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Monte-Carlo studies of energy characteristics of carbon plasma fluxes at deposition of diamond-like films
Diamond and Related Materials, 1 (1992) 290 292 Elsevier Science Publishers B.V., Amsterdam
290
Monte-Carlo studies of energy characteristics of carbon plasma fluxes at deposition of diamond-like films V. V. Lyubimov, A. A. Voevodin, A. L. Yerokhin and S. V. Popova Laboratory ~['Electrophysical and Electrochemical Treatment ~[the Tula Polytechnical Institute, 92 Lenin Aye., 300600 Tula (Russia)
Abstract Using the simulation by the Monte-Carlo method, the distribution of carbon plasma particles over the energies of their arrival at the substrate in the deposition of diamond-like films by the arc evaporation of graphite in vacuum has been investigated. The conditions of separation of fluxes according to the particle energies have been established and the optimum substrate potential for the production of films with a diamond-type lattice has been found. A high-quality separation of fluxes necessitates their preliminary acceleration with the aid of the additional anode with a - 1 0 V potential, placed between the cathode and the separator. The optimum substrate potential is at - 18 V with a permissible drift _+3 V.
1. Introduction One of the methods of production of diamond-like films (DLF) is their deposition in vacuum from a carbon plasma flux generated by arc discharge between a graphite cathode and an anode, in the capacity of which can be used the metal walls of a vacuum chamber or an additional electrode placed in a chamber [1]. For the formations of films with a diamond-type lattice the energy of deposited particles must fall within a narrow range limited by the carbon-binding energy in the diamond lattice of 14.6 eV and by the defect production threshold of 60 eV [2]. A carbon plasma flux, generated by arc discharge, contains 70 90% of single charged C + ions [1,3] of 30 eV energy [2, 4] and a low-energy component consisting of undischarged carbon atoms of up to 1 eV and 3-5% of slowly moving graphite macroblocks 1-5 Jam in size [2]. For obtaining the diamond structure of films it is necessary to separate the low-energy component from the total carbon plasma flux by separating the flux according to the particle energies [5]. The flux of C + ions, obtained after separation, has a deviation A E from the mean energy E, which depends on the initial state of plasma and on the quality of separation. Some of the ions can have energies beyond the range of energies favourable for the formation of the diamond film structure due to the energy spread upon their arrival at the substrate even if the mean energy of arrival is within the given range. The presence of at least 1 2% deposited particles with unfavourable energy qualitatively deteriorates the properties of DLF [4]. The energy spectrum of ions arriving at the substrate can be controlled by applying a negative potential to the substrate with the simultaneous application of a high-frequency field of low intensity [1].
0925 9635/92/$05.00
In the present paper, results are considered of investigations of the distribution of particles of carbon plasma flux over their energies of arrival at the substrate and determinate the conditions of the high-quality separation of the flux and the optimum bias potential of the substrate in the production of DLF. The experimental determination of the energy distribution of particles in a plasma flux, generated by arc discharge, is hindered and the fact that the process of deposition of DLF from carbon plasma flux is scantily explored does not make it possible to carry out an analytical search for the distribution of particles over the arrival energies. Therefore, the energy characteristics of a carbon plasma flux using the simulation of deposition of plasma fluxes by the Monte-Carlo method, have been investigated.
2. Assumptions made in the simulation In the simulations of deposition of carbon plasma fluxes by the Monte-Carlo method, the scheme of vacuum chamber, displayed in Fig. 1, has been adopted, the following assumptions have been made: (i) The flux consists of 70% of C + ions and 30% of uncharged atoms [1]. The deposition of macroblocks was disregarded. (ii) The mean energy of particles in a carbon plasma flux constitutes 30 eV for ions and 0.4 eV for atoms [6, 7]. (iii) On the path from the evaporator to the substrate, carbon plasma particles collide with each other. The collision frequency determined by free path 2 = - •ln(l - J , where X is the mean path of particles between collisions [-8], which depends on the carbon
V. V. L.ruhimor ct al.
3. Results and discussion
m
graph i te ~ cathode
~ h
~
~
add i t i onal----lrr : ~ - - n ] anode
~
291
Monte-('arh* stmlie.', O/carhoJl l~ht.sma lh~xes
"
~71
~separator
i
vacuum chamber
/ substrate J
vaouurn pump
Figure 2(a) shows the energy distribution of particles, which arrive at the substrate, as a function of the substrate bias potential, obtained from the simulation of the cleposition of non-separated carbon plasma fluxes. The maxirna on the distribution p(E) correspond to the arrival C + ions and uncharged C ° atoms. The energies of arrival of uncharged atoms are beyond the lower limit of the energies of formation of the diamond structure of films (Fig. 2(a)) and they should be separated from the plasma flux. At substrate potentials U from 0 to 10 V the maxima on the energy distribution overlap and the separation of particles according to the energies in a carbon plasma flux is hindered. A distinct separation of maxima occurs at the absolute value of the accelerating
I Fig. I. Scheme of the vacuum chamber adopted in the simulation of deposition of carbon plasma fluxesgenerated by arc discharge between the graphite cathode and the chamber walls.
0 plasma density, and is a random number in the interval from 0 to 1. (iv) The change in the kinetic energy during a collision is calculated under the assumption that the deflection, h, of collisions from the central impact is given by the relation [ b = ( 2 7 - 1)(Q + r 2 ) ] where r, and re are the radii of the colliding particles. The collisions differ from the elastic ones if the kinetic energy increase exceeds the excitation or the ionization energy [9] for the carbon atom. The energy difference due to the change of the state of the carbon atom, is considered dissipated. (v) Near the substrate surface ions are affected by an accelerating electrostatic field in the dark cathode space, the dimensions of which are determined by the Child Langmuir relation [10]. (vi) In the simulations of the deposition of the separated carbon plasma flux the uncharged atoms were considered to hit the chamber walls and not the substrale. The deposition process was simulated with the aid of a special software, type DEPOS-1. The substrate bias potential, U, was varied from 0 to - 6 0 V. The distance from the graphite cathode to the substrate, L, was 250 mrn. The deposition of 10000 particles was calculated. Changes in the velocity and position of a particle were continuously c~'lculated in order to compute the instant point and energy of its arrival. On completion of the calculation, the results of the simulation were statistically processed for all particles that arrived at the substrate to find the distribution of particles over the arrival energies p(E) with the normalization condition [j'e; p ( E ) dE = 1].
5'.,., 0. 0 t~
o-
0.0
'l'
1.00
,
r
SO
(a)
'
6O
&O 'ZO
0
Energy (eV)
~_0
L _~.o g, 2-,z0 .-~ 0.6 - ' ~
-30
o o.
% o.ZA 0.0 ~00
(b)
c-
-50 '1 80
'~', 60
-60 ~
20
0
Energy (eV)
Fig. 2. The energy distribution of particles arriving at the substrate in the deposition of diamond-like films from carbon plasma fluxes for different substrate potentials. (a) The deposition of non-separated fluxes containing (7 " ions and uncharged (.c, atoms. (b) The deposition of fluxes after separation of uncharged (' atoms from a flux.
I1". V. Lyubimov et al. / Monte-Carlo studies ~lcarbon plasma fluxes
292
potential of l0 V. This value can be used for preliminary acceleration of a carbon plasma flux with the aid of an additional anode placed between the cathode and the separator (Fig. 1) to facilitate the separation of particles according to the energies. The results of the simulation of the deposition plasma fluxes after the separation of the low-energy component are displayed in Fig. 2(b). The character of the energy distribution of the separated flux is approximated to an accuracy of AE~ = 2.1 eV by the Gaussian distribution which has a maximum of p(E)= 0.65 and a dispersion of 5.8 eV. Analysis of the distribution profile shows that the energy of 99% of ions arriving at the substrate has a spread of A E = 18 e g to either side of the mean value E. Consequently, for the number of ions arriving at the substrate with energies unfavourable for the formation of the diamond structure of films, not to exceed 1% the mean energy of arrival of ions must fall within the range from Emin = 33 eV to Emax = 42 eV. To these values of E there correspond substrate potentials of from Umi, = --13 V to Umax = - 2 2 V (Fig. 3). To the error of the calculation of Fml, and Emax, equal to the error AE,, there corresponds an error in the determination of permissible substrate potentials of A U = 2 V. With allowance for A U the optimum substrate potential for obtaining D L F from carbon plasma fluxes is a potential of Uopt = - 1 8 V with a drift of + 3 V (Fig. 3). The obtained results are in good agreement with the recently published data of the experimental studies of 1
I
I
McKenzie et al. [l 1], which show that the best conditions for producing carbon films having tetrahedrical structure with sp 3 bonding arrangement are achieved at an energy of ion flux in the range 20 50 eV. The optimal potential found in the present study corresponds to the energy range recommended in ref. I I (Fig. 3).
4. Conclusions
Investigations by the Monte-Carlo method of the energy distribution of particles, deposited on the substrate from carbon plasma fluxes generated by arc discharge between the graphite cathode and the walls of a vacuum chamber, allow the following conclusions to be drawn: (i) the realization of a high-quality separation of a carbon plasma flux according to the energies of particles necessitates its preliminary acceleration with the aid of an additional anode with a - 1 0 V potential, placed between the cathode and the separator; (ii) the energy distribution of C + ions arriving at the substrate, after separation of the low-energy component of a carbon plasma flux, is approximated to an accuracy of 2.1 eV by the Gaussian distribution with height of 0.65 and a dispersion of 5.8 eV; (iii) the optimum substrate potential for attaining the energy conditions of formation of a high-quality diamond structure of films is a - 1 8 V potential with a permissible drift of ___3 V.
i
References
50
"-" >,
.
.
.
.
E=rC
40
$
i
In3
"
8O
0
-5
-10 -15 P o t e n t i a l (V)
-20
-25
Fig. 3. The change in the mean energy of arrival of C ~ ions as a function of the substrate potential in the deposition of diamond-like films from the separated carbon plasma flux. Shown schematically is the choice of the optimum substrate potential from the permissible values of the mean energy of arrival.
1 V. E, Strel'nitskij, V. G. Padalka and S. I. Vakula, J. Soy. Tech. Phys., 48 (1978) 377. 2 A. F. Balakov and E. A. Konshina, Optiko-Mechanicheskaja Promyshlennost (USSR), 9 (1982) 52. 3 B. L. Gehman, G. D. Magnuson, J. F. Tooker, J. R. Treglio and J. P. Williams, Surf. Coat. Technol., 41 (1990) 389. 4 E. F. Chajkovsky, V. M. Puzikov and A. V. Semenov, Kristallografl~ia (USSR), 1 (1981) 219. 5 I. I. Aksenov, S. I. Vakula, V. G. Padalka, V. E. Strel'nitskij and V. M. Horoshih, J. Soy. Tech. Phys., 50 (1980) 2000. 6 V. M. Lunev, B. D. Ovcharenko and V. M. Horoshih, J. Soy. Tech. Phys., 43 (1977) 1486. 7 P. A, Lindfors, W. M. Mularie and G. K. Whener, Surf. Coat. Technol., 29 (1986) 275. 8 W. D. Westwood, J. Vac. Sci. Technol.. 15 (1978) 1. 9 E. W. McDaniel, Collision Phenomena in lonized Gases, John Willy & Sons, Inc., New York, 1964, Appendix 3.4. 10 F. F. Chen, in R. H. H ~dlstone and S. L. Leonard (eds.), Plasma Diagnostic Techniques, Academic Press, New York, 1965, Chapter 4.2. 11 D. R. McKenzie, D. Muller, B. A. Pailthorpe, Z. H. Wang, E. Kravtchinskaia, D. Segal, P. B. Lukins, P. D. Swift, P. J. Martin, G. Amaratunga, P. H. Gaskell and A. Saeed, Diamond Rel. Mater., 1 (1991) 51.
290
Monte-Carlo studies of energy characteristics of carbon plasma fluxes at deposition of diamond-like films V. V. Lyubimov, A. A. Voevodin, A. L. Yerokhin and S. V. Popova Laboratory ~['Electrophysical and Electrochemical Treatment ~[the Tula Polytechnical Institute, 92 Lenin Aye., 300600 Tula (Russia)
Abstract Using the simulation by the Monte-Carlo method, the distribution of carbon plasma particles over the energies of their arrival at the substrate in the deposition of diamond-like films by the arc evaporation of graphite in vacuum has been investigated. The conditions of separation of fluxes according to the particle energies have been established and the optimum substrate potential for the production of films with a diamond-type lattice has been found. A high-quality separation of fluxes necessitates their preliminary acceleration with the aid of the additional anode with a - 1 0 V potential, placed between the cathode and the separator. The optimum substrate potential is at - 18 V with a permissible drift _+3 V.
1. Introduction One of the methods of production of diamond-like films (DLF) is their deposition in vacuum from a carbon plasma flux generated by arc discharge between a graphite cathode and an anode, in the capacity of which can be used the metal walls of a vacuum chamber or an additional electrode placed in a chamber [1]. For the formations of films with a diamond-type lattice the energy of deposited particles must fall within a narrow range limited by the carbon-binding energy in the diamond lattice of 14.6 eV and by the defect production threshold of 60 eV [2]. A carbon plasma flux, generated by arc discharge, contains 70 90% of single charged C + ions [1,3] of 30 eV energy [2, 4] and a low-energy component consisting of undischarged carbon atoms of up to 1 eV and 3-5% of slowly moving graphite macroblocks 1-5 Jam in size [2]. For obtaining the diamond structure of films it is necessary to separate the low-energy component from the total carbon plasma flux by separating the flux according to the particle energies [5]. The flux of C + ions, obtained after separation, has a deviation A E from the mean energy E, which depends on the initial state of plasma and on the quality of separation. Some of the ions can have energies beyond the range of energies favourable for the formation of the diamond film structure due to the energy spread upon their arrival at the substrate even if the mean energy of arrival is within the given range. The presence of at least 1 2% deposited particles with unfavourable energy qualitatively deteriorates the properties of DLF [4]. The energy spectrum of ions arriving at the substrate can be controlled by applying a negative potential to the substrate with the simultaneous application of a high-frequency field of low intensity [1].
0925 9635/92/$05.00
In the present paper, results are considered of investigations of the distribution of particles of carbon plasma flux over their energies of arrival at the substrate and determinate the conditions of the high-quality separation of the flux and the optimum bias potential of the substrate in the production of DLF. The experimental determination of the energy distribution of particles in a plasma flux, generated by arc discharge, is hindered and the fact that the process of deposition of DLF from carbon plasma flux is scantily explored does not make it possible to carry out an analytical search for the distribution of particles over the arrival energies. Therefore, the energy characteristics of a carbon plasma flux using the simulation of deposition of plasma fluxes by the Monte-Carlo method, have been investigated.
2. Assumptions made in the simulation In the simulations of deposition of carbon plasma fluxes by the Monte-Carlo method, the scheme of vacuum chamber, displayed in Fig. 1, has been adopted, the following assumptions have been made: (i) The flux consists of 70% of C + ions and 30% of uncharged atoms [1]. The deposition of macroblocks was disregarded. (ii) The mean energy of particles in a carbon plasma flux constitutes 30 eV for ions and 0.4 eV for atoms [6, 7]. (iii) On the path from the evaporator to the substrate, carbon plasma particles collide with each other. The collision frequency determined by free path 2 = - •ln(l - J , where X is the mean path of particles between collisions [-8], which depends on the carbon
V. V. L.ruhimor ct al.
3. Results and discussion
m
graph i te ~ cathode
~ h
~
~
add i t i onal----lrr : ~ - - n ] anode
~
291
Monte-('arh* stmlie.', O/carhoJl l~ht.sma lh~xes
"
~71
~separator
i
vacuum chamber
/ substrate J
vaouurn pump
Figure 2(a) shows the energy distribution of particles, which arrive at the substrate, as a function of the substrate bias potential, obtained from the simulation of the cleposition of non-separated carbon plasma fluxes. The maxirna on the distribution p(E) correspond to the arrival C + ions and uncharged C ° atoms. The energies of arrival of uncharged atoms are beyond the lower limit of the energies of formation of the diamond structure of films (Fig. 2(a)) and they should be separated from the plasma flux. At substrate potentials U from 0 to 10 V the maxima on the energy distribution overlap and the separation of particles according to the energies in a carbon plasma flux is hindered. A distinct separation of maxima occurs at the absolute value of the accelerating
I Fig. I. Scheme of the vacuum chamber adopted in the simulation of deposition of carbon plasma fluxesgenerated by arc discharge between the graphite cathode and the chamber walls.
0 plasma density, and is a random number in the interval from 0 to 1. (iv) The change in the kinetic energy during a collision is calculated under the assumption that the deflection, h, of collisions from the central impact is given by the relation [ b = ( 2 7 - 1)(Q + r 2 ) ] where r, and re are the radii of the colliding particles. The collisions differ from the elastic ones if the kinetic energy increase exceeds the excitation or the ionization energy [9] for the carbon atom. The energy difference due to the change of the state of the carbon atom, is considered dissipated. (v) Near the substrate surface ions are affected by an accelerating electrostatic field in the dark cathode space, the dimensions of which are determined by the Child Langmuir relation [10]. (vi) In the simulations of the deposition of the separated carbon plasma flux the uncharged atoms were considered to hit the chamber walls and not the substrale. The deposition process was simulated with the aid of a special software, type DEPOS-1. The substrate bias potential, U, was varied from 0 to - 6 0 V. The distance from the graphite cathode to the substrate, L, was 250 mrn. The deposition of 10000 particles was calculated. Changes in the velocity and position of a particle were continuously c~'lculated in order to compute the instant point and energy of its arrival. On completion of the calculation, the results of the simulation were statistically processed for all particles that arrived at the substrate to find the distribution of particles over the arrival energies p(E) with the normalization condition [j'e; p ( E ) dE = 1].
5'.,., 0. 0 t~
o-
0.0
'l'
1.00
,
r
SO
(a)
'
6O
&O 'ZO
0
Energy (eV)
~_0
L _~.o g, 2-,z0 .-~ 0.6 - ' ~
-30
o o.
% o.ZA 0.0 ~00
(b)
c-
-50 '1 80
'~', 60
-60 ~
20
0
Energy (eV)
Fig. 2. The energy distribution of particles arriving at the substrate in the deposition of diamond-like films from carbon plasma fluxes for different substrate potentials. (a) The deposition of non-separated fluxes containing (7 " ions and uncharged (.c, atoms. (b) The deposition of fluxes after separation of uncharged (' atoms from a flux.
I1". V. Lyubimov et al. / Monte-Carlo studies ~lcarbon plasma fluxes
292
potential of l0 V. This value can be used for preliminary acceleration of a carbon plasma flux with the aid of an additional anode placed between the cathode and the separator (Fig. 1) to facilitate the separation of particles according to the energies. The results of the simulation of the deposition plasma fluxes after the separation of the low-energy component are displayed in Fig. 2(b). The character of the energy distribution of the separated flux is approximated to an accuracy of AE~ = 2.1 eV by the Gaussian distribution which has a maximum of p(E)= 0.65 and a dispersion of 5.8 eV. Analysis of the distribution profile shows that the energy of 99% of ions arriving at the substrate has a spread of A E = 18 e g to either side of the mean value E. Consequently, for the number of ions arriving at the substrate with energies unfavourable for the formation of the diamond structure of films, not to exceed 1% the mean energy of arrival of ions must fall within the range from Emin = 33 eV to Emax = 42 eV. To these values of E there correspond substrate potentials of from Umi, = --13 V to Umax = - 2 2 V (Fig. 3). To the error of the calculation of Fml, and Emax, equal to the error AE,, there corresponds an error in the determination of permissible substrate potentials of A U = 2 V. With allowance for A U the optimum substrate potential for obtaining D L F from carbon plasma fluxes is a potential of Uopt = - 1 8 V with a drift of + 3 V (Fig. 3). The obtained results are in good agreement with the recently published data of the experimental studies of 1
I
I
McKenzie et al. [l 1], which show that the best conditions for producing carbon films having tetrahedrical structure with sp 3 bonding arrangement are achieved at an energy of ion flux in the range 20 50 eV. The optimal potential found in the present study corresponds to the energy range recommended in ref. I I (Fig. 3).
4. Conclusions
Investigations by the Monte-Carlo method of the energy distribution of particles, deposited on the substrate from carbon plasma fluxes generated by arc discharge between the graphite cathode and the walls of a vacuum chamber, allow the following conclusions to be drawn: (i) the realization of a high-quality separation of a carbon plasma flux according to the energies of particles necessitates its preliminary acceleration with the aid of an additional anode with a - 1 0 V potential, placed between the cathode and the separator; (ii) the energy distribution of C + ions arriving at the substrate, after separation of the low-energy component of a carbon plasma flux, is approximated to an accuracy of 2.1 eV by the Gaussian distribution with height of 0.65 and a dispersion of 5.8 eV; (iii) the optimum substrate potential for attaining the energy conditions of formation of a high-quality diamond structure of films is a - 1 8 V potential with a permissible drift of ___3 V.
i
References
50
"-" >,
.
.
.
.
E=rC
40
$
i
In3
"
8O
0
-5
-10 -15 P o t e n t i a l (V)
-20
-25
Fig. 3. The change in the mean energy of arrival of C ~ ions as a function of the substrate potential in the deposition of diamond-like films from the separated carbon plasma flux. Shown schematically is the choice of the optimum substrate potential from the permissible values of the mean energy of arrival.
1 V. E, Strel'nitskij, V. G. Padalka and S. I. Vakula, J. Soy. Tech. Phys., 48 (1978) 377. 2 A. F. Balakov and E. A. Konshina, Optiko-Mechanicheskaja Promyshlennost (USSR), 9 (1982) 52. 3 B. L. Gehman, G. D. Magnuson, J. F. Tooker, J. R. Treglio and J. P. Williams, Surf. Coat. Technol., 41 (1990) 389. 4 E. F. Chajkovsky, V. M. Puzikov and A. V. Semenov, Kristallografl~ia (USSR), 1 (1981) 219. 5 I. I. Aksenov, S. I. Vakula, V. G. Padalka, V. E. Strel'nitskij and V. M. Horoshih, J. Soy. Tech. Phys., 50 (1980) 2000. 6 V. M. Lunev, B. D. Ovcharenko and V. M. Horoshih, J. Soy. Tech. Phys., 43 (1977) 1486. 7 P. A, Lindfors, W. M. Mularie and G. K. Whener, Surf. Coat. Technol., 29 (1986) 275. 8 W. D. Westwood, J. Vac. Sci. Technol.. 15 (1978) 1. 9 E. W. McDaniel, Collision Phenomena in lonized Gases, John Willy & Sons, Inc., New York, 1964, Appendix 3.4. 10 F. F. Chen, in R. H. H ~dlstone and S. L. Leonard (eds.), Plasma Diagnostic Techniques, Academic Press, New York, 1965, Chapter 4.2. 11 D. R. McKenzie, D. Muller, B. A. Pailthorpe, Z. H. Wang, E. Kravtchinskaia, D. Segal, P. B. Lukins, P. D. Swift, P. J. Martin, G. Amaratunga, P. H. Gaskell and A. Saeed, Diamond Rel. Mater., 1 (1991) 51.