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Growth of plasma pyrolytic carbon
Carbon, Vol. 32, No. 4, pp. 559-562, 1994 Copyright 0 1994Elsevier Science Ltd
Pergamon
Printed in GreatBritain.All rightsreserved 00086223194$6.00 + .OO
CROFTS
OF PLASMA
PYROLYTIC
CARBON
KOPRINAROV, MARIANA KONSTANTINOVA, and GEORGE PCHELAROV CentralLaboratoryfor Solar Energyand New Energy Sources 72 Tzarigradsko shose,
NIKOLA
Sofia-1784, Bulgaria (Receiued
2 August
1993; accepted
in revised form 28 September
1993)
Ah&a&--At arc discharge in a methane ambient, the heat-up of the anodic and cathodic patches can under certain conditions be high enough to initiate gas pyrolysis. Then carbon deposits grow onto the electrodes within the patches. The anodic deposits have a column shape, while the cathodic deposits are radical growths of a hemispherical nature. Because the temperature is relatively low for arc discharge within the patches, the arc ion supply and the electric current limitation by means of the power supply are reasons why we have termed the process abnormal arc discharge. The growth of carbon deposits within the arc patches is observed for the first time and includes three stages, nucleation, growth along the shortest path between the anode and cathode and growth in a direction subtending an angle to the shortest path between the anode and cathode. An analysis of the thermal balance at the anodic and cathodic patches has been conducted, while the parameters of the processes influencing this phenomenon have also been discussed. The growth process observed is presented by a series of consecutive photos. At a work gas pressure of P = 3~Pa, an Hz/CHj ratio of 90110 and a discharge power of 36 W, the growth rate is 15 mm/h. In accordance with the classification for carbon obtained at methane pyrolysis, the growths are considered as “compact silver grey carbon.” Key Words-Plasma,
pyrolitic, methane, pyrolysis, arc, discharge, carbon.
2. EXPERIMENTAL
1. INTRODUCTION
The plasma-chemical process is one of the most widely utilized methods for attaining pure carbon and carbon polymers. It differs from the common chemical methods in that the bonding or decomposition of the initial chemical compounds and the buildup of compound structures obtained occur under extraordinary circumstances. This stems from the fact that by bringing the reacting compounds to a plasma state, their molecules become wholly or partially excited to different degrees. In addition, depending on the reactor chamber dimensions, the compound substances being fed in to the system are stimulated or excited to one or other degree. The course of the chemical reaction change has been investigated[ I]. To obtain plasma and, hence, pure carbon film deposition, which is the aim of our study, different methods such as magneto-microwave dischargef21, microwave discharge[3,4], glow discharge[5], and arc discharge]61 have been utilized. High-quality carbon films with a diamond and diamondlike structure have been obtained by all these approaches, but the detailed analysis of the results attained shows that most suitable is the one that yields concentrated high-energy plasma around the place of growth. This is best achieved by the arc discharge methodl71.
Paper presented at 21st Biennial Conference bon, Buffalo, NY, 13-18 June 1993.
on Car-
Carbon film growth and methane decomposition investigations were conducted with the installation schematically shown on Fig. 1. The discharge chamber (area 16) in Fig. 1) is first evacuated up to 1 x 10m4Pa and then filled to different Ar, Hz, and CH4 gas ratio concentrations. Each of the single gases or their mixtures may be introduced through any of the inlets {I), {Z},and (3). The spot of intense CH4 thermodisso~iation in the vicinity of the arc can thus be altered. An Ar percentage content of from 0 to 10% is utilized in the discharge stabilisation experiments, while past studies have shown that HZ is required in order to obtain a more perfect threedimensional diamond lattice of the deposited carbon. A major technical problem in arc discharge utilization is connected with the heat-up of the electrodes and the possibility of their sputtering and ~lluting the deposits. Long-term experience shows that this problem cannot be solved in a wholesome fashion. As a result of our past experience, we chose graphite as the electrode material. It can withstand very high temperatures so that even if the electrodes are eventually sputtered, this should not contaminate or alter lattice build-up. The graphite electrodes (4) and (5) are connected, respectively, to the bottom positive and the top negative earth power supply interconnects. The electrodes are water cooled in order to maintain their temperature constant. The pressure within the chamber is adjusted not only by the gas stream inlet valves but also by the buffer valve {7}, which adjusts the stream of pump (8). An 559
N. KOPRINAROV et a/.
560
Fig. 1. Column and globular growth deposition set-up.
optical microscope (9) is mounted for observing the carbon formations growing on the electrodes and also for measuring their sizes. The voltage supply can be varied in the range from 0 to 2000 V while the current is varied in the range from 1 to 100 mA. The electric current value is maintained constant during growth.
3. RESULTS AND DISCUSSION In order to avoid the application of an excessively high potential in the initial electrical arc discharge gas break-through, the common practice was to first ignite a glow discharge at a high vacuum and then increase the pressure until an arc discharge is attained. The ability to adjust and maintain the discharge current by means of an external power supply source allowed for a smooth transition from a glow discharge to an arc discharge. In the initial stage of the transition from a glow to an arc discharge, the electron emission current per unit surface of the cathode i is very small due to the low temperature T of the electrode and is determined from the relation; log,, i = log,,, A + 2log,, T - 5040.6)/T.
(1)
Initially the number of emitted electrons is small, and the discharge covers a large area while the temperature of the surface of the cathode is relatively low. In eqn (l), A is Richardson’s constant, A = 60 amp (cm2.K), 0 is the electron work function, 0 = 4.7eV. For the voltage source required current to flow in this case through the circuit the discharge is constrained to envelop the surface of the cathode. The rise in pressure leads to an increase in electrode temperature, an increase in the density of current emitted, and finally to a contraction of the plasma into a plasma cord that remains widened in the region of the cathode and shrinks to a small spot at the anode. For example, in the illustration shown in Fig. 1, the electrodes with an 8-mm diameter and a distance apart of 20 mm at an electric current of I = 100 mA, the contraction of the plasma column
to a size of 0.3 mm takes place at a pressure of P = 200 Torr. The value of the pressure at which the plasma cord contracts in size, is also dependent on the nature of the gas ambient. The patch at the anode is constantly mobile across the electrode surface and eventually settles at the energetically most favourable point. A split of the plasma cord into several branches is observed on some occasions, which is an indication that several energetically equivalent points can exist simultaneously. When the reactant gas contains CH4, independent of whether an arc or glow discharge is utilized for methane decomposition and deposition of carbon on the surfaces and walls of the work chamber, then the quality of the carbon lattice that is built up depends on the temperature and specific characteristics of the growth. At plasma contraction and firm settlement of the spot on the anode, an intense growth of carbon column, whiskers, or dendrite formations are observed. Together with the growths forming on the cathode, these are the subject of the present investigation. As compared with the carbon growing on the anode in the column, whisker, or dendrite form, the carbon growing on the cathode is of a hemispherical branch compact form. A photograph of a hemispherical branch compact growth with a radius of 3 mm is shown in Fig. 3. The photographs shown in Fig. 4 illustrate the growth process between the anode and cathode. The anode column growth structure shown in Fig. 4 has a length of 20 mm in the final stage. The rates of anodic and cathodic growth depend on the discharge current, work pressure, and percentage CH, content in the reactant gas mixture. For a pressure of P = 3 x lo4 Pa and gases’ ratio of H2/CH4 = 90/10, the rate of growth is 15 mm/h. The process of growth of carbon on the electrodes leads to the formation of deposits that approach each other in due course. However, at a certain point during growth, a new phase of growth is observed. The column deposit begins to deviate from its former direction of growth along the straight line connecting the cathode and anode and starts to grow in the perpendicular direction maintaining a constant distance from the cathode. In comparison with the major parameters describing carbon obtained by pyrolysis[8] the carbon deposits can be singled out as “compact silver grey carbon.” Carbon growth (filamentous graphite crystals) at arc discharge have been observed before[9], but these do not grow within the region of the arc discharge patch, and their mechanism of growth is different. The deposition of carbon within the arc patch allows us to consider the discharge as anomalous. The presence of CH, gas within the deposition chamber and the limited charge current are the causes of methane pyrolysis and carbon deposition only within the arc discharge patches. If the column structure has already started to grow and has a height 1 (see Fig. 2) and a radius r, then the heat balance within the anode patch located across the top of the deposit
Growth of plasma pyrolytic carbon
’
reactant gas pyrolysis and dissociation within the region of the patch. The heat flux QE, which is introduced from the external source and dissipates in the region of the anodic arc patch, is:
CHi'
\ I ’ Q.. .J_ AL
Q
QE = (K, - w,,Weo,
T2
2r
561
(3)
where K, is the average energy that electrons from the plasma have before impact with the anode, W, is the work function of the anode material (in this case carbon), I is the discharge current, while e,, is the charge of the electron. In accordance with the law of Stefan Boltzman, the heat flux lost by irradiation will be:
TI
QL =
u(Tj - T&S,
(4)
where:
Fig. 2. Temperature
can be expressed
QE =
balance of the growing carbon.
column
by the relation: QL
+
QG
+
Qc
+
QD.
(2)
Here QE is the heat flux introduced by the arc, QL is the heat flux lost due to anode patch irradiation,
Q, is the heat flux carried from the work gas toward the walls of the work chamber and surrounding objects, Q, is the flux passing through the growing carbon deposit and Q, is the heat flux required for
u = 5.71 x lo-‘* W/cm2K4. T2 is the temperature within the region of the patch, T, is the temperature of the walls while S is the area of the patch. For a high pressure, as in our case, where the free flight of the gas molecules is much smaller than the distance between the hot and cold surfaces, the heat flux that is due to the thermal conductivity of the gas is given by the relation:
A is the heat conductivity of the gas, S is the unit surface area of the growth, Tcx, is the temperature of the growth at a height x from its base, and d is the distance between the hot and cold surfaces. The heat flux through the bulk of the growing column structure with a radius r and length I and coefficient of thermal conductivity a is expressed by the relation: Qc = nr* a(T2 - T,)/I.
(6)
CH, pyrolysis takes place within the region of the arc patches when the temperature exceeds that of the pyrolithic process activation temperature; intense column structure growth is observed as a result. If the energy required for the pyrolysis of a methane molecule and deposition of a carbon atom on the growing column is CD, then the heat flux required to maintain this process will be proportional to the number of the carbon atoms nD. Solving eqn (2) with respect to nD: Fig. 3. Photograph of a hemispherical branch compact growth with a radius of 3 mm.
nD
=
(QE
-
QL
-
QG - Qc)/CD-
(7)
N. KOPRINAROV et al.
562
Fig. 4.
Growth process between the anode and cathode.
we determine the factors that influence the separate heat fluxes in nD and, hence, the rate of carbon deposit growth. Relation (7) is valid for two limiting conditions. The first of these is that for temperatures below that necessary for methane pyrolysis Tps n, tends toward zero and in eqn (2), Qn = 0. The second condition is that rtD cannot exceed the number of gas molecules reaching the arc patch. The first case is always valid in the initial stage, when the deposits are only just about to nucleate. Then the term Qc is irrelevant because 1 = 0; this impedes the creation of the conditions necessary for the initialisation of carbon deposition. nD may, however, tend toward zero when QE becomes small enough during growth, while the arc current is reduced so the patch temperature cools down to less than Tp. From eqn (7), it also follows that at pyrolysis initiation with the discharge power and QE flux increase, the rise in TZ is small because most of the difference in heat flux, Q, = QE - Qo - QL Qc, is spent in methane decomposition. This trend continues until a value for QE is reached such that all the CH, reactant gas molecules decompose. From this moment onwards, Q, becomes a constant, and the increase in QE only leads to an increase of the temperature T2 of the patch region. The heat fluxes in the region of the cathode can be described by a similar equation. The flux due to the thermal conductivity of the growing deposit in this case can no longer be expressed by eqn. (6), because the peculiar form of the growing deposit must be taken account of. QE is not due to electron bombardment but rather to ion bombardment and also depends on the discharge current. Another feature of the anodic growth is that its surface temperature can’t fall below a temperature fixed at Ti, a value that guarantees the current density determined by eqn. (1). The carbon that deposits on the cathode and anode also differs from the carbon that accumulates on the surrounding surfaces within the growth chamber in that during growth, it is subject to plasma bombardment as a result of which, the weakly connected parts of the growing structures are in actual-
ity constantly
etched, so that the structure that possesses the least number of defects is finally grown. The good mechanical properties of the carbon thus obtained are due to the fact that it grows at temperatures higher than that of pyrolysis. The assessment of the heat fluxes within the growth region shows that the main growth factor is the temperature at the spot of arc discharge. 4. CONCLUSION The limited charge current in the CH,/H2 gas mixture leads to methane pyrolysis mainly within the arc patch regions and gives rise to the deposition of carbon with a column structure. The good mechanical properties of the column carbon are due to the fact that it grows at temperatures higher than that required for methane pyrolysis, The assessment of the temperature balance within the region of the patch shows that the principle factor that affects the rate of growth is the patch temperature. Hence, all the factors connected with the discharge and the physical processes in the plasma that change this parameter are decisive for carbon deposit growth. REFERENCES 1. T. Fuyuki, K. Y. Du, S. Okamoto, S. Yasuda, T. Ki-
moto, M. Yoshimoto, and H. Matsunami, IEEE 569 (1987).
2. T. Fuyuki, K. Y. Du, S. Okamoto, S. Yasuda, T. Kimoto, M. Yoshimoto, and H. Matsun~i, .Z. Appi. Phys. 64, 2380 (1988). 3. H. Matsunami. T. Fuvuki. and M. Yoshimoto. IEEE 324 (1988).
-
‘
4. F. Kessler, H. D. Mohring, and G. H. Bauer, ZSPC-9, Pugnochiuso, Italy (1989). 5. W. I. Milne and P. A. Robertson, First international Symposium on Physics and Applications ofAmorphous Semiconductors (Edited by F. Demichelis), Sent. 14-18 1987, Villa Galino, Torino, Italy. 6. W. I. Milne. F. J. Cloueh. S. C. Deane, S. D. Baker. and P. A. Robertson, Alpd Surf. Sci. 43, 277 (1989): 7. P. K. Bachmann, D. Leers, and H. Lydtin, Diamond and Related Materials 1, (1991). 8. S. Jasienko and J. Machnikowski, Carbon 19, 199 (1981).
9. P. A. Tesner and A. I. Echaistova, Dokl. Akad. Nauk SSSR 87, 1029 (1952).
Pergamon
Printed in GreatBritain.All rightsreserved 00086223194$6.00 + .OO
CROFTS
OF PLASMA
PYROLYTIC
CARBON
KOPRINAROV, MARIANA KONSTANTINOVA, and GEORGE PCHELAROV CentralLaboratoryfor Solar Energyand New Energy Sources 72 Tzarigradsko shose,
NIKOLA
Sofia-1784, Bulgaria (Receiued
2 August
1993; accepted
in revised form 28 September
1993)
Ah&a&--At arc discharge in a methane ambient, the heat-up of the anodic and cathodic patches can under certain conditions be high enough to initiate gas pyrolysis. Then carbon deposits grow onto the electrodes within the patches. The anodic deposits have a column shape, while the cathodic deposits are radical growths of a hemispherical nature. Because the temperature is relatively low for arc discharge within the patches, the arc ion supply and the electric current limitation by means of the power supply are reasons why we have termed the process abnormal arc discharge. The growth of carbon deposits within the arc patches is observed for the first time and includes three stages, nucleation, growth along the shortest path between the anode and cathode and growth in a direction subtending an angle to the shortest path between the anode and cathode. An analysis of the thermal balance at the anodic and cathodic patches has been conducted, while the parameters of the processes influencing this phenomenon have also been discussed. The growth process observed is presented by a series of consecutive photos. At a work gas pressure of P = 3~Pa, an Hz/CHj ratio of 90110 and a discharge power of 36 W, the growth rate is 15 mm/h. In accordance with the classification for carbon obtained at methane pyrolysis, the growths are considered as “compact silver grey carbon.” Key Words-Plasma,
pyrolitic, methane, pyrolysis, arc, discharge, carbon.
2. EXPERIMENTAL
1. INTRODUCTION
The plasma-chemical process is one of the most widely utilized methods for attaining pure carbon and carbon polymers. It differs from the common chemical methods in that the bonding or decomposition of the initial chemical compounds and the buildup of compound structures obtained occur under extraordinary circumstances. This stems from the fact that by bringing the reacting compounds to a plasma state, their molecules become wholly or partially excited to different degrees. In addition, depending on the reactor chamber dimensions, the compound substances being fed in to the system are stimulated or excited to one or other degree. The course of the chemical reaction change has been investigated[ I]. To obtain plasma and, hence, pure carbon film deposition, which is the aim of our study, different methods such as magneto-microwave dischargef21, microwave discharge[3,4], glow discharge[5], and arc discharge]61 have been utilized. High-quality carbon films with a diamond and diamondlike structure have been obtained by all these approaches, but the detailed analysis of the results attained shows that most suitable is the one that yields concentrated high-energy plasma around the place of growth. This is best achieved by the arc discharge methodl71.
Paper presented at 21st Biennial Conference bon, Buffalo, NY, 13-18 June 1993.
on Car-
Carbon film growth and methane decomposition investigations were conducted with the installation schematically shown on Fig. 1. The discharge chamber (area 16) in Fig. 1) is first evacuated up to 1 x 10m4Pa and then filled to different Ar, Hz, and CH4 gas ratio concentrations. Each of the single gases or their mixtures may be introduced through any of the inlets {I), {Z},and (3). The spot of intense CH4 thermodisso~iation in the vicinity of the arc can thus be altered. An Ar percentage content of from 0 to 10% is utilized in the discharge stabilisation experiments, while past studies have shown that HZ is required in order to obtain a more perfect threedimensional diamond lattice of the deposited carbon. A major technical problem in arc discharge utilization is connected with the heat-up of the electrodes and the possibility of their sputtering and ~lluting the deposits. Long-term experience shows that this problem cannot be solved in a wholesome fashion. As a result of our past experience, we chose graphite as the electrode material. It can withstand very high temperatures so that even if the electrodes are eventually sputtered, this should not contaminate or alter lattice build-up. The graphite electrodes (4) and (5) are connected, respectively, to the bottom positive and the top negative earth power supply interconnects. The electrodes are water cooled in order to maintain their temperature constant. The pressure within the chamber is adjusted not only by the gas stream inlet valves but also by the buffer valve {7}, which adjusts the stream of pump (8). An 559
N. KOPRINAROV et a/.
560
Fig. 1. Column and globular growth deposition set-up.
optical microscope (9) is mounted for observing the carbon formations growing on the electrodes and also for measuring their sizes. The voltage supply can be varied in the range from 0 to 2000 V while the current is varied in the range from 1 to 100 mA. The electric current value is maintained constant during growth.
3. RESULTS AND DISCUSSION In order to avoid the application of an excessively high potential in the initial electrical arc discharge gas break-through, the common practice was to first ignite a glow discharge at a high vacuum and then increase the pressure until an arc discharge is attained. The ability to adjust and maintain the discharge current by means of an external power supply source allowed for a smooth transition from a glow discharge to an arc discharge. In the initial stage of the transition from a glow to an arc discharge, the electron emission current per unit surface of the cathode i is very small due to the low temperature T of the electrode and is determined from the relation; log,, i = log,,, A + 2log,, T - 5040.6)/T.
(1)
Initially the number of emitted electrons is small, and the discharge covers a large area while the temperature of the surface of the cathode is relatively low. In eqn (l), A is Richardson’s constant, A = 60 amp (cm2.K), 0 is the electron work function, 0 = 4.7eV. For the voltage source required current to flow in this case through the circuit the discharge is constrained to envelop the surface of the cathode. The rise in pressure leads to an increase in electrode temperature, an increase in the density of current emitted, and finally to a contraction of the plasma into a plasma cord that remains widened in the region of the cathode and shrinks to a small spot at the anode. For example, in the illustration shown in Fig. 1, the electrodes with an 8-mm diameter and a distance apart of 20 mm at an electric current of I = 100 mA, the contraction of the plasma column
to a size of 0.3 mm takes place at a pressure of P = 200 Torr. The value of the pressure at which the plasma cord contracts in size, is also dependent on the nature of the gas ambient. The patch at the anode is constantly mobile across the electrode surface and eventually settles at the energetically most favourable point. A split of the plasma cord into several branches is observed on some occasions, which is an indication that several energetically equivalent points can exist simultaneously. When the reactant gas contains CH4, independent of whether an arc or glow discharge is utilized for methane decomposition and deposition of carbon on the surfaces and walls of the work chamber, then the quality of the carbon lattice that is built up depends on the temperature and specific characteristics of the growth. At plasma contraction and firm settlement of the spot on the anode, an intense growth of carbon column, whiskers, or dendrite formations are observed. Together with the growths forming on the cathode, these are the subject of the present investigation. As compared with the carbon growing on the anode in the column, whisker, or dendrite form, the carbon growing on the cathode is of a hemispherical branch compact form. A photograph of a hemispherical branch compact growth with a radius of 3 mm is shown in Fig. 3. The photographs shown in Fig. 4 illustrate the growth process between the anode and cathode. The anode column growth structure shown in Fig. 4 has a length of 20 mm in the final stage. The rates of anodic and cathodic growth depend on the discharge current, work pressure, and percentage CH, content in the reactant gas mixture. For a pressure of P = 3 x lo4 Pa and gases’ ratio of H2/CH4 = 90/10, the rate of growth is 15 mm/h. The process of growth of carbon on the electrodes leads to the formation of deposits that approach each other in due course. However, at a certain point during growth, a new phase of growth is observed. The column deposit begins to deviate from its former direction of growth along the straight line connecting the cathode and anode and starts to grow in the perpendicular direction maintaining a constant distance from the cathode. In comparison with the major parameters describing carbon obtained by pyrolysis[8] the carbon deposits can be singled out as “compact silver grey carbon.” Carbon growth (filamentous graphite crystals) at arc discharge have been observed before[9], but these do not grow within the region of the arc discharge patch, and their mechanism of growth is different. The deposition of carbon within the arc patch allows us to consider the discharge as anomalous. The presence of CH, gas within the deposition chamber and the limited charge current are the causes of methane pyrolysis and carbon deposition only within the arc discharge patches. If the column structure has already started to grow and has a height 1 (see Fig. 2) and a radius r, then the heat balance within the anode patch located across the top of the deposit
Growth of plasma pyrolytic carbon
’
reactant gas pyrolysis and dissociation within the region of the patch. The heat flux QE, which is introduced from the external source and dissipates in the region of the anodic arc patch, is:
CHi'
\ I ’ Q.. .J_ AL
Q
QE = (K, - w,,Weo,
T2
2r
561
(3)
where K, is the average energy that electrons from the plasma have before impact with the anode, W, is the work function of the anode material (in this case carbon), I is the discharge current, while e,, is the charge of the electron. In accordance with the law of Stefan Boltzman, the heat flux lost by irradiation will be:
TI
QL =
u(Tj - T&S,
(4)
where:
Fig. 2. Temperature
can be expressed
QE =
balance of the growing carbon.
column
by the relation: QL
+
QG
+
Qc
+
QD.
(2)
Here QE is the heat flux introduced by the arc, QL is the heat flux lost due to anode patch irradiation,
Q, is the heat flux carried from the work gas toward the walls of the work chamber and surrounding objects, Q, is the flux passing through the growing carbon deposit and Q, is the heat flux required for
u = 5.71 x lo-‘* W/cm2K4. T2 is the temperature within the region of the patch, T, is the temperature of the walls while S is the area of the patch. For a high pressure, as in our case, where the free flight of the gas molecules is much smaller than the distance between the hot and cold surfaces, the heat flux that is due to the thermal conductivity of the gas is given by the relation:
A is the heat conductivity of the gas, S is the unit surface area of the growth, Tcx, is the temperature of the growth at a height x from its base, and d is the distance between the hot and cold surfaces. The heat flux through the bulk of the growing column structure with a radius r and length I and coefficient of thermal conductivity a is expressed by the relation: Qc = nr* a(T2 - T,)/I.
(6)
CH, pyrolysis takes place within the region of the arc patches when the temperature exceeds that of the pyrolithic process activation temperature; intense column structure growth is observed as a result. If the energy required for the pyrolysis of a methane molecule and deposition of a carbon atom on the growing column is CD, then the heat flux required to maintain this process will be proportional to the number of the carbon atoms nD. Solving eqn (2) with respect to nD: Fig. 3. Photograph of a hemispherical branch compact growth with a radius of 3 mm.
nD
=
(QE
-
QL
-
QG - Qc)/CD-
(7)
N. KOPRINAROV et al.
562
Fig. 4.
Growth process between the anode and cathode.
we determine the factors that influence the separate heat fluxes in nD and, hence, the rate of carbon deposit growth. Relation (7) is valid for two limiting conditions. The first of these is that for temperatures below that necessary for methane pyrolysis Tps n, tends toward zero and in eqn (2), Qn = 0. The second condition is that rtD cannot exceed the number of gas molecules reaching the arc patch. The first case is always valid in the initial stage, when the deposits are only just about to nucleate. Then the term Qc is irrelevant because 1 = 0; this impedes the creation of the conditions necessary for the initialisation of carbon deposition. nD may, however, tend toward zero when QE becomes small enough during growth, while the arc current is reduced so the patch temperature cools down to less than Tp. From eqn (7), it also follows that at pyrolysis initiation with the discharge power and QE flux increase, the rise in TZ is small because most of the difference in heat flux, Q, = QE - Qo - QL Qc, is spent in methane decomposition. This trend continues until a value for QE is reached such that all the CH, reactant gas molecules decompose. From this moment onwards, Q, becomes a constant, and the increase in QE only leads to an increase of the temperature T2 of the patch region. The heat fluxes in the region of the cathode can be described by a similar equation. The flux due to the thermal conductivity of the growing deposit in this case can no longer be expressed by eqn. (6), because the peculiar form of the growing deposit must be taken account of. QE is not due to electron bombardment but rather to ion bombardment and also depends on the discharge current. Another feature of the anodic growth is that its surface temperature can’t fall below a temperature fixed at Ti, a value that guarantees the current density determined by eqn. (1). The carbon that deposits on the cathode and anode also differs from the carbon that accumulates on the surrounding surfaces within the growth chamber in that during growth, it is subject to plasma bombardment as a result of which, the weakly connected parts of the growing structures are in actual-
ity constantly
etched, so that the structure that possesses the least number of defects is finally grown. The good mechanical properties of the carbon thus obtained are due to the fact that it grows at temperatures higher than that of pyrolysis. The assessment of the heat fluxes within the growth region shows that the main growth factor is the temperature at the spot of arc discharge. 4. CONCLUSION The limited charge current in the CH,/H2 gas mixture leads to methane pyrolysis mainly within the arc patch regions and gives rise to the deposition of carbon with a column structure. The good mechanical properties of the column carbon are due to the fact that it grows at temperatures higher than that required for methane pyrolysis, The assessment of the temperature balance within the region of the patch shows that the principle factor that affects the rate of growth is the patch temperature. Hence, all the factors connected with the discharge and the physical processes in the plasma that change this parameter are decisive for carbon deposit growth. REFERENCES 1. T. Fuyuki, K. Y. Du, S. Okamoto, S. Yasuda, T. Ki-
moto, M. Yoshimoto, and H. Matsunami, IEEE 569 (1987).
2. T. Fuyuki, K. Y. Du, S. Okamoto, S. Yasuda, T. Kimoto, M. Yoshimoto, and H. Matsun~i, .Z. Appi. Phys. 64, 2380 (1988). 3. H. Matsunami. T. Fuvuki. and M. Yoshimoto. IEEE 324 (1988).
-
‘
4. F. Kessler, H. D. Mohring, and G. H. Bauer, ZSPC-9, Pugnochiuso, Italy (1989). 5. W. I. Milne and P. A. Robertson, First international Symposium on Physics and Applications ofAmorphous Semiconductors (Edited by F. Demichelis), Sent. 14-18 1987, Villa Galino, Torino, Italy. 6. W. I. Milne. F. J. Cloueh. S. C. Deane, S. D. Baker. and P. A. Robertson, Alpd Surf. Sci. 43, 277 (1989): 7. P. K. Bachmann, D. Leers, and H. Lydtin, Diamond and Related Materials 1, (1991). 8. S. Jasienko and J. Machnikowski, Carbon 19, 199 (1981).
9. P. A. Tesner and A. I. Echaistova, Dokl. Akad. Nauk SSSR 87, 1029 (1952).