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A single quality factor for the deposition process of reactively sputtered thin a-C:H:N films
Journal of Non-Crystalline Solids 318 (2003) 322–330 www.elsevier.com/locate/jnoncrysol
A single quality factor for the deposition process of reactively sputtered thin a-C:H:N films G. Messina a, S. Santangelo
a,*
, A. Tagliaferro b, A. Tucciarone
c
a
INFM, Dipartimento di Meccanica e Materiali, Facolt a di Ingegneria, Universit a ÔMediterraneaÕ, localit a Feo di Vito, 89060 Reggio Calabria, Italy b INFM, Dipartimento di Fisica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy c INFM, Dipartimento di Scienze e Tecnologie Fisiche ed Energetiche, Universit a di Roma ÔTor VergataÕ, via Tor Vergata 110, 00133 Rome, Italy Received 12 December 2001; received in revised form 19 June 2002
Abstract The carbon bonding modifications, produced by the different deposition conditions in nitrogenated a-C:H films (a-C:H:N) prepared by reactive-sputtering of a graphite target, are investigated by quantitatively analysing the evolution of the D- and G-bands in the Raman spectra. The film C content is evaluated and shown to depend on the many variables involved into the a-C:H:N film growth through a single quality factor, dimensionless combination of the dimensional process-variables. The film structural changes observed are understood in terms of the decreasing sp3 :sp2 ratio achieved with the diminishing film C content. The quality factor introduced, able to indicate how the variableconfiguration can eventually change without significantly affecting the result in terms of C content and resulting film properties, represents a simple scaling law for the a-C:H:N film deposition, whose validity is preliminarily demonstrated for variations of rf power, total pressure and reactive-gas flow-rate in the ranges from 180 to 300 W, from 20 to 38 mTorr and from 5 to 27 sccm, respectively. A very simple model is therewith proposed accounting for the particular variable combination ultimately effective in determining the final issue of the deposition process. The generality of the proposed method is finally demonstrated. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 02.60.)x; 81.15.Cd; 78.30.Ly; 78.30.)j
1. Introduction
* Corresponding author. Tel.: +39-965 875 305; fax: +39-965 875 201. E-mail address: [email protected] (S. Santangelo).
In the last two decades, a considerable scientific and technological interest has been placed in both hydrogen-free (a-C) and hydrogenated (a-C:H) amorphous carbon films, whose outstanding physical properties, such as chemical inertness, high electrical-resistivity and mechanical-hardness, low
0022-3093/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-3093(02)01892-6
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friction-coefficient, high optical-transparency and wear-resistance, determine their wide applicability in a variety of fields ranging from optics to tribology, from electronics to biomedics. Recently, as a consequence of the great efforts made in the attempt to synthesise the hypothetical b-C3 N4 phase of crystalline carbon-nitride, expected, on the basis of a first-principles pseudopotential study [1], to be harder than diamond, the focus of attention has been enlarged to the nitrogen incorporation into amorphous carbon films. This has started and rapidly developed a novel exciting research field, centred on the progress in performances of current materials and open to the discovery of possible new related compounds endowed with improved physical properties for the realisation of future technological applications. In this ambit, N incorporation in a-C and a-C:H films has been demonstrated to result in a strong decrease in the internal compressive stress with consequent improved adhesion and only minor changes in hardness characteristics [2–4], as concerns mechanical behaviour, or in a significant increase of electrical conductivity and a substantial reduction of both optical band-gap width and defect-density [5–7], as regards electrical and optical properties. However, as the optimisation of the deposition conditions aimed at the attainment of the maximum sp3 :sp2 C bonding ratio still represents a crucial problem, the understanding of the dependence of the film physical properties on the growth conditions constitutes a fundamental issue in view of the achievement of a well-controlled growth process. Raman spectroscopy, able to monitor the C bonding modifications produced by the different deposition conditions, is widely used for non-destructive structural characterisation of a-C and related materials [8–14]. The 1000–2000 cm1 Raman spectra of a-C based films are dominated by two broad bands approximately centred at 1360 and 1550 cm1 , the well-known D- and G-bands [8,9]. As frequency positions, widths and intensity ratio of these bands reflect the C bonding-nature of the grown film, the deposition process can be optimised on the basis of the indications achieved by analysing the evolution of the D- and G-bands in the Raman spectra.
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Unfortunately, due to the complexity of the growth process and the great number of variables involved, it can be not easy to understand the role of each deposition variable in determining the film characteristics resulting from the Raman analysis and, even less, to predict the effect produced by any variable-configuration change on the final issue of the growth process. In this paper, this question is solved thanks to an extended application of BuckinghamÕs theorem of Dimensional Analysis [15], already successfully applied to the case of Monte Carlo modelling of electron scattering [16–18], analogously involving a lot of independent process-variables. The C bonding modifications, produced by the different deposition conditions in sputter-deposited a-C:H:N films, evidenced by quantitatively analysing the shape evolution of the Raman spectra, are understood in the light of the variation of the calculated film C content. A dimensionless combination of the dimensional deposition-variables is introduced and shown to behave as a quality factor for a-C:H:N film deposition by graphite sputtering. A simple scaling law for the growth process is therewith determined, indicating how the configuration of the variables involved can eventually change without affecting the result in terms of C content and resulting film properties. 2. Experimental details Thin films of a-C:H:N were deposited on (1 0 0) c-silicon substrates by a 13.56 MHz rf diode sputtering system, operating with an Ar–He–N2 – H2 gas mixture. The (99.999% purity) graphite target was set at 25 mm from the grounded electrode holding the substrate. No external bias was applied. During the deposition, the substrate temperature was kept at 100 °C. The rf power, the total pressure and the flow-rate of the reactive gases were respectively varied between 180 and 300 W, 20 and 38 mTorr and 5 and 27 sccm (standard cubic centimetres per minute), as reported in Table 1. An Ar:He flow ratio of 7:3 was used, except for films #1 and #2, prepared with inverse Ar:He flow ratio. Further details about growth process are reported elsewhere [19,20]. The samples were not compositionally characterised.
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Table 1 Frequency position (fG ) and band width (wG ) of the G-band and D/G intensity ratio (ID =IG ) as a function of the deposition conditions of the investigated a-C:H:N samplesa Film
Wrf (W)
ptot (mTorr)
UN2 (sccm)
UH2 (sccm)
xC (ad.u.)
fG (cm1 )
wG (cm1 )
ID =IG (ad.u.)
LC (nm)
Q (ad.u.)
#a #b #c #d #e #f #g
300 300 300 300 220 200 180
20 25 38 38 38 30 38
20.0 10.0 4.2 8.4 4.2 4.2 3.0
7.0 7.0 3.0 3.0 3.0 2.2 2.2
0.704 0.711 0.769 0.704 0.734 0.776 0.767
1575 1574 1563 1575 1568 1562 1564
140 146 150 123 128 148 140
1.66 1.82 3.07 3.32 3.17 2.73 3.38
1.74 1.82 1.40 1.33 1.39 1.61 1.30
0.55 0.71 1.10 0.69 0.80 1.04 0.91
The film C content (xC ) and the average graphitic cluster size (LC ), as respectively estimated from fG and ID =IG , are also reported, together with the values obtained for the dimensionless growth quality-factor (Q) in correspondence of the given deposition conditions. a Rf power (Wrf ), total pressure (ptot ), N2 flow-rate (UN2 ) and H2 flow-rate (UH2 ).
The Raman characterisation of nitrogenated a-C:H films was carried out, at room temperature, by using a Jobin Yvon Ramanor U-1000 double monochromator equipped with an electrically cooled Hamamatsu R943-02 photomultiplier as a detector and photon counting electronics. A Coherent Innova 70 Arþ laser, operating at 514.5 nm wavelength was utilised as excitation source. The S/N ratio was improved by recording multiple scans. In order to prevent laser-annealing effects, a spot size of about 50 lm diameter and a power of 40 mW at the sample surface were used, so as to achieve a power density by far below the damagethreshold [21]. The Stokes-shifted spectra were recorded in the region between 1000 and 2000 cm1 . According to the conventional approach [22], Gaussian bands, superimposed to a linear photoluminescence background, were considered in order to decompose the spectra and monitor, through the evolution of the D- and G-bands, the structural modifications produced by the different growth conditions. The frequency position, width (FWHM) and intensity of these bands were chosen, via a least-square best-fit method, utilising a commercially available spectroscopic analysis software package.
3. Results The Raman spectra of the a-C:H:N investigated samples are shown in Fig. 1. As can be seen, the independent variation of four process variables
Fig. 1. Evolution of the D- and G-bands in the Raman spectra of the investigated a-C:H:N films. The spectra of samples #c and #f are practically superimposed.
(namely, rf power, total pressure and flow-rate of the two reactive gases) results in a considerable increase of photoluminescence background intensity and in a gradual change of the spectral profile. The main parameters describing the evolution of the D- and G-bands, obtained by the fitting procedure, are listed in Table 1. No clear correlation between the variations in growth conditions and the corresponding changes in Raman spectra fitting parameters does seem to exist. This is shown in case of the frequency position of the G-band, fG , plotted in Fig. 2(a), as a function of the flow-
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Fig. 2. Dependence on the flow-rate of reactive-gases, UN2 þH2 , of (a) the frequency position, fG , of the G-band and of (b) the correspondingly estimated film C content, xC .
rate of the reactive gases, UN2 þH2 . The simultaneous variations of total pressure and rf power cause a confused spreading of the representative fG -points into the (UN2 þH2 ; fG )-plane, thus making it not easy to readily understand in what direction the effect of a change in reactive-gas flow-rate goes. The same (Fig. 2(b)) is for the film C content, xC , as evaluated, from fG -values of Table 1, via the empirical relationship [23]. 4. Discussion According to the current interpretation [10], the upshift and shrinking of the G-band (Table 1), observed in films deposited under lower reactivegas flow rates (from sample #c to #g) are indica-
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tive of a gradual diminishing of the sp3 :sp2 C bonding fraction; meanwhile, the increase in average size of the graphitic domains, as estimated from the D/G intensity ratio 1 by means of Tuinstra–Koenig [24] and Ferrari–Robertson [25] relationships, evidences the occurrence of a progressive clustering process. Such a tendency towards graphitisation is understood in terms of the observed film C content diminishing [26]. However, due to the complexity of the growth process and the great number of variables involved (rf power, chamber pressure and geometry, gasmixture composition and flow-rates of inlet gases, target/substrate distance, deposition temperature,. . .), the role played by each deposition variable in determining the film characteristics resulting from the Raman analysis remains unclear. This hinders from predicting the effect produced by any variable-configuration change on the final issue of the growth process, also in cases where, similarly to the investigated one, only a few process-parameters are actually changed. A simpler picture may derive from eventually finding a dependence of xC on combinations of the variables, such as the dimensionless parameters introduced by Buckingham in the theorem on physically similar systems [15]. Therefore, a dimensionless combination of dimensional variables is introduced, Q¼
Wrf ; ptot UN2 þH2
ð1Þ
with Wrf (W), ptot (mTorr) and UN2 þH2 (sccm) respectively denoting the rf power, the total pressure and the flow rate of the reactive-gases, N2 and H2 , that can be reasonably assumed, on a physicalbesides a dimensional- basis, as important in determining xC . Then, a xC -dependence on the argument Q is tentatively supposed, to be verified by comparison with the numerical data. In Fig. 3(a) the estimated film C content is plotted as a function of Q, with evident simplification in comparison with Fig. 2(b). In spite of the variation
1
The Tuinstra–Koenig [24] or the Ferrari–Robertson [25] relationship has been used depending on the D/G intensity ratio exceeded or not the critical value of 2.2 [25], respectively.
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a scaling law for the growth a-C:H:N films by reactive sputtering: if, f.i., the Wrf is varied, Q indicates how UN2 þH2 should correspondingly scale, at a given ptot , in order to compensate for the desired variation with no or very small changes in the film C content; i(ii) All the variation of xC , in the range of Q considered, is well accounted for by the simple empirical law, 8 ! Q 0:230 ; xC ðQÞ ¼ 0:774 0:074 exp 0:607
ð2Þ
Fig. 3. Dependence on the dimensionless argument Q of (a) the film C content, xC , and of (b) the frequency position, fG , of the G-band. The data of Fig. 2(b) and (a) are shown, respectively. In case (b) a dotted line is drawn as a visual help; the dashed line of case (a) represents the fitted curve, xC ðQÞ ¼ 0:774 0:074fexp½ðQ 0:230Þ=0:6078 g.
of rf power from 180 to 300 W, total pressure from 20 to 38 mTorr and reactive-gas flow-rate from 5 to 27 sccm, xC -points line up, within the experimental errors, along a single curve, thus demonstrating the existence of the assumed xC ðQÞ law and the effectiveness of the variable-combination (1) in determining the film C content and related [26] properties. This finding has many remarkable outcomes: ii(i) In a first approximation, Q contains all the dependence of xC on the varying depositionconditions. Hence, although within the variable-range considered, it actually constitutes
fully satisfactory for all practical purposes (the explicit form of the law utilised for interpolating numerical data has been deduced by the model derivation of Q exposed in Section 5). The attainment of a practical expression, approximating in a simple way the physical law governing the growth of a-C:H:N samples, is clearly of crucial importance. The existence of an analytical dependence of xC on Q, in fact, (a) not only makes capable of predicting the effect, in terms of film C content, produced by any variable-configuration change on the deposition process, (b) but further enables the film-quality tailoring by properly tuning the growth parameters: the desired xC value can be obtained, even starting from different deposition-conditions, provided that these finally give the suited value of Q; (iii) Finally, as the changes in the growth conditions determine an increase of Q, xC correspondingly raises, suggesting a possible improvement [23,26] of the deposited-film quality. Actually, if the fG -data of Fig. 2(a) are plotted against the film-quality factor Q (Fig. 3(b)), the representative fG -points are found to show a well-defined decreasing trend for increasing Q. Since the G-band downshift is indicative of an enhancement of the sp3 :sp2 bonding fraction [10], the argument Q is concluded to be a reliable quality-factor for aC:N:H film deposition by graphite reactivesputtering.
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5. Derivation of the empirical law Far from establishing a model of the growth process applicable to all the variables actually involved into the film deposition, the aim of this Section is rather to get more insight into the role of those, whose variation has been here investigated, in determining the structural and bonding characteristics of the samples under study. Thus, in order to understand the qualitative behaviour of the empirical xC ðQÞ curve in Fig. 3(a), we consider closely how the sputtering of the graphite target progresses for increasing Q. The sp3 :sp2 C bonding ratio of a-C based materials seem to be determined by the amount of C species trapped into the growing film [27]. Moreover, it has been shown that an increasingly higher sp3 C bonding component can be obtained with increasing the energy of C ions up to tens of eV [27–29]. Hence, the average ion impact energy on the film surface, ECi , and the flux of sputtered C atoms that actually reach the substrate, FC!sub , are both thought of as important in ultimately deciding the bonding configuration of the C atoms forming the film. Arbitrarily assuming that the dimensionless combination of the depositionparameters effective in determining the film C content can be derived from ECi and FC!sub , Q is tentatively written, according to [15], as a power product of these microscopic process-variables, namely, a
c
Q ¼ ðECi Þ ðFC!sub Þ ;
ð3Þ
with a and c exponents to be empirically determined. Supposing FC!sub to be controlled, in a basic approximation, by both density, qrg , and permanence-times into the deposition chamber, srg , of the reactive gases, which carry on a competitive action against carbon to the ends of the incorporation within the film, it is assumed r
s
FC!sub / ðqrg Þ ðsrg Þ ; with r and s standing for positive exponents. Under the present deposition conditions, i(i) qrg and ECi , on turns, result respectively roughly proportional to the partial pressure
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of reactive gases, pN2 þH2 , and to a power product of rf power and total pressure (namely, n qrg / pN2 þH2 and ECi / Wrfm ptot , with m ¼ 1=2 and n ¼ 1 [30]), meanwhile the permanencetime of the gas X being approximately determined by the ratio between its partial-pressure and flow-rate (i.e., sX / pX =UX , if the fixed deposition-chamber volume is neglected, so as sN2 ffi sH2 ); and (ii) being DUN2 þH2 =UN2 þH2 DUtot =Utot , the flowrate of all the gases let in the deposition chamber, Utot , is taken as coarsely constant. Aiming chiefly at clarifying the role played by the changes in growth-conditions in producing the C bonding modifications evidenced by Raman analysis, in the light of points (i) and (ii), the variations of qrg / ptot UN2 þH2 U1 and srg / tot ptot U1 , will be below considered as mostly detertot mined by those of ptot UN2 þH2 and ptot , respectively. On the basis of these simplifications, the combination of microscopic variables (3), that, rewritten in terms of measurable deposition-variables 1=2 1 a r is given by ðWrf ptot Þ ½ðptot UN2 þH2 U1 tot Þ 1 s c ðptot Utot Þ , becomes 1=2
1 a sr r Þ ðptot UN2 þH2 Þc ðWrf ptot
ð4Þ
and results dimensionless for a=2 ¼ rc ¼ a þ ðr sÞc. If, for the sake of simplicity, without loss of generality, it is arbitrarily set a=2 ¼ 1, expression (4) simplifies to Eq. (1). In addition, since a ¼ 2 is found, Q results proportional to the square of ECi . Such a finding implies that the effective variable-combination depends more than linearly on (4th power of) the fraction of forward-sputtered ions [31]. Contrarily, some further hypothesis has to be formulated in order to obtain the exponent c. If FC!sub is basically supposed inversely proportional to qrg (i.e. r ¼ 1 is taken), s ¼ 2 and c ¼ 1 are derived. The former result corresponds to assume 1 2 that FC!sub / q1 rg srg , i.e. / ptot UN2 þH2 . The latter finding, instead, assesses that the flux of sputtered C atoms, which actually reach the substrate, is linearly involved in the derived combination of microscopic variables, ðECi Þ2 FC!sub . One can reasonably conceive that different growth regimes take place with varying the deposition variables:
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(i) Until, f.i., a low Wrf is utilised, films with lower C content are grown, as an effect of the low ECi (low Q regime); (ii) As, f.i., UN2 þH2 is diminished, as an effect of the minor amount N and H atoms actually reaching the substrate, FC!sub raises and progressively C-richer a-C:H:N films are grown (high Q regime); (iii) If the growth conditions are still changed in the same direction, f.i., decreasing ptot , i.e. enhancing ECi while simultaneously decreasing qrg and srg , the deposition process at 100 °C ultimately reaches a limiting regime and xC raises no longer.
of xC produced by the changing growth conditions in the range of Q considered. In this model, Q can be thought of as the critical value of Q, which discriminates the two different regimes taking place in the deposition process. In the low-Q regime (namely, Q Q þ Q0 ), C atoms are mainly sp2 -bonded in the C-poorer film network; oppositely, in the high-Q regime, C-richer films are attained with improved sp3 :sp2 C bonding ratio.
The behaviour of the derived physical approximant to the xC -data (2) can be qualitatively understood on the basis of the simple model proposed below. Under the described conditions, the number of sputtered C atoms which ultimately reach the substrate during deposition, effectively acquires a more-than linear dependence on the argument Q. xC can be thus supposed Qa -dependent, with a an exponent >1. If the variation, dxC , undergone for an increment of the effective-variable Qa is taken as proportional, according to the simplest possibility, besides to d(Qa ), to the residual ÔdistanceÕ of xC from its saturation value, xC , namely,
(i) The presented method, far from representing a rigorous theoretical model of the growth process, exactly accounting for the behaviour of the microscopic variables (average ion impact energy, atom impact velocity onto the substrate, flux of C atoms towards the plasma and of each atomic species towards substrate and target, sputtering yield of Ar and N atoms, gas permanence time, plasma potential, . . .), that rule the complex chemical and physical deposition-mechanisms and ultimately decide the C bonding configurations of the grown films, constitutes a semiempirical approach, rather aimed at achieving an approximated solution in terms of the varying measurable deposition-parameters involved into the problem; (ii) Several drastically simplifying hypothesises and arbitrary assumptions have been made to deduce the expression relating Q with the microscopic variables. However, it has to be emphasised that the effective combination consequently obtained is actually able to account for the experimental results, as demonstrated; (iii) Moreover, the present analysis refers to the quite limited set of investigated films and, therefore, the shown results have to be regarded only as a preliminary solution to the problem; (iv) The generality of the method, here applied to the case of a-C:N:H film deposition by reactive-sputtering of a graphite target, suggests
dxC / ðxC xC ÞdðQa Þ; the differential equation obtained can be solved, finally giving a xC ðQÞ xC Q Q0 ¼ exp ; x0 xC Q where xC , x0 , Q , Q0 and a are constants to be empirically determined. In order to test the above equation, verify the hypothesis about the exponent a and determine numerical values of xC , x0 , Q and Q0 the data of Fig. 3(a) are fitted. By this procedure, the functional dependence, theoretically deduced, is actually demonstrated and a > 1 confirmed. In particular, by fitting the data, xC ¼ 0:774, x0 ¼ 0:700, Q ¼ 0:607, Q0 ¼ 0:230 and a ¼ 8 are derived (i.e. relation (2) is obtained). The resulting expression accurately approximates the variation
5.1. Additional remarks It is, finally, worthwhile to point out that:
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the possibility of its extensive application to all growth techniques, involving systems and physical processes susceptible to being mathematically modelled. This is demonstrated in Fig. 4, where the dependence on Q ¼ 1 1 Wrf ptot Urg (Urg standing for the flow rate of reactive gases), is shown, of fG -data relative to hard a-C:H:N films, grown by plasma enhanced chemical vapour deposition, in methylamine containing mixture [32] and in methane–ammonia atmosphere [33]. Of course, some coefficient refinement in the empirical law derived could be necessary in the presence of a wider Q variation-range. Instead, a generalisation of the quality-factor introduced is required if cases are considered, where a greater number of deposition parameters is allowed varying, as found for a-C:N and a-C:N:O films deposited, by rf magnetron sputtering, respectively in Ar–N2 and N2 –O2 atmospheres [34], as well as, for a-C:N samples prepared in N2 atmosphere and annealed [35]. Nevertheless, the semiempirical approach here proposed constitutes a powerful tool for gaining hints for an easy-understanding, as well as, for achieving a ready-predicting capability about the final issue of the growth process.
1 1 Fig. 4. Dependence of fG on Q ¼ Wrf ptot Urg (Urg denoting the flow rate of reactive gases) for presently investigated samples and literature hard a-C:H:N films, grown by plasma enhanced chemical vapour deposition, in methylamine containing mixture and in methane–ammonia atmosphere (a line is drawn as a visual help).
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6. Conclusion Hydrogenated amorphous carbon films containing nitrogen are deposited, at 100 °C, by graphite sputtering in Ar–He atmosphere with the addition of N2 and H2 as reactive gases. Aiming at the optimisation of the growth process, a Raman analysis is carried out in order to clarify the role played by each variable involved into the film deposition, in determining the a-C:H:N properties. The evolution of the D- and G-bands in the Raman spectra, reflecting the C bonding modifications produced by the different deposition conditions, is quantitatively analysed and the film C content is evaluated. The film C content, whose diminishing is thought as responsible for the decreasing of the sp3 :sp2 C bonding ratio evidenced by the Raman characterisation results, is shown to depend on the variables involved into the a-C:H:N film growth through a single dimensionless combination of the 1 1 dimensional process-variables, Wrf ptot UN2 þH2 , where rf power Wrf , total pressure ptot and reactivegas flow-rate UN2 þH2 are expressed in W, mTorr and sccm, respectively. The dimensionless argument introduced, able to indicate how the variable-configuration can eventually change without significantly affecting the result in terms of C content and resulting film properties, constitutes a scaling law for the a-C:H:N film deposition, whose validity is here preliminarily demonstrated for variations of rf power, total pressure and reactive-gas flow-rate in the ranges from 180 to 300 W, from 20 to 38 mTorr and from 5 to 27 sccm, respectively. By interpolating the experimental data, a simple empirical law is therewith found, accounting for all the variation of the C content in the range of process-variables considered. The analysis of the Raman characterisation results in the light of these findings suggests that the derived dimensionless variable-combination can be regarded as a reliable quality-factor for the a-C:H:N film deposition process. A very simple derivation model is proposed, accounting for the chosen variable-combination and the explicit form of the empirical law approximating the physical laws governing the process and its final issue, and
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the generality of the presented method finally evidenced.
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[18] G. Messina, A. Paoletti, S. Santangelo, A. Tucciarone, Il Nuovo Cimento D 20 (1998) 1201. [19] G. Fusco, F. Giorgis, C.F. Pirri, A. Tagliaferro, E. Tresso, C. De Martino, P. Rava, Defects Diff. Forum 134&135 (1996) 3. [20] C. De Martino, F. De Michelis, G. Fusco, A. Tagliaferro, Diamond Relat. Mater. 5 (1996) 461. [21] M. Bowden, D.J. Gardiner, J.M. Southall, J. Appl. Phys. 71 (1992) 521. [22] M.A. Tamor, W.C. Vassel, J. Appl. Phys. 76 (1994) 3823. [23] G. Messina, S. Santangelo, G. Fanchini, A. Tagliaferro, A. Tucciarone, in: G. Messina, S. Santangelo (Eds.), GNSR2001: State-of-art and Future Development in Raman Spectroscopy and Related Techniques, IOS, Amsterdam, 2002, p. 244. [24] F. Tuinstra, J.L. Koenig, J. Chem. Phys. 53 (1970) 1126. [25] A.C. Ferrari, J. Robertson, Phys. Rev. B 61 (2000) 14095. [26] G. Fanchini, G. Messina, A. Paoletti, S.C. Ray, S. Santangelo, A. Tagliaferro, A. Tucciarone, Surf. Coat. Technol. 151&152 (2002) 257. [27] Y. Lifshitz, Diamond Relat. Mater. 5 (1996) 388. [28] M. Chhowalla, J. Robertson, C.W. Chen, S.R.P. Silva, C.A. Davis, G.A.J. Amaratunga, W.I. Milne, J. Appl. Phys. 81 (1997) 139. [29] M.P. Siegal, P.N. Provencio, D.R. Tallant, R.L. Simpson, Appl. Phys. Lett. 76 (2000) 2047. [30] G. Messina, S. Santangelo, G. Fanchini, A. Tagliaferro, C.E. Nobili, G. Ottaviani, A. Paoletti, A. Tucciarone, Diamond Relat. Mater. 11 (2002) 1166. [31] P.J. Fallon, V.S. Veerasamy, C.A. Davis, J. Robertson, G.A.J. Amaratunga, W.I. Milne, J. Koskinen, Phys. Rev. B 48 (1993) 4777, and references cited therein. [32] D.F. Franceschini, F.L. Freire Jr., C.A. Achete, G. Mariotto, Diamond Relat. Mater. 5 (1996) 471, and private communication. [33] M.M. Lacerda, D.F. Franceschini, F.L. Freire Jr., G. Mariotto, Diamond Relat. Mater. 6 (1997) 631. iroky, J. Sobota, V. Perina, V. Zelezny, [34] V.G. Vorlıcek, P. S J. Hrdina, Diamond Relat. Mater. 5 (1996) 570. [35] M.M. Lacerda, F.L. Freire Jr., G. Mariotto, Diamond Relat. Mater. 7 (1998) 412.
A single quality factor for the deposition process of reactively sputtered thin a-C:H:N films G. Messina a, S. Santangelo
a,*
, A. Tagliaferro b, A. Tucciarone
c
a
INFM, Dipartimento di Meccanica e Materiali, Facolt a di Ingegneria, Universit a ÔMediterraneaÕ, localit a Feo di Vito, 89060 Reggio Calabria, Italy b INFM, Dipartimento di Fisica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy c INFM, Dipartimento di Scienze e Tecnologie Fisiche ed Energetiche, Universit a di Roma ÔTor VergataÕ, via Tor Vergata 110, 00133 Rome, Italy Received 12 December 2001; received in revised form 19 June 2002
Abstract The carbon bonding modifications, produced by the different deposition conditions in nitrogenated a-C:H films (a-C:H:N) prepared by reactive-sputtering of a graphite target, are investigated by quantitatively analysing the evolution of the D- and G-bands in the Raman spectra. The film C content is evaluated and shown to depend on the many variables involved into the a-C:H:N film growth through a single quality factor, dimensionless combination of the dimensional process-variables. The film structural changes observed are understood in terms of the decreasing sp3 :sp2 ratio achieved with the diminishing film C content. The quality factor introduced, able to indicate how the variableconfiguration can eventually change without significantly affecting the result in terms of C content and resulting film properties, represents a simple scaling law for the a-C:H:N film deposition, whose validity is preliminarily demonstrated for variations of rf power, total pressure and reactive-gas flow-rate in the ranges from 180 to 300 W, from 20 to 38 mTorr and from 5 to 27 sccm, respectively. A very simple model is therewith proposed accounting for the particular variable combination ultimately effective in determining the final issue of the deposition process. The generality of the proposed method is finally demonstrated. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 02.60.)x; 81.15.Cd; 78.30.Ly; 78.30.)j
1. Introduction
* Corresponding author. Tel.: +39-965 875 305; fax: +39-965 875 201. E-mail address: [email protected] (S. Santangelo).
In the last two decades, a considerable scientific and technological interest has been placed in both hydrogen-free (a-C) and hydrogenated (a-C:H) amorphous carbon films, whose outstanding physical properties, such as chemical inertness, high electrical-resistivity and mechanical-hardness, low
0022-3093/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-3093(02)01892-6
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friction-coefficient, high optical-transparency and wear-resistance, determine their wide applicability in a variety of fields ranging from optics to tribology, from electronics to biomedics. Recently, as a consequence of the great efforts made in the attempt to synthesise the hypothetical b-C3 N4 phase of crystalline carbon-nitride, expected, on the basis of a first-principles pseudopotential study [1], to be harder than diamond, the focus of attention has been enlarged to the nitrogen incorporation into amorphous carbon films. This has started and rapidly developed a novel exciting research field, centred on the progress in performances of current materials and open to the discovery of possible new related compounds endowed with improved physical properties for the realisation of future technological applications. In this ambit, N incorporation in a-C and a-C:H films has been demonstrated to result in a strong decrease in the internal compressive stress with consequent improved adhesion and only minor changes in hardness characteristics [2–4], as concerns mechanical behaviour, or in a significant increase of electrical conductivity and a substantial reduction of both optical band-gap width and defect-density [5–7], as regards electrical and optical properties. However, as the optimisation of the deposition conditions aimed at the attainment of the maximum sp3 :sp2 C bonding ratio still represents a crucial problem, the understanding of the dependence of the film physical properties on the growth conditions constitutes a fundamental issue in view of the achievement of a well-controlled growth process. Raman spectroscopy, able to monitor the C bonding modifications produced by the different deposition conditions, is widely used for non-destructive structural characterisation of a-C and related materials [8–14]. The 1000–2000 cm1 Raman spectra of a-C based films are dominated by two broad bands approximately centred at 1360 and 1550 cm1 , the well-known D- and G-bands [8,9]. As frequency positions, widths and intensity ratio of these bands reflect the C bonding-nature of the grown film, the deposition process can be optimised on the basis of the indications achieved by analysing the evolution of the D- and G-bands in the Raman spectra.
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Unfortunately, due to the complexity of the growth process and the great number of variables involved, it can be not easy to understand the role of each deposition variable in determining the film characteristics resulting from the Raman analysis and, even less, to predict the effect produced by any variable-configuration change on the final issue of the growth process. In this paper, this question is solved thanks to an extended application of BuckinghamÕs theorem of Dimensional Analysis [15], already successfully applied to the case of Monte Carlo modelling of electron scattering [16–18], analogously involving a lot of independent process-variables. The C bonding modifications, produced by the different deposition conditions in sputter-deposited a-C:H:N films, evidenced by quantitatively analysing the shape evolution of the Raman spectra, are understood in the light of the variation of the calculated film C content. A dimensionless combination of the dimensional deposition-variables is introduced and shown to behave as a quality factor for a-C:H:N film deposition by graphite sputtering. A simple scaling law for the growth process is therewith determined, indicating how the configuration of the variables involved can eventually change without affecting the result in terms of C content and resulting film properties. 2. Experimental details Thin films of a-C:H:N were deposited on (1 0 0) c-silicon substrates by a 13.56 MHz rf diode sputtering system, operating with an Ar–He–N2 – H2 gas mixture. The (99.999% purity) graphite target was set at 25 mm from the grounded electrode holding the substrate. No external bias was applied. During the deposition, the substrate temperature was kept at 100 °C. The rf power, the total pressure and the flow-rate of the reactive gases were respectively varied between 180 and 300 W, 20 and 38 mTorr and 5 and 27 sccm (standard cubic centimetres per minute), as reported in Table 1. An Ar:He flow ratio of 7:3 was used, except for films #1 and #2, prepared with inverse Ar:He flow ratio. Further details about growth process are reported elsewhere [19,20]. The samples were not compositionally characterised.
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Table 1 Frequency position (fG ) and band width (wG ) of the G-band and D/G intensity ratio (ID =IG ) as a function of the deposition conditions of the investigated a-C:H:N samplesa Film
Wrf (W)
ptot (mTorr)
UN2 (sccm)
UH2 (sccm)
xC (ad.u.)
fG (cm1 )
wG (cm1 )
ID =IG (ad.u.)
LC (nm)
Q (ad.u.)
#a #b #c #d #e #f #g
300 300 300 300 220 200 180
20 25 38 38 38 30 38
20.0 10.0 4.2 8.4 4.2 4.2 3.0
7.0 7.0 3.0 3.0 3.0 2.2 2.2
0.704 0.711 0.769 0.704 0.734 0.776 0.767
1575 1574 1563 1575 1568 1562 1564
140 146 150 123 128 148 140
1.66 1.82 3.07 3.32 3.17 2.73 3.38
1.74 1.82 1.40 1.33 1.39 1.61 1.30
0.55 0.71 1.10 0.69 0.80 1.04 0.91
The film C content (xC ) and the average graphitic cluster size (LC ), as respectively estimated from fG and ID =IG , are also reported, together with the values obtained for the dimensionless growth quality-factor (Q) in correspondence of the given deposition conditions. a Rf power (Wrf ), total pressure (ptot ), N2 flow-rate (UN2 ) and H2 flow-rate (UH2 ).
The Raman characterisation of nitrogenated a-C:H films was carried out, at room temperature, by using a Jobin Yvon Ramanor U-1000 double monochromator equipped with an electrically cooled Hamamatsu R943-02 photomultiplier as a detector and photon counting electronics. A Coherent Innova 70 Arþ laser, operating at 514.5 nm wavelength was utilised as excitation source. The S/N ratio was improved by recording multiple scans. In order to prevent laser-annealing effects, a spot size of about 50 lm diameter and a power of 40 mW at the sample surface were used, so as to achieve a power density by far below the damagethreshold [21]. The Stokes-shifted spectra were recorded in the region between 1000 and 2000 cm1 . According to the conventional approach [22], Gaussian bands, superimposed to a linear photoluminescence background, were considered in order to decompose the spectra and monitor, through the evolution of the D- and G-bands, the structural modifications produced by the different growth conditions. The frequency position, width (FWHM) and intensity of these bands were chosen, via a least-square best-fit method, utilising a commercially available spectroscopic analysis software package.
3. Results The Raman spectra of the a-C:H:N investigated samples are shown in Fig. 1. As can be seen, the independent variation of four process variables
Fig. 1. Evolution of the D- and G-bands in the Raman spectra of the investigated a-C:H:N films. The spectra of samples #c and #f are practically superimposed.
(namely, rf power, total pressure and flow-rate of the two reactive gases) results in a considerable increase of photoluminescence background intensity and in a gradual change of the spectral profile. The main parameters describing the evolution of the D- and G-bands, obtained by the fitting procedure, are listed in Table 1. No clear correlation between the variations in growth conditions and the corresponding changes in Raman spectra fitting parameters does seem to exist. This is shown in case of the frequency position of the G-band, fG , plotted in Fig. 2(a), as a function of the flow-
G. Messina et al. / Journal of Non-Crystalline Solids 318 (2003) 322–330
Fig. 2. Dependence on the flow-rate of reactive-gases, UN2 þH2 , of (a) the frequency position, fG , of the G-band and of (b) the correspondingly estimated film C content, xC .
rate of the reactive gases, UN2 þH2 . The simultaneous variations of total pressure and rf power cause a confused spreading of the representative fG -points into the (UN2 þH2 ; fG )-plane, thus making it not easy to readily understand in what direction the effect of a change in reactive-gas flow-rate goes. The same (Fig. 2(b)) is for the film C content, xC , as evaluated, from fG -values of Table 1, via the empirical relationship [23]. 4. Discussion According to the current interpretation [10], the upshift and shrinking of the G-band (Table 1), observed in films deposited under lower reactivegas flow rates (from sample #c to #g) are indica-
325
tive of a gradual diminishing of the sp3 :sp2 C bonding fraction; meanwhile, the increase in average size of the graphitic domains, as estimated from the D/G intensity ratio 1 by means of Tuinstra–Koenig [24] and Ferrari–Robertson [25] relationships, evidences the occurrence of a progressive clustering process. Such a tendency towards graphitisation is understood in terms of the observed film C content diminishing [26]. However, due to the complexity of the growth process and the great number of variables involved (rf power, chamber pressure and geometry, gasmixture composition and flow-rates of inlet gases, target/substrate distance, deposition temperature,. . .), the role played by each deposition variable in determining the film characteristics resulting from the Raman analysis remains unclear. This hinders from predicting the effect produced by any variable-configuration change on the final issue of the growth process, also in cases where, similarly to the investigated one, only a few process-parameters are actually changed. A simpler picture may derive from eventually finding a dependence of xC on combinations of the variables, such as the dimensionless parameters introduced by Buckingham in the theorem on physically similar systems [15]. Therefore, a dimensionless combination of dimensional variables is introduced, Q¼
Wrf ; ptot UN2 þH2
ð1Þ
with Wrf (W), ptot (mTorr) and UN2 þH2 (sccm) respectively denoting the rf power, the total pressure and the flow rate of the reactive-gases, N2 and H2 , that can be reasonably assumed, on a physicalbesides a dimensional- basis, as important in determining xC . Then, a xC -dependence on the argument Q is tentatively supposed, to be verified by comparison with the numerical data. In Fig. 3(a) the estimated film C content is plotted as a function of Q, with evident simplification in comparison with Fig. 2(b). In spite of the variation
1
The Tuinstra–Koenig [24] or the Ferrari–Robertson [25] relationship has been used depending on the D/G intensity ratio exceeded or not the critical value of 2.2 [25], respectively.
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a scaling law for the growth a-C:H:N films by reactive sputtering: if, f.i., the Wrf is varied, Q indicates how UN2 þH2 should correspondingly scale, at a given ptot , in order to compensate for the desired variation with no or very small changes in the film C content; i(ii) All the variation of xC , in the range of Q considered, is well accounted for by the simple empirical law, 8 ! Q 0:230 ; xC ðQÞ ¼ 0:774 0:074 exp 0:607
ð2Þ
Fig. 3. Dependence on the dimensionless argument Q of (a) the film C content, xC , and of (b) the frequency position, fG , of the G-band. The data of Fig. 2(b) and (a) are shown, respectively. In case (b) a dotted line is drawn as a visual help; the dashed line of case (a) represents the fitted curve, xC ðQÞ ¼ 0:774 0:074fexp½ðQ 0:230Þ=0:6078 g.
of rf power from 180 to 300 W, total pressure from 20 to 38 mTorr and reactive-gas flow-rate from 5 to 27 sccm, xC -points line up, within the experimental errors, along a single curve, thus demonstrating the existence of the assumed xC ðQÞ law and the effectiveness of the variable-combination (1) in determining the film C content and related [26] properties. This finding has many remarkable outcomes: ii(i) In a first approximation, Q contains all the dependence of xC on the varying depositionconditions. Hence, although within the variable-range considered, it actually constitutes
fully satisfactory for all practical purposes (the explicit form of the law utilised for interpolating numerical data has been deduced by the model derivation of Q exposed in Section 5). The attainment of a practical expression, approximating in a simple way the physical law governing the growth of a-C:H:N samples, is clearly of crucial importance. The existence of an analytical dependence of xC on Q, in fact, (a) not only makes capable of predicting the effect, in terms of film C content, produced by any variable-configuration change on the deposition process, (b) but further enables the film-quality tailoring by properly tuning the growth parameters: the desired xC value can be obtained, even starting from different deposition-conditions, provided that these finally give the suited value of Q; (iii) Finally, as the changes in the growth conditions determine an increase of Q, xC correspondingly raises, suggesting a possible improvement [23,26] of the deposited-film quality. Actually, if the fG -data of Fig. 2(a) are plotted against the film-quality factor Q (Fig. 3(b)), the representative fG -points are found to show a well-defined decreasing trend for increasing Q. Since the G-band downshift is indicative of an enhancement of the sp3 :sp2 bonding fraction [10], the argument Q is concluded to be a reliable quality-factor for aC:N:H film deposition by graphite reactivesputtering.
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5. Derivation of the empirical law Far from establishing a model of the growth process applicable to all the variables actually involved into the film deposition, the aim of this Section is rather to get more insight into the role of those, whose variation has been here investigated, in determining the structural and bonding characteristics of the samples under study. Thus, in order to understand the qualitative behaviour of the empirical xC ðQÞ curve in Fig. 3(a), we consider closely how the sputtering of the graphite target progresses for increasing Q. The sp3 :sp2 C bonding ratio of a-C based materials seem to be determined by the amount of C species trapped into the growing film [27]. Moreover, it has been shown that an increasingly higher sp3 C bonding component can be obtained with increasing the energy of C ions up to tens of eV [27–29]. Hence, the average ion impact energy on the film surface, ECi , and the flux of sputtered C atoms that actually reach the substrate, FC!sub , are both thought of as important in ultimately deciding the bonding configuration of the C atoms forming the film. Arbitrarily assuming that the dimensionless combination of the depositionparameters effective in determining the film C content can be derived from ECi and FC!sub , Q is tentatively written, according to [15], as a power product of these microscopic process-variables, namely, a
c
Q ¼ ðECi Þ ðFC!sub Þ ;
ð3Þ
with a and c exponents to be empirically determined. Supposing FC!sub to be controlled, in a basic approximation, by both density, qrg , and permanence-times into the deposition chamber, srg , of the reactive gases, which carry on a competitive action against carbon to the ends of the incorporation within the film, it is assumed r
s
FC!sub / ðqrg Þ ðsrg Þ ; with r and s standing for positive exponents. Under the present deposition conditions, i(i) qrg and ECi , on turns, result respectively roughly proportional to the partial pressure
327
of reactive gases, pN2 þH2 , and to a power product of rf power and total pressure (namely, n qrg / pN2 þH2 and ECi / Wrfm ptot , with m ¼ 1=2 and n ¼ 1 [30]), meanwhile the permanencetime of the gas X being approximately determined by the ratio between its partial-pressure and flow-rate (i.e., sX / pX =UX , if the fixed deposition-chamber volume is neglected, so as sN2 ffi sH2 ); and (ii) being DUN2 þH2 =UN2 þH2 DUtot =Utot , the flowrate of all the gases let in the deposition chamber, Utot , is taken as coarsely constant. Aiming chiefly at clarifying the role played by the changes in growth-conditions in producing the C bonding modifications evidenced by Raman analysis, in the light of points (i) and (ii), the variations of qrg / ptot UN2 þH2 U1 and srg / tot ptot U1 , will be below considered as mostly detertot mined by those of ptot UN2 þH2 and ptot , respectively. On the basis of these simplifications, the combination of microscopic variables (3), that, rewritten in terms of measurable deposition-variables 1=2 1 a r is given by ðWrf ptot Þ ½ðptot UN2 þH2 U1 tot Þ 1 s c ðptot Utot Þ , becomes 1=2
1 a sr r Þ ðptot UN2 þH2 Þc ðWrf ptot
ð4Þ
and results dimensionless for a=2 ¼ rc ¼ a þ ðr sÞc. If, for the sake of simplicity, without loss of generality, it is arbitrarily set a=2 ¼ 1, expression (4) simplifies to Eq. (1). In addition, since a ¼ 2 is found, Q results proportional to the square of ECi . Such a finding implies that the effective variable-combination depends more than linearly on (4th power of) the fraction of forward-sputtered ions [31]. Contrarily, some further hypothesis has to be formulated in order to obtain the exponent c. If FC!sub is basically supposed inversely proportional to qrg (i.e. r ¼ 1 is taken), s ¼ 2 and c ¼ 1 are derived. The former result corresponds to assume 1 2 that FC!sub / q1 rg srg , i.e. / ptot UN2 þH2 . The latter finding, instead, assesses that the flux of sputtered C atoms, which actually reach the substrate, is linearly involved in the derived combination of microscopic variables, ðECi Þ2 FC!sub . One can reasonably conceive that different growth regimes take place with varying the deposition variables:
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(i) Until, f.i., a low Wrf is utilised, films with lower C content are grown, as an effect of the low ECi (low Q regime); (ii) As, f.i., UN2 þH2 is diminished, as an effect of the minor amount N and H atoms actually reaching the substrate, FC!sub raises and progressively C-richer a-C:H:N films are grown (high Q regime); (iii) If the growth conditions are still changed in the same direction, f.i., decreasing ptot , i.e. enhancing ECi while simultaneously decreasing qrg and srg , the deposition process at 100 °C ultimately reaches a limiting regime and xC raises no longer.
of xC produced by the changing growth conditions in the range of Q considered. In this model, Q can be thought of as the critical value of Q, which discriminates the two different regimes taking place in the deposition process. In the low-Q regime (namely, Q Q þ Q0 ), C atoms are mainly sp2 -bonded in the C-poorer film network; oppositely, in the high-Q regime, C-richer films are attained with improved sp3 :sp2 C bonding ratio.
The behaviour of the derived physical approximant to the xC -data (2) can be qualitatively understood on the basis of the simple model proposed below. Under the described conditions, the number of sputtered C atoms which ultimately reach the substrate during deposition, effectively acquires a more-than linear dependence on the argument Q. xC can be thus supposed Qa -dependent, with a an exponent >1. If the variation, dxC , undergone for an increment of the effective-variable Qa is taken as proportional, according to the simplest possibility, besides to d(Qa ), to the residual ÔdistanceÕ of xC from its saturation value, xC , namely,
(i) The presented method, far from representing a rigorous theoretical model of the growth process, exactly accounting for the behaviour of the microscopic variables (average ion impact energy, atom impact velocity onto the substrate, flux of C atoms towards the plasma and of each atomic species towards substrate and target, sputtering yield of Ar and N atoms, gas permanence time, plasma potential, . . .), that rule the complex chemical and physical deposition-mechanisms and ultimately decide the C bonding configurations of the grown films, constitutes a semiempirical approach, rather aimed at achieving an approximated solution in terms of the varying measurable deposition-parameters involved into the problem; (ii) Several drastically simplifying hypothesises and arbitrary assumptions have been made to deduce the expression relating Q with the microscopic variables. However, it has to be emphasised that the effective combination consequently obtained is actually able to account for the experimental results, as demonstrated; (iii) Moreover, the present analysis refers to the quite limited set of investigated films and, therefore, the shown results have to be regarded only as a preliminary solution to the problem; (iv) The generality of the method, here applied to the case of a-C:N:H film deposition by reactive-sputtering of a graphite target, suggests
dxC / ðxC xC ÞdðQa Þ; the differential equation obtained can be solved, finally giving a xC ðQÞ xC Q Q0 ¼ exp ; x0 xC Q where xC , x0 , Q , Q0 and a are constants to be empirically determined. In order to test the above equation, verify the hypothesis about the exponent a and determine numerical values of xC , x0 , Q and Q0 the data of Fig. 3(a) are fitted. By this procedure, the functional dependence, theoretically deduced, is actually demonstrated and a > 1 confirmed. In particular, by fitting the data, xC ¼ 0:774, x0 ¼ 0:700, Q ¼ 0:607, Q0 ¼ 0:230 and a ¼ 8 are derived (i.e. relation (2) is obtained). The resulting expression accurately approximates the variation
5.1. Additional remarks It is, finally, worthwhile to point out that:
G. Messina et al. / Journal of Non-Crystalline Solids 318 (2003) 322–330
the possibility of its extensive application to all growth techniques, involving systems and physical processes susceptible to being mathematically modelled. This is demonstrated in Fig. 4, where the dependence on Q ¼ 1 1 Wrf ptot Urg (Urg standing for the flow rate of reactive gases), is shown, of fG -data relative to hard a-C:H:N films, grown by plasma enhanced chemical vapour deposition, in methylamine containing mixture [32] and in methane–ammonia atmosphere [33]. Of course, some coefficient refinement in the empirical law derived could be necessary in the presence of a wider Q variation-range. Instead, a generalisation of the quality-factor introduced is required if cases are considered, where a greater number of deposition parameters is allowed varying, as found for a-C:N and a-C:N:O films deposited, by rf magnetron sputtering, respectively in Ar–N2 and N2 –O2 atmospheres [34], as well as, for a-C:N samples prepared in N2 atmosphere and annealed [35]. Nevertheless, the semiempirical approach here proposed constitutes a powerful tool for gaining hints for an easy-understanding, as well as, for achieving a ready-predicting capability about the final issue of the growth process.
1 1 Fig. 4. Dependence of fG on Q ¼ Wrf ptot Urg (Urg denoting the flow rate of reactive gases) for presently investigated samples and literature hard a-C:H:N films, grown by plasma enhanced chemical vapour deposition, in methylamine containing mixture and in methane–ammonia atmosphere (a line is drawn as a visual help).
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6. Conclusion Hydrogenated amorphous carbon films containing nitrogen are deposited, at 100 °C, by graphite sputtering in Ar–He atmosphere with the addition of N2 and H2 as reactive gases. Aiming at the optimisation of the growth process, a Raman analysis is carried out in order to clarify the role played by each variable involved into the film deposition, in determining the a-C:H:N properties. The evolution of the D- and G-bands in the Raman spectra, reflecting the C bonding modifications produced by the different deposition conditions, is quantitatively analysed and the film C content is evaluated. The film C content, whose diminishing is thought as responsible for the decreasing of the sp3 :sp2 C bonding ratio evidenced by the Raman characterisation results, is shown to depend on the variables involved into the a-C:H:N film growth through a single dimensionless combination of the 1 1 dimensional process-variables, Wrf ptot UN2 þH2 , where rf power Wrf , total pressure ptot and reactivegas flow-rate UN2 þH2 are expressed in W, mTorr and sccm, respectively. The dimensionless argument introduced, able to indicate how the variable-configuration can eventually change without significantly affecting the result in terms of C content and resulting film properties, constitutes a scaling law for the a-C:H:N film deposition, whose validity is here preliminarily demonstrated for variations of rf power, total pressure and reactive-gas flow-rate in the ranges from 180 to 300 W, from 20 to 38 mTorr and from 5 to 27 sccm, respectively. By interpolating the experimental data, a simple empirical law is therewith found, accounting for all the variation of the C content in the range of process-variables considered. The analysis of the Raman characterisation results in the light of these findings suggests that the derived dimensionless variable-combination can be regarded as a reliable quality-factor for the a-C:H:N film deposition process. A very simple derivation model is proposed, accounting for the chosen variable-combination and the explicit form of the empirical law approximating the physical laws governing the process and its final issue, and
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the generality of the presented method finally evidenced.
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