic2) (M2/M1 )2m (4) 1 where c1 is the concentration of the1.3. i-component. For 4~C/cI~Hf equals m =In0.05 the ratio conclusion, we can say that the steady-state energy distributions of atoms sputtered from compound with a large difference in mass of the constituents are properly approximated the formula 3. The form of thisbyequation is the4~’-’E/(E same for dif+ Eb.) ferent components of the target. A possible nonstoichiometric energy sharing process in the collision cascade, as predicted by zero-fluence calculations, does not affect the equilibrium energy spectra of the sputtered atoms.
where Eb 1 is the surface binding energy and a1 is the mass dependent parameter. a1 = 2 m~for zero-fluence sputtering and 2m2 ~ a1 ~ 2m1 for steady-state conditions. Eq. (3) for zero-fluence can be readily obtained from formula (1) by including the effect of the planar binding force. Formula (3) was fitted to the experimental points using the CERN-library computer program MINUIT. The best fits were obtained for the following values of the parameters: 1) for the C spectrum, Eb1 = 4.8 ± 0.3 eV and a1 = 0.0 ± 0.1, 2) for the Hf distribution,Eb2 = 6.7±0.1eY and a2 = 0.12 ± 0.1. The theoretical distributions (3) with the above parameters Eb1 and m~are plotted as solid lmes in fig. 1. It seems justified, therefore, to say that energy distributions of both constituents of the HfC target •
204
•
The author wishes to thank Prof. J. Kistemaker and Dr. A.E. de Yries for making possible the measurements of the energy distributions at the FOM Institute of Atomic and Molecular Physics in Amsterdam, and Mr. A. Haring for supplying the sample. The fruitful discussions with Prof. P. Sigmund, Dr. A.E. de Vries and Dr. JB. Sanders are gratefully acknowledged. References [11 N. Andersen and P. Sigmund, Mat. Fys. Medd. Dan. Vid. Selsk. 39, no.3(1974). [2] K.B. Winterbon, P. Sigmund and J.B. Sanders, Mat. Fys. Medd. Dan. Vid. Seisk. 37, no- 14 (1970). [3] M. Szymoñski, H. Overeijnder and A.E. de Vries Rad. Effects 36 (1978) 189. [4] MW. Thompson, Phil. Mag. 18 (1968) 377. [5] H.H. Andersen, J. Vac. Sci. Technol. 16 (1979) 770.
PHYSICS LETTERS
23 March 1981
THE ENERGY DISTRIBUTIONS OF ATOMS SPUTI’ERED FROM HfC ~ Marek SZYMONSKI Institute ofPhysics, Jagiellonian University, Reymonta 4, FL 30-059 Krakow, Poland
Received 22 October 1980 Revised manuscript received 18 November 1980 The energy spectra of Hf and C atoms sputtered from an HfC target with a 6 keV Xe+ beam have been measured. It was found that the target constituents of widely different masses were sputtered with energy distributions of the same form. The results are compared with the collision cascade theory for compound targets.
In order to describe the sputtering process of cornpound targets at least three effects which may lead to nonstoichiometry in the fluxes of sputtered particles
the lower eV-region, which corresponds to Thomas— Fermi scattering [1]. For heavier particles, however, m2 ~O.O55 should be more appropriate. The ratio of
must be taken into consideration. A basic problem concerns the sharing of the projectile energy between the different atomic constituents of a sample. This process may not only depend on the actual composition of the solid, but also on the atomic masses of its constituents. The effect of different binding energies and mobiities of the atomic components additionally complicate the picture, making investigations of preferential sputtering very difficult. A theoretical treatment of the collision cascade process in a homogeneous compound was given by Andersen and Sigmund [1] According to their theory a pronounced nonstoichiometric effect in sputtering from random collision cascades is expected for cornpounds containing atoms of very different masses. The particle flux of i-atoms in binary targets depends on the spectral2(mi_l) energy E in the following way [1]:
fluxes of the light and the heavy constituent, therefore, should depend 2mon energy E: ~ 1(E)I~2 (E) E 1—m2) (2)
.
~
i’~ -‘ -~ E
‘
~‘
where 0 ~ m~~ 1 is the parameter of the simplified power cross section describing the scattering of i-atoms over a limited range of energy [2]. For low-mass atoms, up to about oxygen, m 1 ~0.333 is expected, even in ‘~
The experiment has been performed at the FOM-Instituut voorNetherlands. The Atoom- en Molecuulfysica, Kruislaan 407, Amsterdam,
This result must not be generalized, however, for highfluence bombardment, i.e. under steady-state conditions. According to eq. (2) the fraction of moving atoms of the lighter species increases in the upper parts of the energy spectrum. This means that the light atoms can be ejected from a broader range in depth. Thus the deeper layers are more depleted in the light component than the heavy one. This depletion goes until it balances the increased sputtering yield of fast atoms. The same effect alters the spectrum of the heavy component in quite opposite way. The steadystate energy spectra of both components, therefore, shouldone be would much more perhaps identical,calculathan what expectsimilar, from the zero-fluence tions. Furthermore these spectra should have an intermediate form between those at zero-fluence. In this letter we will present the results of the first experimental test of this prediction. In this regard, the mass selected energy distributions of sputtered Hf and C atoms were measured during bombardment of an HfC target with 6 keY 2. The Xe~measurements ions. The ion current were perdensity formed wasusing 0.5 mA/cm the time of flight spectrometer of the
0 03 1—9163/81/0000—0000/s 02.50 © North-Holland Publishing Company
203
Volume 82A, number 4
PHYSICS LETTERS
are described by eq. (3) with nearly the same param-
Xe4-’ HfC
etersa
1~ua2~0.1.
100 Hf >. t_10
/.
•.......&•
C ,—;~
\. •“.,
\\
~ x
1
\ \
\.
\
\
\
23 March 1981
I
1 10 100 ENERGY (eV) • 1. Hf and C atoms sputtered from an HfC target with Fig. 6 keV Xe~ions. The theoretical energy distributions (solid lines) are presented together with the experimental points. FOM Institute of Atomic and Molecular Physics in Amsterdam described in detail elsewhere [3]. The mass ratio of constituents of this compound is M 2/M1 14.9. energy distributions ed The in fig.experimental 1. In order to analyse the spectraare wepresentextended well known Thompson’s formula [3,4]. Thus the differential flux of i-type sputtered atoms reads as: E/(E + E )(3_t) (3)
Contrary to what was usually expected [5] the steady-state energy distributions of the heavy and the light constituents of the compound are nearly identi. cal except the small difference of binding energies. As was discussed above, this is most likely due to composition gradients induced by nonstoichiometric sputtering of the surface layers. Alternatively the following reasoning can be made. The values of a1 are equal or nearly equal zero. Since 2m2 ~ a~•~<2m1it seems plausible to say that m1 m2 ~ 0.5. Thus the scattering law with m near zero would be appropriate for describing the slowing-down atoms of this compound. Consequently, the possible preferential sputtering due to energy sharing would not be significant, since the ratio of the fluxes for m1 m~ mmaybe written [1]: ~ — (~Ic2) (M2/M1 )2m (4) 1 where c1 is the concentration of the1.3. i-component. For 4~C/cI~Hf equals m =In0.05 the ratio conclusion, we can say that the steady-state energy distributions of atoms sputtered from compound with a large difference in mass of the constituents are properly approximated the formula 3. The form of thisbyequation is the4~’-’E/(E same for dif+ Eb.) ferent components of the target. A possible nonstoichiometric energy sharing process in the collision cascade, as predicted by zero-fluence calculations, does not affect the equilibrium energy spectra of the sputtered atoms.
where Eb 1 is the surface binding energy and a1 is the mass dependent parameter. a1 = 2 m~for zero-fluence sputtering and 2m2 ~ a1 ~ 2m1 for steady-state conditions. Eq. (3) for zero-fluence can be readily obtained from formula (1) by including the effect of the planar binding force. Formula (3) was fitted to the experimental points using the CERN-library computer program MINUIT. The best fits were obtained for the following values of the parameters: 1) for the C spectrum, Eb1 = 4.8 ± 0.3 eV and a1 = 0.0 ± 0.1, 2) for the Hf distribution,Eb2 = 6.7±0.1eY and a2 = 0.12 ± 0.1. The theoretical distributions (3) with the above parameters Eb1 and m~are plotted as solid lmes in fig. 1. It seems justified, therefore, to say that energy distributions of both constituents of the HfC target •
204
•
The author wishes to thank Prof. J. Kistemaker and Dr. A.E. de Yries for making possible the measurements of the energy distributions at the FOM Institute of Atomic and Molecular Physics in Amsterdam, and Mr. A. Haring for supplying the sample. The fruitful discussions with Prof. P. Sigmund, Dr. A.E. de Vries and Dr. JB. Sanders are gratefully acknowledged. References [11 N. Andersen and P. Sigmund, Mat. Fys. Medd. Dan. Vid. Selsk. 39, no.3(1974). [2] K.B. Winterbon, P. Sigmund and J.B. Sanders, Mat. Fys. Medd. Dan. Vid. Seisk. 37, no- 14 (1970). [3] M. Szymoñski, H. Overeijnder and A.E. de Vries Rad. Effects 36 (1978) 189. [4] MW. Thompson, Phil. Mag. 18 (1968) 377. [5] H.H. Andersen, J. Vac. Sci. Technol. 16 (1979) 770.