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Some fundamental aspects of glow discharges in plasma-assisted processes
Surface and Coatings Technology, 33 (1987) 17
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SOME FUNDAMENTAL ASPECTS OF GLOW DISCHARGES IN PLASMA-ASSISTED PROCESSES* K. S. FANCEY and A. MATTHEWS Department of Engineering Design and Manufacture, University of Hull, Hull HU6 7RX (U.K.) (Received March 22, 1987)
Summary The applicability of some theoretical models for ionization-assisted processes, such as those of Davis and Vanderslice and Child—Langmuir, are discussed using data obtained by the authors and other researchers in the field. Information derived from argon discharges is used as a basis, and provides a convenient foundation from which to compare different system layouts, such as the direct current diode, and various triode systems. Detailed information is given on the estimation of the cathode fall distance L and the LIX ratio, where X is the mean free path for charge exchange collision. This allows the estimation of energy distributions for both ions and neutrals. Other important parameters are also discussed, such as ionization efficiency, as well as the effect of additional species within the discharge. 1. Introduction Much theoretical work has been carried out on gaseous discharges during this century. Unfortunately, most of it relates to pressure ranges, voltages and geometries which are inappropriate to modem ionizationassisted deposition systems. The result has been that classical theories and assumptions have been misunderstood or inappropriately applied in many cases. Here we attempt to try to clarify some of the important features of deposition plasmas, and to establish the applicability of some of the theoretical models that presently exist.
2. The direct current argon diode discharge We will begin by considering a simple direct current (d.c.) diode discharge, in an inert gas such as argon. Under typical pressure and voltage *paper presented at the 14th International Conference on Metallurgical Coatings, San Diego, CA, U.S.A., March 23 - 27, 1987. 0257-8972/87/$3.50
© Elsevier Sequoia/Printed in The Netherlands
18
conditions, and for the case in which the vacuum chamber is metallic and earthed (forming a large anode), the ‘negative glow’ fills most of the chamber volume and is slightly positive with respect to the chamber walls. Secondary electron emission at the cathode is primarily a consequence of the mechanism of potential emission during the arrival of ions, though contributions from metastables, photons and higher energy neutrals may also play a part. The electrons gain kinetic energy by accelerating across the cathode dark space, where the greatest potential drop occurs in the discharge. These are then known as primary electrons and can cause ionization by impact with gas atoms; and in so doing can create other classes of electrons (known as secondary and ultimate electrons) which may also partake in impact ionization processes. Argon ions produced in the negative glow which accelerate across the cathode dark space can make charge transfer collisions en route. This produces ions and neutrals with a range of energies, mostly much less than eVe, as they strike the cathode. The neutral species which arise from charge exchange are designated high energy neutrals. There are also lower energy (thermal) neutrals which are the most numerous species. Although multiply charged ions also occur, the dominant ionic species is Art Other species, such as those from evaporation, reactive gases or background impurities, are referred to later. 3. Ion and neutral energy distributions 3.1. Background The pioneering work of Davis and Vanderslice [1] demonstrated that the factors which govern the distribution of energies for ions and neutrals arriving at the cathode are the cathode fall length L (also known as the cathode sheath thickness or the dark space distance) and the mean free path for charge exchange collision A. Their analysis made four assumptions. (i) All ions originate in the negative glow. (ii) In a charge exchange collision, an energetic ion interacts with its neutral counterpart, producing an equally energetic neutral and an ion with zero energy. (iii) The collision cross-section for charge transfer is independent of incident ion energy. (iv) The electric field decreases linearly from the cathode to the edge of the negative glow. Rickards [21 modified the above model, producing a more general form which enables field distributions other than the linear case (iv) to be considered. This defines the number of ions per energy interval as dN
N0L =
~1_E)u’m)_lexp
L —-~
+
L
where E defines the ion energy relative to the maximum, and lies between zero and unity. N0 is the number of ions entering the cathode fall region from the negative glow. When m = 2, the equation is equivalent to the Davis and Vanderslice model. When m = 4/3, the field corresponds to the more realistic space
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charge limited (free-fall) case, though it has been shown that the value of m chosen has minimal effect on the distribution shape. The value of LIX, however, critically influences the distribution. Reducing LIX produces an energy spectrum in which a greater proportion of the ions have energies nearer the maximum. Thus, if there is a need for more ions to exceed some critical minimum energy, this can be aided by decreasing LIX, in effect producing a more ‘efficient’ discharge from the point of view of its ability to influence film formation and growth processes. A number of workers have used energy and mass spectroscopy to investigate the energy distributions of real systems, by using a sampling orifice in the cathode. There have been some significant deviations from theory reported (e.g. refs. 3 6). However, closer inspection reveals that these discrepancies appear to be attributable to the orifice diameter used. It seems that low energy ions may not be detected in some analyser systems, typically when the product of pressure and orifice diameter is greater than about 10 mTorr mm. This is probably because of the pressure drop caused by too large a sampling orifice in the cathode. A lower pressure nearer the cathode will lead to fewer collisions there, and therefore fewer low energy ions. Valizadeh [7] has also explained the lack of low energy ions as arising from particle scattering which is said to increase as ion energy reduces. Rickards [21 also studied neutral energy distributions, and showed that these are in general displaced to lower energies than is the case for the ion energy distributions. Experimental results from ref. 5 support this observation. -
3.2. Evaluation of L We have indicated that the ratio LIX is a very important parameter. To evaluate it, we must first determine the value of L. Chapman [8] has shown that L can be calculated, knowing the current density, by using the free-fall version of the Child—Langmuir equation ~..
4e(2~y/2 v3!2 9 \M/ L2
This is quoted in SI units, where J is the cathode current density, ~ is the permittivity of free space, q is the ionic charge, M is the ion mass and V is the potential drop across L. The equation was derived for situations in which the following apply. (i) The cathode is bombarded on one face only, which is flat and infinitely large. (ii) Only one type of ionic species is present. (iii) The ions originate from the negative glow with an initial energy of zero. We investigated the applicability of the above equation, using a flat round steel cathode (24.6 cm in diameter), bombarded on one face only. Direct observation was used to determine L. We also considered results reported by other workers.
20 10 0
2
oOU• — 0
1.0
°
0.1 I
0.1
1.0
LPRED
(~s)
10
Fig. 1. Measured vs. predicted cathode fall lengths in argon discharges using a flat cathode with bombardment on one face only: 0, d.c. diode, refs. 3, 9, 10 and this work; S triode (thermionic support), ref. 11 and this work; •, triode (positive electrode), ref. 12.
Figure 1 shows how these measured values compare with those predicted by the equation, assuming Ar~to be the only species present. Layouts other than the simple d.c. diode were also used in these studies. We observed that the deviations for the published data were greater than those for our own work, partly because of our uncertainty about the methods and accuracies employed by other workers. Nevertheless the predicted line is a good fit through the points. It was also noticed that the diode predictions for our results were in general higher than those measured, though still nearer than for a supported or “enhanced” discharge, characterized by the designation of “triode” in the graph. These enhanced discharges used either an additional positive electrode, or a negative electron emitter. In our work, when the latter was used, its brightness to some extent obscured clear observation of the fall region. Another factor to bear in mind is that there will be an inaccuracy in the measurement of ion current density, as the current carried by secondary electrons is not known (though it is usually claimed to be typically 10% of the total). Higher gas pressures (up to 100 mTorr) were used in the diode experiments. Mobility limiting effects might then be expected to become more important. An alternative form of the Child—Langmuir equation is available to cover this situation, though this requires a mobility value which is difficult to ascertain. Gras-Marti et al. [13] have developed a model which can
21
consider situations intermediate between the free-fall and mobility-limited regimes. Our investigation of their data has not, however, proved their model to have any greater applicability than the free-fall Child—Langmuir equation above. 3.3. Evaluation of A To determine A, it is necessary to have a value for a, the collision crosssection for charge exchange (Ar~—Ar°). As can be seen from Fig. 2, there was for many years a high degree of uncertainty about this value. Recent data by Hegerberg and coworkers [14, 15] are now probably more reliable, and we have fitted a predictive equation for a reported by Sheldon [161 to these data and achieved good correlation. This is shown in Fig. 2.
IU~’
100
10’
10’
10’
10
EN~RG~(eV)
Fig. 2. Collision cross-section for Ark, Ar°charge transfer as a function of ion energy: ———, range of data by various authors up to 1964 [8], data points from Hegerberg and 1’2 exp(—k 2), coworkers [14, 15]; —, equation given by Sheldon [16], E = k fitted to the Hegerberg data where k 1u 20” 1 5.1985 X ~ h2 = 2.8954 x 108 (E in electronvolts, a in square centimetres).
Clearly, the original assumption of Davis and Vanderslice that a is independent of energy is not true. Since a spread of energies is usually encountered in practical systems, it is necessary to take an average value to evaluate A, which is equal to 1/na, where n is the number density the gas 3atof300 K, (e.g. if the pressure is 1 mTorr, then n = 3.211 X iO’~ cm~ assuming ideal gas conditions). For most of the practical systems with which we are familiar, an appropriate value for a is about 4 X 10-15 cm2, based on the estimated average energy of ions arriving at the cathode.
22
3.4. Use of LIX values Knowing L and A, we are able to use the resulting LIX values in the determination of ion energy spectra. Figure 3 shows two revealing curves whose evaluation is thus made possible. The first curve, showing the fraction of ions with maximum energy, is derived using the Davis and Vanderslice assumptions and collision theory, to take account of the fact that the collision probability increases exponentially with distance travelled. The fraction of ions that do not undergo collision (and therefore have maximum energy) will thus be equal to ~ which is field-independent. The second curve is derived from work by Rickards [2], converting his neutral average energy predictions into ion energy predictions for the space charge limited field case, where m = 4/3. 100
%
-
~ 80
-
60
-
\
\ \ \
£4Q
.
\ \
20
-
o
I 0,1
1111111
\
\
\
I 1.0
I’I~.4.._IIIII LI).,
10
Fig. 3. The variation of ion energy transportation characteristics with L/X: — — —, fraction of ions arriving at the cathode with maximum energy; , fraction of energy transported by ions (as opposed to that carried by neutrals).
4. Ion intensity and ionization efficiency Although the assessment of LIX and energy distributions as discussed in Section 3 are important, the overall intensity of energization (as dictated
23
by the degree of ionization) is also highly relevant. An indication of the intensity of ions arriving at the cathode is given by the cathode current density, but this on its own does not take account of the total number of bombarding particles, most of which are non-ionized in present systems. Although a proportion of these particles will be high energy neutrals (ions that have undergone charge exchange) the majority are thermal neutrals and their population will tend to increase with pressure. Thus, two discharge systems may have similar energy spectra and current density values, but if one system requires a higher pressure than the other to obtain these characteristics, it may in practice be inferior, as the greater number of thermal neutrals will tend to dilute any beneficial effects (e.g. on film formation and growth) from the more energetic species. We therefore need a further performance parameter which considers both pressure and current density: the ionization efficiency meets this requirement. This is defined as ef
—
N~x 100% N~0
where N6 is the number of ions arriving at the sample per square centimetre per second and ~ is the total number of bombardments per square centimetre per second. Previously reported values for ‘ef (e.g. ref. 17) have been based on the measured cathode current and overall pressure, regardless of the relative proportion of atomic species present (e.g. argon, nitrogen, titanium etc.). Thus Matthews, for example, used argon data in determining the ~ value. This, although not strictly representative, allowed the convenient comparison of data. Also, since the argon mass is between that of titanium and N2, the error will not be large; a more significant error lies in the assumption that the overall pressure represents the “pressure” at the cathode surface, although again this error can be estimated, and is usually small [17]. We have carried out studies on various discharge configurations, to confirm their relative performances in terms of ionization efficiency, and some of these results are reported in Section 5. However, we should re-emphasize that ionization efficiency is not the sole governing parameter for systems. In some ways, the word efficiency may cause confusion, as it has connotations of relative superiority. It is clear that some systems do not need to be operated at as high an ‘ef values as others [17], and indeed, provided the bias voltage levels are also low, these systems might well be considered to have an advantage in needing less discharge power to operate satisfactorily. On the subject of bias voltage it is also worth mentioning that, regarding film growth, we believe that the actual bias levels used need not be as high as was previously thought. Provided sufficient ion current can be obtained without needing to increase voltage, then the actual bias levels can be quite low (say, below 100 V). There is, however, likely to be a minimum required cathode fall potential, which we suggest can be expected to be 40 70 V on consideration of the collision cross-section for electron impact ionization -
24
and also the sputtering threshold. Above this critical value, increased cathode fall potentials may not necessarily have a beneficial effect on film properties. This has important implications, as discussed in Section 3, in optimizing energy distributions. 5. Studies on practical discharge systems 5.1. Systems with argon only We have outlined how LIX and ‘ef are particularly important parameters in plasma-assisted processes. Our initial approach was to evaluate these parameters for discharge configurations in argon only. Although this does not account for the presence of other species, it provides a relative indication of system performance, and also allows readily obtainable published data to be analysed. The possible contributions to system performance from other species will be discussed in Section 5.2. Table 1 summarizes energy transportation and ionization efficiency evaluations using data by various authors and ourselves for different argon discharge layouts. The following observations can be made. (i) LIX for diode systems is always greater than 10. This agrees with the findings of other workers, e.g. it is 15 in ref. 1 and 12 in ref. 18. In fact, LIX will not change appreciably for a diode configuration operating in the abnormal discharge mode because L, like A, is inversely proportional to discharge pressure. (ii) A triode discharge using a positively biased third electrode reduces LIX [12] and therefore increases the energy transported by ions compared with that transported by high energy neutrals. ‘ef is also seen to increase significantly compared with the equivalent diode system. (iii) Thode discharges using thermionic support can give very low LIX values, resulting in much of the energy being transported to the cathode by maximum energy ions. ‘ef values of several per cent can also be achieved. 5.2. Other considerations 5.2.1. Evaporant source and metal flux In general, the presence of the evaporant source and resulting metal flux reduces the current density in diodes, and also in triodes which use a positive third electrode (e.g. Fig. 4). This may be caused by several factors. Firstly, preferential ionization of the metal species will occur by argon metastables (Penning ionization), which may otherwise have become argon ions as a result of low energy electron impact. It is arguable that if the metal has a higher mass than the argon, then the current will fall (in agreement with the Child—Langmuir equation, for a given L). Alternatively, the effect may be purely one of distortion of the discharge producing a separate localized discharge and enhancement away from the cathode. With the thermionic negative electrode, the situation is even more complicated [191, and counteracting effects apparently operate (as shown in Fig. 4). —
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Fig. 4. Effect of electron beam gun power and evaporation on an argon triode discharge (argon pressure is 5 mTorr, titanium evaporation, ref. 19): •, thermionic negative biased electrode; 0, positive biased electrode.
There are limited data available on the energy distribution of metal ions in argon discharges. For metal species produced by sputtering at the cathode of an argon d.c. diode, estimated LIX values of 3 and 4 have been reported [12, 18]. For silver evaporated in an argon d.c. diode LIX for the metal was 1.5 [20]. These LIX values show that metal ions suffer less charge transfer collisions than argon in the cathode dark space (though the dominant charge transfer process is not clear) and therefore metal ion energy distributions will tend to have a greater high energy content than that for the Ar~ions. Further evidence for this is given by Armour et al. [5] who studied the evaporation of copper through an argon d.c. diode glow discharge. We have found no definite information on the effect of metal ions on the Ar~energy distribution, although it could be inferred from the total ion energy distribution results of Ahmed [4] (evaporation of lead) that the Ar~energy characteristics do not change appreciably. 5.2.2. Reactive gases and gas mixtures We have studied nitrogen and argon plus nitrogen discharges to ascertain the effect of a typical reactive gas on the discharge characteristics. These observations, we emphasize, may not apply for other gases, especially oxygen which has been widely reported to produce negative ions. In our studies the following was observed. (i) The nitrogen diode discharge was found to obey the free-fall Child— Langmuir equation, agreement being better when assuming N~rather than N2~ions. This concurs with the ion mass spectroscopy results of Valizadeh [7]. One of the mechanisms for the production of N~ions could be dissociative charge transfer of N2~within the cathode fall region. (ii) For a nitrogen triode with a negative thermionic emitter, we found that the improvement in current density was significantly less than that
found for argon under otherwise similar conditions. We believe that N2~is
27
more likely to be the dominant ionic species in this case, as dissociative charge transfer will be less likely, owing to the smaller cathode fall distance. This alone cannot, however, account for the lower improvement in current density compared with argon, neither can reductions in secondary electron emission at the steel cathode (because it is nitrided) fully account for this. One possible explanation follows from work by Natarajan et al. [21] who state that the cross-section for excitation of nitrogen molecules is very large and therefore thermalization of low energy electrons occurs. This in turn reduces the probability of subsequent ionizing collisions by the electrons. (iii) For equal partial pressure mixtures of argon and nitrogen, the measured L value was the mean of those measured for argon only and nitrogen only discharges at the same total pressure (measured with a capacitance manometer). Using the measured current density values, the predicted L for the mixture (using the average mass) was also found to be the mean of the predicted L values for the pure cases. This suggests that an argon—nitrogen mixture also follows the Child—Langmuir relationship (possibly indicating that there is little or no net interaction between the gas species). There are few published data available on the energy distribution characteristics of nitrogen-only discharges. Armour et al. [5] have, however, reported that the N~species in such discharges, under diode conditions, have similar energy distributions to those of Art This has been confirmed by the results of Valizadeh [7]. We may not, however, necessarily conclude that this also applies to thermionic triode conditions because of the observations outlined in (ii), above. 5.2.3. Impurities Background impurities can significantly affect discharges, and we believe that they have in the past been given insufficient attention. Hydrogenous contaminants were discussed by Knewstubb and Tickner [221, who mention the formation of ArH~and H3O~by the action of argon metastables on hydrogen, and water metastables on other water metastables respectively. Coburn and Kay [23 25] found large amounts of these species in the substrate plane (grounded anode) of an argon diode sputtering system. Although it is not known what the amounts were on the cathode, and there are little other reported data, it can be assumed that practical systems with even trace quantities of water vapour may produce significant hydrogenous ion populations in argon discharges, which may be detrimental to film properties. -
6. Conclusions An appraisal of the theoretical background to ionization-assisted deposition systems has been presented. The paper has demonstrated that the main theories and equations developed by plasma physicists for simplified discharge layouts are applicable to the practical deposition systems now widely used in industry, and can be used to characterize and optimize such systems. In particular, the followingcan be evaluated for optimization purposes.
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(i) The cathode fall length, which has important implications on field uniformity around components being coated and the glow penetration within holes. (ii) The cathode fall length to charge exchange mean free path ratio, which allows determination of the ion and neutral energy transportation characteristics. (iii) Ionization efficiency, which has been used to indicate the ratio between the ion flux and total particle flux at the cathode. The intention of the paper has been to provide an introduction to the theoretical background to discharges and to show how this can have practical use. We have shown, for example, that the thermionically assisted triode layout can provide benefits in terms of ion energy transportation characteristics and cathode fall length control. Clearly, though, there is much fundamental research work needed before a full understanding of plasma-assisted processes can be achieved. In particular, the complex interactions between species in enhanced systems (especially when used for reactive deposition) need further attention. We believe that this can only be achieved by ensuring co-operation between the plasma physicists (often working on idealized systems) and those other scientists and engineers who must strive to optimize real industrial equipments.
Acknowledgments We have been aided in this work by helpful discussions with many individuals; we record our thanks to them all, especially to our coworkers within the Surface Engineering Laboratory at Hull University. We also gratefully acknowledge the SERC and Tecvac Limited who provided one of us (K.S.F.) with financial support during the course of this work. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14
W. D. Davis and T. A. Vanderslice, Phys. Rev., 131 (1963) 219. J. Rickards, Vacuum, 34 (1984) 559. Z. Wronski, Vacuum, 36 (1986) 329. N. A. G. Ahmed, J. Phys. E, 13 (1980) 1305. D. G. Armour, H. Valizadeh, F. A. H. Soliman and G. Carter, Vacuum, 34 (1984) 295. C. G. Crockett, Vacuum, 23 (1973) 11. H. Valizadeh, Ph.D. thesis, Salford University, 1982. B. N. Chapman, Glow Discharge Processes, Wiley, New York, 1980. W. D. Westwood and R. Boynton, J. App!. Phys., 43 (1972) 2691. G. Lamperiere, J. M. Poitevin and C. Fourrier, J. Phys. D, 11 (1978) 293. T. C. Tisone and P. D. Cruzan, J. Vac. Sci. Technol., 12 (1975) 1058. P. Saulnier, A. Debhi and J. Machet, Vacuum, 34 (1984) 765. A. Gras-Marti, I. Abril and J. A. Valles-Abarca, Thin Solid Films, 124 (1985) 59. R. Hegerberg, T. Stefansson and M. T. Elford, J. Phys. B, 11(1978) 133.
29 15 R. Hegerberg, M. T. Elford and H. R. Skullerud, J. Phys. B, 15 (1982) 797. 16 J. W. Sheldon, Phys. Rev. Lett., 8 (1962) 64. 17 A. Matthews, in W. D. Sproul, J. E. Greene and J. A. Thornton (eds.), Proc. Topical Symp. Physics and Chemistry of Protective Coatings, American Vacuum Society, Series 2, American Institute of Physics Conf. Proc., 149, AlP, New York, 1986. 18 J. E. Houston and J. E. Uhi, Report SC RR 0122, Sandia Laboratories, 1971. 19 A. Matthews, Ph. D. thesis, Salford University, 1980. 20 J. Machet, G. Gadet, P. Saulnier and J. Guille, in F. Abeles and M. Croset (eds.), 8th mt. Vacuum Con!., Cannes, France, Société Francaise Du Vide, 1980. 21 B. R. Natarajan, A. H. Eltoukhy, J. E. Greene and T. L. Barr, Thin Solid Films, 69 (1980) 201. 22 P. F. Knewstubb and A. W. Tickner, J. Chem. Phys., 36 (1962) 684. 23 J. W. Coburn, Rev. Sci. Instrum., 41 (1970) 1219. 24 J. W. Coburn and E. Kay, Appi. Ploys. Lett., 18(1971)435. 25 J. W. Coburn and E. Kay,Solid State Technol., Dec. (1971)49.
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SOME FUNDAMENTAL ASPECTS OF GLOW DISCHARGES IN PLASMA-ASSISTED PROCESSES* K. S. FANCEY and A. MATTHEWS Department of Engineering Design and Manufacture, University of Hull, Hull HU6 7RX (U.K.) (Received March 22, 1987)
Summary The applicability of some theoretical models for ionization-assisted processes, such as those of Davis and Vanderslice and Child—Langmuir, are discussed using data obtained by the authors and other researchers in the field. Information derived from argon discharges is used as a basis, and provides a convenient foundation from which to compare different system layouts, such as the direct current diode, and various triode systems. Detailed information is given on the estimation of the cathode fall distance L and the LIX ratio, where X is the mean free path for charge exchange collision. This allows the estimation of energy distributions for both ions and neutrals. Other important parameters are also discussed, such as ionization efficiency, as well as the effect of additional species within the discharge. 1. Introduction Much theoretical work has been carried out on gaseous discharges during this century. Unfortunately, most of it relates to pressure ranges, voltages and geometries which are inappropriate to modem ionizationassisted deposition systems. The result has been that classical theories and assumptions have been misunderstood or inappropriately applied in many cases. Here we attempt to try to clarify some of the important features of deposition plasmas, and to establish the applicability of some of the theoretical models that presently exist.
2. The direct current argon diode discharge We will begin by considering a simple direct current (d.c.) diode discharge, in an inert gas such as argon. Under typical pressure and voltage *paper presented at the 14th International Conference on Metallurgical Coatings, San Diego, CA, U.S.A., March 23 - 27, 1987. 0257-8972/87/$3.50
© Elsevier Sequoia/Printed in The Netherlands
18
conditions, and for the case in which the vacuum chamber is metallic and earthed (forming a large anode), the ‘negative glow’ fills most of the chamber volume and is slightly positive with respect to the chamber walls. Secondary electron emission at the cathode is primarily a consequence of the mechanism of potential emission during the arrival of ions, though contributions from metastables, photons and higher energy neutrals may also play a part. The electrons gain kinetic energy by accelerating across the cathode dark space, where the greatest potential drop occurs in the discharge. These are then known as primary electrons and can cause ionization by impact with gas atoms; and in so doing can create other classes of electrons (known as secondary and ultimate electrons) which may also partake in impact ionization processes. Argon ions produced in the negative glow which accelerate across the cathode dark space can make charge transfer collisions en route. This produces ions and neutrals with a range of energies, mostly much less than eVe, as they strike the cathode. The neutral species which arise from charge exchange are designated high energy neutrals. There are also lower energy (thermal) neutrals which are the most numerous species. Although multiply charged ions also occur, the dominant ionic species is Art Other species, such as those from evaporation, reactive gases or background impurities, are referred to later. 3. Ion and neutral energy distributions 3.1. Background The pioneering work of Davis and Vanderslice [1] demonstrated that the factors which govern the distribution of energies for ions and neutrals arriving at the cathode are the cathode fall length L (also known as the cathode sheath thickness or the dark space distance) and the mean free path for charge exchange collision A. Their analysis made four assumptions. (i) All ions originate in the negative glow. (ii) In a charge exchange collision, an energetic ion interacts with its neutral counterpart, producing an equally energetic neutral and an ion with zero energy. (iii) The collision cross-section for charge transfer is independent of incident ion energy. (iv) The electric field decreases linearly from the cathode to the edge of the negative glow. Rickards [21 modified the above model, producing a more general form which enables field distributions other than the linear case (iv) to be considered. This defines the number of ions per energy interval as dN
N0L =
~1_E)u’m)_lexp
L —-~
+
L
where E defines the ion energy relative to the maximum, and lies between zero and unity. N0 is the number of ions entering the cathode fall region from the negative glow. When m = 2, the equation is equivalent to the Davis and Vanderslice model. When m = 4/3, the field corresponds to the more realistic space
19
charge limited (free-fall) case, though it has been shown that the value of m chosen has minimal effect on the distribution shape. The value of LIX, however, critically influences the distribution. Reducing LIX produces an energy spectrum in which a greater proportion of the ions have energies nearer the maximum. Thus, if there is a need for more ions to exceed some critical minimum energy, this can be aided by decreasing LIX, in effect producing a more ‘efficient’ discharge from the point of view of its ability to influence film formation and growth processes. A number of workers have used energy and mass spectroscopy to investigate the energy distributions of real systems, by using a sampling orifice in the cathode. There have been some significant deviations from theory reported (e.g. refs. 3 6). However, closer inspection reveals that these discrepancies appear to be attributable to the orifice diameter used. It seems that low energy ions may not be detected in some analyser systems, typically when the product of pressure and orifice diameter is greater than about 10 mTorr mm. This is probably because of the pressure drop caused by too large a sampling orifice in the cathode. A lower pressure nearer the cathode will lead to fewer collisions there, and therefore fewer low energy ions. Valizadeh [7] has also explained the lack of low energy ions as arising from particle scattering which is said to increase as ion energy reduces. Rickards [21 also studied neutral energy distributions, and showed that these are in general displaced to lower energies than is the case for the ion energy distributions. Experimental results from ref. 5 support this observation. -
3.2. Evaluation of L We have indicated that the ratio LIX is a very important parameter. To evaluate it, we must first determine the value of L. Chapman [8] has shown that L can be calculated, knowing the current density, by using the free-fall version of the Child—Langmuir equation ~..
4e(2~y/2 v3!2 9 \M/ L2
This is quoted in SI units, where J is the cathode current density, ~ is the permittivity of free space, q is the ionic charge, M is the ion mass and V is the potential drop across L. The equation was derived for situations in which the following apply. (i) The cathode is bombarded on one face only, which is flat and infinitely large. (ii) Only one type of ionic species is present. (iii) The ions originate from the negative glow with an initial energy of zero. We investigated the applicability of the above equation, using a flat round steel cathode (24.6 cm in diameter), bombarded on one face only. Direct observation was used to determine L. We also considered results reported by other workers.
20 10 0
2
oOU• — 0
1.0
°
0.1 I
0.1
1.0
LPRED
(~s)
10
Fig. 1. Measured vs. predicted cathode fall lengths in argon discharges using a flat cathode with bombardment on one face only: 0, d.c. diode, refs. 3, 9, 10 and this work; S triode (thermionic support), ref. 11 and this work; •, triode (positive electrode), ref. 12.
Figure 1 shows how these measured values compare with those predicted by the equation, assuming Ar~to be the only species present. Layouts other than the simple d.c. diode were also used in these studies. We observed that the deviations for the published data were greater than those for our own work, partly because of our uncertainty about the methods and accuracies employed by other workers. Nevertheless the predicted line is a good fit through the points. It was also noticed that the diode predictions for our results were in general higher than those measured, though still nearer than for a supported or “enhanced” discharge, characterized by the designation of “triode” in the graph. These enhanced discharges used either an additional positive electrode, or a negative electron emitter. In our work, when the latter was used, its brightness to some extent obscured clear observation of the fall region. Another factor to bear in mind is that there will be an inaccuracy in the measurement of ion current density, as the current carried by secondary electrons is not known (though it is usually claimed to be typically 10% of the total). Higher gas pressures (up to 100 mTorr) were used in the diode experiments. Mobility limiting effects might then be expected to become more important. An alternative form of the Child—Langmuir equation is available to cover this situation, though this requires a mobility value which is difficult to ascertain. Gras-Marti et al. [13] have developed a model which can
21
consider situations intermediate between the free-fall and mobility-limited regimes. Our investigation of their data has not, however, proved their model to have any greater applicability than the free-fall Child—Langmuir equation above. 3.3. Evaluation of A To determine A, it is necessary to have a value for a, the collision crosssection for charge exchange (Ar~—Ar°). As can be seen from Fig. 2, there was for many years a high degree of uncertainty about this value. Recent data by Hegerberg and coworkers [14, 15] are now probably more reliable, and we have fitted a predictive equation for a reported by Sheldon [161 to these data and achieved good correlation. This is shown in Fig. 2.
IU~’
100
10’
10’
10’
10
EN~RG~(eV)
Fig. 2. Collision cross-section for Ark, Ar°charge transfer as a function of ion energy: ———, range of data by various authors up to 1964 [8], data points from Hegerberg and 1’2 exp(—k 2), coworkers [14, 15]; —, equation given by Sheldon [16], E = k fitted to the Hegerberg data where k 1u 20” 1 5.1985 X ~ h2 = 2.8954 x 108 (E in electronvolts, a in square centimetres).
Clearly, the original assumption of Davis and Vanderslice that a is independent of energy is not true. Since a spread of energies is usually encountered in practical systems, it is necessary to take an average value to evaluate A, which is equal to 1/na, where n is the number density the gas 3atof300 K, (e.g. if the pressure is 1 mTorr, then n = 3.211 X iO’~ cm~ assuming ideal gas conditions). For most of the practical systems with which we are familiar, an appropriate value for a is about 4 X 10-15 cm2, based on the estimated average energy of ions arriving at the cathode.
22
3.4. Use of LIX values Knowing L and A, we are able to use the resulting LIX values in the determination of ion energy spectra. Figure 3 shows two revealing curves whose evaluation is thus made possible. The first curve, showing the fraction of ions with maximum energy, is derived using the Davis and Vanderslice assumptions and collision theory, to take account of the fact that the collision probability increases exponentially with distance travelled. The fraction of ions that do not undergo collision (and therefore have maximum energy) will thus be equal to ~ which is field-independent. The second curve is derived from work by Rickards [2], converting his neutral average energy predictions into ion energy predictions for the space charge limited field case, where m = 4/3. 100
%
-
~ 80
-
60
-
\
\ \ \
£4Q
.
\ \
20
-
o
I 0,1
1111111
\
\
\
I 1.0
I’I~.4.._IIIII LI).,
10
Fig. 3. The variation of ion energy transportation characteristics with L/X: — — —, fraction of ions arriving at the cathode with maximum energy; , fraction of energy transported by ions (as opposed to that carried by neutrals).
4. Ion intensity and ionization efficiency Although the assessment of LIX and energy distributions as discussed in Section 3 are important, the overall intensity of energization (as dictated
23
by the degree of ionization) is also highly relevant. An indication of the intensity of ions arriving at the cathode is given by the cathode current density, but this on its own does not take account of the total number of bombarding particles, most of which are non-ionized in present systems. Although a proportion of these particles will be high energy neutrals (ions that have undergone charge exchange) the majority are thermal neutrals and their population will tend to increase with pressure. Thus, two discharge systems may have similar energy spectra and current density values, but if one system requires a higher pressure than the other to obtain these characteristics, it may in practice be inferior, as the greater number of thermal neutrals will tend to dilute any beneficial effects (e.g. on film formation and growth) from the more energetic species. We therefore need a further performance parameter which considers both pressure and current density: the ionization efficiency meets this requirement. This is defined as ef
—
N~x 100% N~0
where N6 is the number of ions arriving at the sample per square centimetre per second and ~ is the total number of bombardments per square centimetre per second. Previously reported values for ‘ef (e.g. ref. 17) have been based on the measured cathode current and overall pressure, regardless of the relative proportion of atomic species present (e.g. argon, nitrogen, titanium etc.). Thus Matthews, for example, used argon data in determining the ~ value. This, although not strictly representative, allowed the convenient comparison of data. Also, since the argon mass is between that of titanium and N2, the error will not be large; a more significant error lies in the assumption that the overall pressure represents the “pressure” at the cathode surface, although again this error can be estimated, and is usually small [17]. We have carried out studies on various discharge configurations, to confirm their relative performances in terms of ionization efficiency, and some of these results are reported in Section 5. However, we should re-emphasize that ionization efficiency is not the sole governing parameter for systems. In some ways, the word efficiency may cause confusion, as it has connotations of relative superiority. It is clear that some systems do not need to be operated at as high an ‘ef values as others [17], and indeed, provided the bias voltage levels are also low, these systems might well be considered to have an advantage in needing less discharge power to operate satisfactorily. On the subject of bias voltage it is also worth mentioning that, regarding film growth, we believe that the actual bias levels used need not be as high as was previously thought. Provided sufficient ion current can be obtained without needing to increase voltage, then the actual bias levels can be quite low (say, below 100 V). There is, however, likely to be a minimum required cathode fall potential, which we suggest can be expected to be 40 70 V on consideration of the collision cross-section for electron impact ionization -
24
and also the sputtering threshold. Above this critical value, increased cathode fall potentials may not necessarily have a beneficial effect on film properties. This has important implications, as discussed in Section 3, in optimizing energy distributions. 5. Studies on practical discharge systems 5.1. Systems with argon only We have outlined how LIX and ‘ef are particularly important parameters in plasma-assisted processes. Our initial approach was to evaluate these parameters for discharge configurations in argon only. Although this does not account for the presence of other species, it provides a relative indication of system performance, and also allows readily obtainable published data to be analysed. The possible contributions to system performance from other species will be discussed in Section 5.2. Table 1 summarizes energy transportation and ionization efficiency evaluations using data by various authors and ourselves for different argon discharge layouts. The following observations can be made. (i) LIX for diode systems is always greater than 10. This agrees with the findings of other workers, e.g. it is 15 in ref. 1 and 12 in ref. 18. In fact, LIX will not change appreciably for a diode configuration operating in the abnormal discharge mode because L, like A, is inversely proportional to discharge pressure. (ii) A triode discharge using a positively biased third electrode reduces LIX [12] and therefore increases the energy transported by ions compared with that transported by high energy neutrals. ‘ef is also seen to increase significantly compared with the equivalent diode system. (iii) Thode discharges using thermionic support can give very low LIX values, resulting in much of the energy being transported to the cathode by maximum energy ions. ‘ef values of several per cent can also be achieved. 5.2. Other considerations 5.2.1. Evaporant source and metal flux In general, the presence of the evaporant source and resulting metal flux reduces the current density in diodes, and also in triodes which use a positive third electrode (e.g. Fig. 4). This may be caused by several factors. Firstly, preferential ionization of the metal species will occur by argon metastables (Penning ionization), which may otherwise have become argon ions as a result of low energy electron impact. It is arguable that if the metal has a higher mass than the argon, then the current will fall (in agreement with the Child—Langmuir equation, for a given L). Alternatively, the effect may be purely one of distortion of the discharge producing a separate localized discharge and enhancement away from the cathode. With the thermionic negative electrode, the situation is even more complicated [191, and counteracting effects apparently operate (as shown in Fig. 4). —
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Fig. 4. Effect of electron beam gun power and evaporation on an argon triode discharge (argon pressure is 5 mTorr, titanium evaporation, ref. 19): •, thermionic negative biased electrode; 0, positive biased electrode.
There are limited data available on the energy distribution of metal ions in argon discharges. For metal species produced by sputtering at the cathode of an argon d.c. diode, estimated LIX values of 3 and 4 have been reported [12, 18]. For silver evaporated in an argon d.c. diode LIX for the metal was 1.5 [20]. These LIX values show that metal ions suffer less charge transfer collisions than argon in the cathode dark space (though the dominant charge transfer process is not clear) and therefore metal ion energy distributions will tend to have a greater high energy content than that for the Ar~ions. Further evidence for this is given by Armour et al. [5] who studied the evaporation of copper through an argon d.c. diode glow discharge. We have found no definite information on the effect of metal ions on the Ar~energy distribution, although it could be inferred from the total ion energy distribution results of Ahmed [4] (evaporation of lead) that the Ar~energy characteristics do not change appreciably. 5.2.2. Reactive gases and gas mixtures We have studied nitrogen and argon plus nitrogen discharges to ascertain the effect of a typical reactive gas on the discharge characteristics. These observations, we emphasize, may not apply for other gases, especially oxygen which has been widely reported to produce negative ions. In our studies the following was observed. (i) The nitrogen diode discharge was found to obey the free-fall Child— Langmuir equation, agreement being better when assuming N~rather than N2~ions. This concurs with the ion mass spectroscopy results of Valizadeh [7]. One of the mechanisms for the production of N~ions could be dissociative charge transfer of N2~within the cathode fall region. (ii) For a nitrogen triode with a negative thermionic emitter, we found that the improvement in current density was significantly less than that
found for argon under otherwise similar conditions. We believe that N2~is
27
more likely to be the dominant ionic species in this case, as dissociative charge transfer will be less likely, owing to the smaller cathode fall distance. This alone cannot, however, account for the lower improvement in current density compared with argon, neither can reductions in secondary electron emission at the steel cathode (because it is nitrided) fully account for this. One possible explanation follows from work by Natarajan et al. [21] who state that the cross-section for excitation of nitrogen molecules is very large and therefore thermalization of low energy electrons occurs. This in turn reduces the probability of subsequent ionizing collisions by the electrons. (iii) For equal partial pressure mixtures of argon and nitrogen, the measured L value was the mean of those measured for argon only and nitrogen only discharges at the same total pressure (measured with a capacitance manometer). Using the measured current density values, the predicted L for the mixture (using the average mass) was also found to be the mean of the predicted L values for the pure cases. This suggests that an argon—nitrogen mixture also follows the Child—Langmuir relationship (possibly indicating that there is little or no net interaction between the gas species). There are few published data available on the energy distribution characteristics of nitrogen-only discharges. Armour et al. [5] have, however, reported that the N~species in such discharges, under diode conditions, have similar energy distributions to those of Art This has been confirmed by the results of Valizadeh [7]. We may not, however, necessarily conclude that this also applies to thermionic triode conditions because of the observations outlined in (ii), above. 5.2.3. Impurities Background impurities can significantly affect discharges, and we believe that they have in the past been given insufficient attention. Hydrogenous contaminants were discussed by Knewstubb and Tickner [221, who mention the formation of ArH~and H3O~by the action of argon metastables on hydrogen, and water metastables on other water metastables respectively. Coburn and Kay [23 25] found large amounts of these species in the substrate plane (grounded anode) of an argon diode sputtering system. Although it is not known what the amounts were on the cathode, and there are little other reported data, it can be assumed that practical systems with even trace quantities of water vapour may produce significant hydrogenous ion populations in argon discharges, which may be detrimental to film properties. -
6. Conclusions An appraisal of the theoretical background to ionization-assisted deposition systems has been presented. The paper has demonstrated that the main theories and equations developed by plasma physicists for simplified discharge layouts are applicable to the practical deposition systems now widely used in industry, and can be used to characterize and optimize such systems. In particular, the followingcan be evaluated for optimization purposes.
28
(i) The cathode fall length, which has important implications on field uniformity around components being coated and the glow penetration within holes. (ii) The cathode fall length to charge exchange mean free path ratio, which allows determination of the ion and neutral energy transportation characteristics. (iii) Ionization efficiency, which has been used to indicate the ratio between the ion flux and total particle flux at the cathode. The intention of the paper has been to provide an introduction to the theoretical background to discharges and to show how this can have practical use. We have shown, for example, that the thermionically assisted triode layout can provide benefits in terms of ion energy transportation characteristics and cathode fall length control. Clearly, though, there is much fundamental research work needed before a full understanding of plasma-assisted processes can be achieved. In particular, the complex interactions between species in enhanced systems (especially when used for reactive deposition) need further attention. We believe that this can only be achieved by ensuring co-operation between the plasma physicists (often working on idealized systems) and those other scientists and engineers who must strive to optimize real industrial equipments.
Acknowledgments We have been aided in this work by helpful discussions with many individuals; we record our thanks to them all, especially to our coworkers within the Surface Engineering Laboratory at Hull University. We also gratefully acknowledge the SERC and Tecvac Limited who provided one of us (K.S.F.) with financial support during the course of this work. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14
W. D. Davis and T. A. Vanderslice, Phys. Rev., 131 (1963) 219. J. Rickards, Vacuum, 34 (1984) 559. Z. Wronski, Vacuum, 36 (1986) 329. N. A. G. Ahmed, J. Phys. E, 13 (1980) 1305. D. G. Armour, H. Valizadeh, F. A. H. Soliman and G. Carter, Vacuum, 34 (1984) 295. C. G. Crockett, Vacuum, 23 (1973) 11. H. Valizadeh, Ph.D. thesis, Salford University, 1982. B. N. Chapman, Glow Discharge Processes, Wiley, New York, 1980. W. D. Westwood and R. Boynton, J. App!. Phys., 43 (1972) 2691. G. Lamperiere, J. M. Poitevin and C. Fourrier, J. Phys. D, 11 (1978) 293. T. C. Tisone and P. D. Cruzan, J. Vac. Sci. Technol., 12 (1975) 1058. P. Saulnier, A. Debhi and J. Machet, Vacuum, 34 (1984) 765. A. Gras-Marti, I. Abril and J. A. Valles-Abarca, Thin Solid Films, 124 (1985) 59. R. Hegerberg, T. Stefansson and M. T. Elford, J. Phys. B, 11(1978) 133.
29 15 R. Hegerberg, M. T. Elford and H. R. Skullerud, J. Phys. B, 15 (1982) 797. 16 J. W. Sheldon, Phys. Rev. Lett., 8 (1962) 64. 17 A. Matthews, in W. D. Sproul, J. E. Greene and J. A. Thornton (eds.), Proc. Topical Symp. Physics and Chemistry of Protective Coatings, American Vacuum Society, Series 2, American Institute of Physics Conf. Proc., 149, AlP, New York, 1986. 18 J. E. Houston and J. E. Uhi, Report SC RR 0122, Sandia Laboratories, 1971. 19 A. Matthews, Ph. D. thesis, Salford University, 1980. 20 J. Machet, G. Gadet, P. Saulnier and J. Guille, in F. Abeles and M. Croset (eds.), 8th mt. Vacuum Con!., Cannes, France, Société Francaise Du Vide, 1980. 21 B. R. Natarajan, A. H. Eltoukhy, J. E. Greene and T. L. Barr, Thin Solid Films, 69 (1980) 201. 22 P. F. Knewstubb and A. W. Tickner, J. Chem. Phys., 36 (1962) 684. 23 J. W. Coburn, Rev. Sci. Instrum., 41 (1970) 1219. 24 J. W. Coburn and E. Kay, Appi. Ploys. Lett., 18(1971)435. 25 J. W. Coburn and E. Kay,Solid State Technol., Dec. (1971)49.