- Email: [email protected]
Quantitative analysis of diamond deposition reactor efficiency
Chemical Physics 398 (2012) 239–247
Contents lists available at SciVerse ScienceDirect
Chemical Physics journal homepage: www.elsevier.com/locate/chemphys
Quantitative analysis of diamond deposition reactor efficiency A. Gicquel a,b,⇑, N. Derkaoui a,b, C. Rond a,b, F. Benedic a,b, G. Cicala c, D. Moneger a,b, K. Hassouni a,b a
Laboratoire des Sciences des Procédés et des Matériaux, UPR3407, CNRS, Université Paris 13, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France Laboratoire d’Excellence Sciences and Engineering for Advanced Materials and devices, PRES Sorbonne Paris Cité, France c CNR-IMIP (Istituto di Metodologie Inorganiche e dei Plasmi), Sezione di Bari, Via G. Amendola 122/D, 70126 Bari, Italy b
a r t i c l e
i n f o
Article history: Available online 6 September 2011 Keywords: Microwave plasma Diamond deposition Emission spectroscopy Actinometry Plasma modelling
a b s t r a c t Optical emission spectroscopy has been used to characterize diamond deposition microwave chemical vapour deposition (MWCVD) plasmas operating at high power density. Electron temperature has been deduced from H atom emission lines while H-atom mole fraction variations have been estimated using actinometry technique, for a wide range of working conditions: pressure 25–400 hPa and MW power 600–4000 W. An increase of the pressure from 14 hPa to 400 hPa with a simultaneous increase in power causes an electron temperature decrease from 17,000 K to 10,000 K and a H atom mole fraction increase from 0.1 to up to 0.6. This last value however must be considered as an upper estimate due to some assumptions made as well as experimental uncertainties. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction At long term, single crystal diamond films with very high purity is believed to outperform silicon in devices such as switches working at voltages of 10 and up to 20 kV. Some key bottlenecks must however be over-passed to reach this era. They concern mostly today the ability to synthesize very high quality bi-polar (intrinsic, n-doped, pdoped and p+ doped) or even uni-polar (intrinsic, p-doped and p+ doped) multilayers all in diamond, to reduce substantially the dislocation density inside the crystals (typically of 104/cm2 for the state of the art), to enlarge the diamond single crystal layers and to grow 100 lm to 1 mm thick films at very high growth rates. Part of these issues, in particular the last one, is based on the capability to produce very energetic and very high purity plasma able to run for long deposition time (for thick films). The goal is to produce a large amount of atomic hydrogen in the plasma that diffuses towards the substrate as well as CH3 radicals at the plasma/surface interface, these species being key for diamond deposition. Microwave plasma reactors, running at pressure typically in the range of 100–400 hPa with some kilowatts power coupled to the plasma, answer pretty well to this purpose. These reactors have been extensively studied for conditions of moderate power density (less than 30 W cm3), in particular by Gicquel’s group in collaboration with different laboratories [1–12], but also by Ashfold and Mankelevich [13–20], as well as Grotjohn et al. [21–23]. However the conditions of very high power density (high pressure and high microwave ⇑ Corresponding author at: Laboratoire des Sciences des Procédés et des Matériaux, UPR3407, CNRS, Université Paris 13, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France. E-mail address: [email protected] (A. Gicquel). 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.08.022
power coupled to the plasma) have not been studied so much. In particular, even if some works have been carried out [6,18], there is still lacks in experimental validations of the simulation codes and basic studies aiming to determine the main parameters (species, flow, . . .) responsible for doping as well as for soot formation which has been observed under conditions of high power density coupled to high methane input, and more recently in presence of diborane in the plasma. In the past, different spectroscopic methods have been employed to monitor the gas phase chemistry and composition in diamond deposition reactors. In particular, absorption spectroscopy and laser induced fluorescence (LIF) spectroscopy have been used due to their capability in accessing ground state species. Thus, ground state H atoms, which is a key factor for CVD diamond deposition, has been studied in microwave plasma reactors at low to moderate power density by Two-photon laser induced fluorescence (TALIF) [2–4] to estimate the temperature and relative mole fraction of H atoms, while ground state molecular hydrogen temperature have been measured through coherent anti-stokes Raman spectroscopy (CARS) spectroscopy [1,2,24]. Concerning carbon containing species, the ultraviolet absorption of CH3 at 216 nm was used for number density measurements firstly in hot filament reactors and later on in plasma reactors. Most recent experimental advances derive from the improvement of laser absorption spectroscopy methods that have allowed accessing to stable hydrocarbon species like CH4, C2H2 as well as transient species such as CH3 radicals through IR absorption using tunable diode laser [8,12,25–27] and quantum cascade laser (QCL) [19,28]. Furthermore, CH3 radicals have also been monitored in microwave reactors using cavity ring-down spectroscopy (CRDS) [20]. Finally, laser induced fluorescence (LIF) observations of CH and C2 radicals
240
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
have been also reported in dc-arcjet plasma for diamond deposition providing gas temperature [29,30] and absolute concentration of C2 [31]. These diagnostics are powerful methods for probing species on their ground electronic states. However the nonflexible and expensive characteristics of these advanced techniques make them unfit for diagnosing industrial reactors, and then comparison between different MW reactors seems hard to be considered. Optical emission spectroscopy (OES) measurements on radiative species can be a powerful technique for accessing plasma characteristics, provided it is coupled with a very detailed analysis of all the electronic excitation processes to obtain ground state density information. Actinometry technique has been demonstrated to be valid in diamond CVD reactor for probing hydrogen atom [4] and then was used to determine the spatially resolved H relative density for low to medium pressure conditions (100 hPa > p > 25 hPa, 2000 W > P > 600 W). Lang et al. also reported results at low pressure conditions (50–100 hPa; 400–880 W) [32], and recently Ma et al. [13] proposed a spatially resolved studies of H relative density for higher pressure conditions (<200 hPa; 1.5 kW). Increasing power and pressure (i.e. power density) enhances drastically CVD diamond growth rates [33,34] and quality [35–37]. Indeed, increasing the MW power density results in a lower electronic temperature but in a higher gas temperature [6,9]. As at high power density (>15 Wcm3, i.e. p > 50 hPa, P > 1000 W), the main Hatom production channel is thermal dissociation [9], as a result: the higher the MW power density, the higher the H density and the more efficient the diamond CVD process. Previous works referred above have been carried out for moderate power density conditions. This paper focused on the study of the plasma phase for high power density growing conditions using actinometry method. Another goal is to analyze the validity of this technique for H atom at high pressure/power conditions by comparing experimental and simulated results. Variations of both electron temperature and H-atom density as a function of the power density, monitored by the couple (pressure, microwave power coupled to the plasma) will be discussed. This paper constitutes a first part of a larger program aiming to put forward our knowledge of diamond deposition reactor operation, when running at high power density.
relatively to the plug-in power that is lower due to the Joule effect energy loss. This has been made in a bell jar reactor operating at low power density evidencing that more than 90% of power was coupled to the plasma [56]. Under conditions of high power density this is obviously not the case as evidenced by the observed strong heating of the microwave guides and quartz windows. This necessarily leads to errors in defining the average power density, expressed in W cm3. As a consequence, the experimental conditions of (pressure-MP power) couple will be most of the time specified rather than the power density. In the frame of this study, large ranges of pressure (25–400 hPa) and MW power (600–4000 W) were used, focusing our attention on high power density conditions. It is worth noting that the results obtained previously at low pressure and power in a bell jar reactor are reported in this paper. The link between these sets of experimental results is provided through calibrations. 2.2. OES measurements A scheme of the MW reactor and the OES set-up is shown in Fig. 1. The steel cavity contains three optical fused silica windows. An Acton 2500i spectrometer equipped with an ICCD camera was used to perform emission spectroscopy. Most of the measurements have been carried out using a 1800 g/mm grating blazed at 500 nm, except for Hb (n = 4) spectra obtained with a 2400 g/mm holographic visible grating. The light emitted from the plasma was collected by an afocal lens system and transported via a 1 mm optical fibre core to the entrance slit (10 lm) of the monochromator. This device enables a spatial resolution of 1 mm and a spectral resolution of 0.03 nm. The optical system was mounted on computer controlled translation stages, allowing axial and radial measurements. Emission intensity, averaged on a line of sight, is measured at 90° to the axis of the reactor. At a given location in the plasma, as the plasma volume is kept as much as possible constant, the line-of-sight averaged emission intensities are always measured within approximately the same plasma volume. Spectra of Ha (k = 656.5 nm), Hb (k = 486.1 nm), and 4p ? 4s argon transition (transition 2p1 ? 1s2 at k = 750.3 nm) were recorded systematically (Fig. 2a). Table 1 gives the different transitions used.
2. Experimental set-up and diagnostics 2.1. Microwave reactor The microwave diamond deposition reactor, which was described elsewhere [35], is a water-cooled stainless steel resonant cavity that operates at moderate pressure and dedicated to high power density operations (Fig. 1). The discharge is generated by a 2.45 GHz MW generator delivering a maximum power of 6 kW along a rectangular waveguide up to a cylindrical chamber. At the centre of this chamber, a 5 cm in diameter substrate holder is supporting a either polycrystalline or single crystal diamond substrate. Both are immersed in a close to hemispheric plasma emerging from MW activation of the feed gas. The gas consists in a mixture of CH4 (0–4%) and Ar (3–4%) diluted in hydrogen and supplied by a total flow rate range of 100–500 sccm. Substrate temperature, monitored using a monochromatric IR pyrometer, can be varied from 620 °C to 915 °C, independently from the plasma conditions. For this specific study, it was maintained at 850 °C. The total pressure in the reactor chamber was adjusted in order to keep as much as possible constant the plasma volume (the dimension of which reminding anyway difficult to estimate). The goal of this procedure is to maintain the ratio of the power coupled to the plasma over the total density constant. However, we cannot report the estimation of the input power fraction really coupled to the plasma
2.2.1. Actinometry method Actinometry was introduced in the early 80’s [38] in order to estimate relative densities of a ground state species from OES measurements. The principle and the validation of the method applied to H-atom relative density measurements has been thoroughly described previously [1,4] and then by Ma et al. [13]. Briefly, actinometry requires the introduction of a small amount of an inert gas (here argon) to the mixture, which constitutes the actinometer. The emission intensity ratio (probed species over actinometer) is proportional to the species electronic ground state relative concentration, provided that (i) the two species are excited from their electronic ground state by a single electron impact; (ii) the excitation cross section of these processes are similar (same energy threshold, proportional for the considered electron energy range); (iii) radiative de-excitation processes are predominant. Quenching processes have to be taken into account for high pressure conditions. Argon has been chosen as actinometer to study the relative density of H atom in diamond CVD plasma, since its excited state (4p) is produced by direct electron impact processes from the 3p6 ground state under the conditions studied here, the excitation cross section of which being similar in shape as that of H(n = 3). The main processes involved in the production and loss of H(n = 3) and Ar(4p) (sublevel 2p1) have been widely studied and presented in [4]. As well
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
241
Fig. 1. MW reactor scheme and OES set-up.
the relationship linking H-atom mole fraction to emission intensity measurements has been established: Ar
½H xH k ¼ ¼ F eHa ½Ar xAr ke Ar
mAr Q I =I mHa T H Ar
ð1Þ
Ha
where ke and ke are excitation rate constants for the transition Ar(3p) ? Ar(4p) and H(n = 1) ? H(n = 3); mi is the de-excitation frequency of species i; xi is the mole fraction of species i; QT is the term relative to radiative and quenching processes and F is an optical device factor. Giving the cross sections (r) in Å2, the gas temperature (T) in K, the pressure (P) in hPa and xH2 the molecular hydrogen mole fraction, QT is equal to [4]:
QT ¼
1 þ PT 1=2 ½0132rHa=H2 xH2 þ 0152rHa=H ð1 xH2 Þ
ð2Þ
1 þ PT 1=2 ½0162rAr =H2 xH2 þ 0226rAr =H ð1 xH2 Þ Ar
Ha
The estimation of the excitation rate constants ke and ke needs the knowledge of the electron temperature that, in these kinds of plasma, cannot be measured by Langmuir probe due to the highly collisional character at these pressures. In the plasmas studied here, the electron energy distribution function is characterized by two sets of electrons (the hot electrons with an energy above 12 eV and the cold electrons with an energy below 8 eV) [6,39]. Each group presents a Boltzmann distribution characterized by an electron temperature, the cold electron having a temperature higher 10,000–20,000 K than the hot electrons 6000–10,000 K. As a matter of fact, the electron energy distribution function of the hot electrons drops faster than that of the cold electrons. From the analysis of the electron distribution and the adequacy with the main processes occurring in the plasma, it was deduced that the average energy heei based on the set of the colder electrons was a relevant parameter to use. While the gas heating leading to very high gas temperature is driven by the energy of around 1 eV, it is not the case for direct electron impact electronic excitation from ground state, in particular for atomic hydrogen and argon. These processes require electrons with energy higher than 12 eV that is located at the frontier of the two sets of electrons. As a consequence, they are driven either by the hottest electrons of the cold electron Maxwellian distribution or by the coldest electrons of the hot electrons distribution function. Taking into consideration the relative density of these two sets of electrons, we have based our method on the estimation of the electron temperature characterizing the set of the colder electrons.
In Ref. [4], the processes of production of both Ar(4p) and H(n = 3) have been established. For power density higher than 9 W cm3 (25 hPa, 600 W) the direct electron impact process is responsible for the electronic excitation of both H(n = 3) and Ar(4p). As far as H(n = 4) is concerned, the same conclusion can be stated since the different mechanisms of production of this electronic state is similar to that of H(n = 3). One additional question however must be raised for condition of very high pressure; the possibility that self absorption processes may participate to populate the electronic excitated states n = 3 and n = 4 of atomic hydrogen from overpopulated level H(n = 2). Unlike the Lyman a radiation (in the VUV range) is assumed to be entirely absorbed by the H(n = 1) atoms (optically thick plasma) in the LSPM 0 D collisional radiative model, the Balmer radiations are assumed not to be reabsorbed (the plasma is considered for these transitions optically thin) [13]. This assumption is supported on the one hand by the ratio value of the H(n = 2)/H(n = 1) evaluated both by us and by the Ashfold group [13,14] at around 108. On the other hand, very little broadening is observed in the Ha emission intensity spectra as the pressure and power are increased, as shown in Fig. 2b. This can be attributed to the Doppler effect but not to a change in the production mechanism of this state. 2.2.2. Electron temperature analysis The estimation of [H] relative concentration through actinometry method is based on the knowledge of both the electronic excitation cross sections of the species studied and the electron temperature. For estimating the electron temperature, we have used the emission intensity ratio of two hydrogen lines. The procedure is valid upon provided that the excited states are populated from their ground state through a direct electron impact. This aspect has been established in the previous section. Electron temperature is linked to the emission intensity ratio by the relation: Ha
I Ha k ¼ F eHb IHb ke Ha
m656 Q m486 T;H Hb
ð3Þ
where ke and ke are excitation rate constants for the transition H(n = 1) ? H(n = 3) and H(n = 1) ? H(n = 4), respectively [40]; m656 and m486 are the de-excitation frequency for H(n = 3) and H(n = 4); F is an optical device factor. Finally QT,H is the term relative to radiative and quenching processes which can be expressed as:
242
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
a
Wavelenghts (nm) 740
745
750
755 80
50000
150 mbar - 2500 W 250 mbar - 3500 W
70
Ar750
Relative intensity (a.u.)
40000
60
50
30000
40 20000
30
20
Hα
10000
Relative intensity (a.u.)
735
10
0
0 652
656
660
664
668
Wavelenghts (nm)
b Hα emission intensity (normalized)
1.0
40 mbar 800 W 70 mbar 1500 W 200 mbar 3000 W 270 mbar 4000 W 400 mbar 3000 W
0.8
0.6
0.4
0.2
0.0
656,10
656,15
656,20
656,25
656,30
656,35
656,40
656,45
656,50
Wavelengths (nm) Fig. 2. (a) Optical emission spectra of Ha (656.3 nm) and Ar750 (750.4 nm) for two experimental conditions of pressure/MW power (note that the scales for Ha and Ar750 are indicated respectively on the bottom left corner and on the upper right corner); (b) Ha profiles as a function of different pressure and power couples.
Q T;H ¼
1 þ PT 1=2 ½0132rHa=H2 xH2 þ 0152rHa=H ð1 xH2 Þ 1 þ PT 1=2 ½0426rHb=H2 xH2 þ 0492rHb=H ð1 xH2 Þ
ð4Þ
where pressure is expressed in hPa, rHa=H2 and rHa/H (in Å2) are the quenching cross sections of Ha by the H2 molecules and by the H atoms respectively, which are given in [41,42] and [4], and rHb=H2 and rHb/H (in Å2) are the quenching cross sections of Hb by the H2 molecules and by the H atoms respectively. No data concerning the quenching cross sections of Hb by the H2 molecules, under the conditions of pressure studied here could be found, although Lewis et al. [43], Catherinot et al. [44] and Glass-Maujean et al. [45] provide values for H(n = 3) and H(n = 4) states at much lower pressures (less than 2 hPa). Due to the strong pressure dependence of the quenching cross sections observed by these authors, we have decided not to take into account for the quenching for the excited states. The obvious consequence is that we will only access to an estimate of the electron temperature and its variation as a function of the pressure. It is worth noting that the quenching effect of carbon containing species has not also been taken into account, since
Table 1 Species, transition wavelengths, upper and lower level assignments, and energies for tracers monitored in the OES study. Species
k (nm)
Upper level
Energy (eV)
Lower level
Energy (eV)
Ha Hb Ar750
656.3 486.1 750.4
n=3 n=4 2p1
12.10 12.75 13.48
n=2 n=2 1s2
10.20 10.20 11.86
no more that 7% and most of the time 4% of methane was introduced in the feed gas.
3. Experimental results 3.1. Positioning of the problem Under medium pressure microwave diamond deposition reactor, as it is largely accepted by the community, H atoms and CH3
243
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
kðTsÞ½CH3 s ½Hs
ð5Þ
5109 þ ½Hs
where k(Ts) = 1.8 1011 at Ts = 1200 K and, [H]s and [CH3]s are the concentrations of surface H-atom and CH3-radical (in mol cm3) respectively. Transforming Eq. (5), it comes:
Growth rate ¼ kðTsÞ½CH3 s
5:109 1þ ½Hs
!1 ð6Þ
Eq. (6) clearly shows that the higher [H]s the higher the growth rate. A maximum value of 106 mol cm3 has been predicted by Goodwin for fully dissociated plasma flowing at very high speed and at two atmospheres. We will estimate in this paper how the type of plasma studied here (2.45 GHz cavity based reactors working at low Peclet number) are positioned relatively to this maximum value. In addition, based on calculations, we have established [34,51] that surface CH3 radical density varies linearly with the H-atom density in the plasma bulk at high power density (Fig. 3). Then we can state that, for a given CH4 percentage introduced in the discharge and a given location of its injection, the growth rate will be an only function of H-atom density produced into the plasma. For very high energetic condition, an almost linear variation may even be expected. This statement strengthens the fact that studying a diamond deposition reactor implies first to explicit the spatial H atom production and loss terms as a function of the plasma conditions. This is the goal of this paper.
One of the best ways to increase H atom density and then growth rates is to increase the power density of the plasma. This can be done either by increasing simultaneously pressure and power keeping constant the plasma volume or by increasing only pressure while keeping constant the power (in this latter case the plasma volume decreases). The emission intensity ratio of Ha and Hb lines is a relevant measurement of the electron temperature provided that a calibration is available. This latter has been obtained from electron temperature calculated in [52] for the following couple of power and pressure (1000 W and 50 hPa; 15 W cm3). Experimental axial distributions of the electron temperature for different conditions of power and pressure have been obtained (Fig. 4a and b). A rather good agreement between experimental and calculated results can be observed in Fig. 5, although as discussed above the quenching cross sections of the H atom excited states were not taken into account. A decrease in the electron temperature from 16,000 K to around 11,000 K is observed as the pressure is increased from 25 hPa to 270 Pa, and simultaneously the power is increased from 600 W to 4000 W. It is worth noting that, within the error bar that can be estimated at ±1000 K, at 400 hPa, 3000 W and 7% of CH4, the
a 14000
6000
0.0
0.5
1.0
1.5
2.0
0.6 0.4
2.5
3.0
3.5
4.0
Axial position [cm] 20000
Actinometry experiments Calculations 1D model
16000 14000 12000 10000
Substrate
Electron temperature [K]
-3 14
8000
18000
1.2
[CH3]surf (.10 cm )
10000
2000
1.4
0.8
12000
4000
b
1.0
Actinometry experiments Calculations 1D model
Substrate
Growth rate ¼
3.2. Influence of microwave power density on the H atom density in the plasma bulk
Electron temperature [K]
radical constitute the main governing species for growing polycrystalline and single crystal diamond layers. The first diamond growth model proposed by Harris, was then improved by different authors [36,37,46–49] and a very complete review paper of diamond growth can be found in references [17,50]. Although it only applies to growth on (1 0 0) faces, the simplified model is clearly based on the key role of CH3 radicals and H atoms. From this mechanism, the authors stated on a very simple growth law valid for concentrations of the CH3 and H-atom in the range of [3 1010, 105] mol cm3 and [1011, 106] mol cm3 respectively [36]:
8000 6000 4000
0.2 2000 0.0
0.0 0
5
10
15
20 16
25
-3
plasma [H]max (.10 cm ) Fig. 3. Variation of the surface CH3-radical density as a function of the plasma bulk H-atom density. The pressure and power couples were varied from 25 hPa/600 W to 270 hPa/4000 W. Percentage of CH4 added in the feed gas: 4% [34,48].
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Axial position [cm] Fig. 4. Simulated (red diamond) and experimental (black square) electron temperature profiles for two power densities (couples (pressure, power)): (a) 110 hPa/ 2500 W, (b) 200 hPa/3000 W. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
a
600 W 800 W 1000 W 1250 W 1500 W 2000 W 2500 W 3000 W 3500 W 4000 W Calculation
16000
14000
0.35
Actinometry experiments Calculations 1D model
0.30
H mole fraction
Electron temperature (K)
18000
12000
0.25 0.20 0.15
Substrate
244
0.10
7% CH4
0.05
10000 0
100
200
300
400
0.00
500
0.0
0.5
1.0
Pressure (hPa)
1.5
2.0
2.5
3.0
3.5
4.0
Axial position [cm]
Fig. 5. Electron temperature fractions as a function of pressure for different powers, obtained from the measurement of the ratio IH/IHb. %CH4 = 4% except for one condition (indicated onto the figure).
b
0.35
Actinometry experiments Calculations 1D model
3.3. Estimation of the H atom density at the surface From the spatial distributions of XH (H-atom mole fraction) shown in Fig. 7a and b, the mass boundary layer thicknesses, corresponding to characteristic length scales for diffusion, can be defined locally at the surface by:
dH ¼
X H1 X H0 ðdX H =dzÞjz¼0
ð7Þ
1.0
0.8
H mole fraction
7% CH4 0.6 600 W 800 W 1000 W 1250 W 1500 W 2000 W 2500 W 3000 W 3500 W 4000 W Calculation
0.4
0.2
0.0
0
100
200
300
400
500
Pressure (hPa) Fig. 6. Maximal plasma H-atom mole fraction as a function of pressure for different powers, obtained from actinometry measurements.
0.25 0.20 0.15
Substrate
electron temperature is equal to that obtained at 270 hPa, 4000 W and 4% CH4. The variation of the H mole fraction in the plasma bulk as a function of the pressure and for different powers coupled to the plasma is shown is Fig. 6. These measurements are deduced from the emission intensity ratio of the Ha line over that of the 750 nm argon line using Eq. (1), and after calibration made using the lower power density that provides H atoms from thermal dissociation, i.e. 1000 W and 50 hPa. Results show a strong increase in the H-atom mole fraction: it rises from 0.01 at 25 hPa and 600 W up to around 0.5 at 270 hPa and 4000 W. At 300 hPa and 3000 W, it reaches 0.6 ± 0.1, evidencing the strong effect of pressure.
H mole fraction
0.30
0.10 0.05 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Axial position [cm] Fig. 7. Experimental and calculated spatial distribution of H-atom mole fractions for two power densities (couples (pressure, power)): (a) 110 hPa/2500 W, (b) 200 hPa/3000 W.
The experimental values that appear higher than the calculated ones, give a variation from 16.8 mm at 25 hPa and 600 W, to 9.7 mm at 3 kW and 200 hPa. The decrease in dH as a function of the power density (increase in power and pressure) is attributed to that of the thermal boundary layer thickness dT. As a matter of fact, since molecular hydrogen dissociation is controlled by thermal processes, the H atom mole fraction distribution is directly correlated to that of the gas temperature. Since in addition gas temperature is driven by the energy transfer from the electrons, it depends on the location where the microwave energy is deposited into the plasma. As shown from the measurements of the emission argon line intensity profile (IAr750,4), the maximum of IAr750,4 is displaced towards the surface as the pressure and power increases, evidencing that the higher the power density, the closer to the surface, the power is absorbed (Fig. 8). The good agreement between the electron temperature (Te) axial profiles obtained from the emission intensity ratio IHa/IHb and the calculated axial profiles of electron temperature for different couples pressure and power, confirms the slight increase in the absorbed power in the nearest vicinity of the surface as the power density is increased (Fig. 4a and b). In addition, the decrease in dT is also attributed to the decrease of the thermal diffusivity at high power density, i.e. high pressure (Fig. 9). The spatial net H-atom production yields for different reactions and as a function of the power density (pressure/power) are shown in Fig. 10. As already discussed in references [6,51] where the
245
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
DH ð@X H =@zÞ ¼ RSH
2000W, 100 hPa 3000W, 200 hPa
7000000
where RSH is the total H-atom surface consumption reaction rate. At steady state and without any convective flux (stagnation point condition), it comes:
6000000 5000000
Intensité Ar7
ð9Þ
DH ð@ 2 X H =@z2 Þ þ RH ¼ 0
ð10Þ
4000000 3000000 2000000 1000000 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Position axiales [cm] Fig. 8. IAr750,4 emission intensity axial profiles for two power/pressure sets.
chemical kinetics model is given, the thermal dissociation of molecular hydrogen clearly dominates at high power density. Two processes are responsible for the production of H atoms: H2 + H2 ? 2H + H2, and H2 + H ? 3H. Under conditions of high Hatom density the second process dominates. At 9 W cm3 (25 hPa/600 W) (Fig. 10a), atomic hydrogen is mainly produced by electron collisional dissociation process, the gas temperature being not high enough to ensure high molecular hydrogen vibrational excitation, and the consequent thermal dissociation due to successive inelastic collisions. At 270 hPa/4000 W (Fig. 10c and d), molecular hydrogen electronic dissociation is totally inefficient versus the thermal dissociation. Due to the low mass Peclet number (PeM = 0.1), in these systems, diffusion towards locations of lower H-atom density ensures an efficient transport of H-atom through the surface boundary layer (dH thickness), where they recombine. Once the H atoms are produced, the H atom spatial evolution is given by the continuity equation. In one dimension, it is written as it follows:
uð@X H =@zÞ þ dX H =dt ¼ DH ð@ 2 X H =@z2 Þ þ RH
ð8Þ
where u is the gas velocity, XH the H-atom mole fraction, and RH the H-atom loss rate due to reaction in volume. The associated boundary condition is:
To solve this problem, we need evaluating the respective contributions of volume reactions and diffusion process to the H-atom loss rate. Although the considered pressures are somewhat high, whatever it is, there is no contribution of the volume reactions. Even at 270 hPa, the volume recombination is un-significant (Fig. 10c and d). This means that once atomic hydrogen is produced, it is free to travel into the gas phase until the reactor walls or the diamond substrate. At low power density, the H-atom density is low and the reactor metallic walls recombination reaction is seen to contribute to the consumption of H atoms (reaction R106 in Fig. 10a). At high Hatom density (high power density) this process becomes negligible (Fig. 10d). The diffusion process, driven by the high H-atom density gradient at the plasma/surface interface, is the only process responsible for extracting H atoms from the gas phase. The H atom consumption at the surface acts as a well for H-atom and diffusion constitutes its supplier. It is worth noting that in addition to the diamond surface recombination process, recombination on the reactor walls is also taken into account in the calculations (as a radial diffusion loss). This channel is however much less important than diamond recombination due to the low temperature of the walls that are water cooled.
Finally; the continuity equation becomes : DH ð@ 2 X H =@z2 Þ ¼0
ð11Þ
with the boundary condition : DH ð@X H =@zÞ ¼ RSH
ð9Þ
At the diamond surface, the H atoms recombine and/or participate to surface reactions, such as abstraction for instance. In principle, one should identify the main processes, together with their reaction rates to obtain an expression for RHS. However, using the global parameter cH, the H-atom recombination coefficient allows one simulating all the processes with a single parameter. cH has been determined by different authors [36,37,53,54] on diamond surface, and Goodwin proposed the following expression as a function of the surface temperature:
cH ¼ 4104 þ 1:95 expð3025=TÞ
ð12Þ 3
0.35
DH/H2
2
Diffusion coefficient (m /s)
0.30
DCH3/H2 0.25 0.20 0.15 0.10 0.05 0.00 0
50
100
150
200
250
300
Pressure (hPa) Fig. 9. H-atom and CH3 radical diffusion coefficients as a function of the pressure. Power is simultaneously increased from 600 W to 4000 W as pressure is increased from 25 hPa to 270 hPa.
At 1100 K, cH = 0.12. In addition cHis generally taken at 10 –104 for recombination on quartz surfaces [55], and cH has been taken at 102 for recombination on the water cooled stainless steel walls. Since diffusion is responsible for the H-atom transport to the surface, the surface H-atom mole fraction is linearly related to its maximum value into the plasma volume, this latter being a function of the maximum gas temperature reached into the plasma. Also, the location of the maximum of H-atom mole fraction is defined by the location where Tg is maximal. The higher the power density is, the stiffer the H-atom mole fraction gradient and the higher the atomic hydrogen flux towards the surface are. Since the H-atom surface balance equation will express that the H-atom flux to the surface is equal to the surface consumption of the Hatom at the surface (that is a strong function of the surface temperature), we can state that the higher the flux, the higher the surface H-atom density. Eqs. (11) and (12) allow us obtaining the H-atom mole fraction (and density) at the surface:
v ~ ns ~ Ds r njwall ¼ RSH ¼ cs s nsw for H-atoms 4
Written in 1 dimension, it comes:
ð13Þ
246
c
0.0020
1.2
0.0015
1.0
0.0010
0.8
R85: CH4 + H
CH4 + M
CH3 + H2
R90: C2H + H2 ⇔ C2H2 + H
-
-
R1: e + H2
e + 2H
R77: CH3 + H + M
-0.0005
R85: CH4 + H
CH4 + M
CH3 + H2
R93: C2H2 + H + M ⇔ C2H3 + M
-0.0010
R97: C2H4 + H ⇔ C2H3 + H2
-0.0015
Diffusion D R10-7: 2H2 ⇔ 2H + H2
R106: H
0.6 0.4
R93: C2H2 + H + M ⇔ C2H3 + M
Substrate
0.0000
-
e + 2H
R92: C2H + H + M ⇔ C2H2 + M
Production rate
0.0005
-
R1: e + H2
R77: CH3 + H + M
Substrate
Net production rate
a
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
R94: C2H3 + H ⇔ C2H2 + H2 R97: C2H4 + H ⇔ C2H3 + H2 R106: H
0.5H2 (metallic surface)
Diffusion D R10-7: 2H2 ⇔ 2H + H2 R11-8: H2 + H ⇔3H
0.2 0.0
0.5H2 (metallic surface)
-0.2
R11-8: H2 + H ⇔3H
-0.0020 0
2
4
6
8
0
10
2
4
6
8
b
d
-
R85: CH4 + H
CH4 + M
CH3 + H2
R90: C2H + H2 ⇔ C2H2 + H R92: C2H + H + M ⇔ C2H2 + M
0.4
R93: C2H2 + H + M ⇔ C2H3 + M
0.02
R94: C2H3 + H ⇔ C2H2 + H2
0.3
R97: C2H4 + H ⇔ C2H3 + H2
-
R1: e + H2
e + 2H
R77: CH3 + H + M R85: CH4 + H
CH4 + M
CH3 + H2
R90: C2H + H2 ⇔ C2H2 + H R92: C2H + H + M ⇔ C2H2 + M R93: C2H2 + H + M ⇔ C2H3 + M
-0.04
R94: C2H3 + H ⇔ C2H2 + H2
-0.06
0.1
0.5H2 (metallic surface)
Diffusion D R10-7: 2H2 ⇔ 2H + H2 R11-8: H2 + H ⇔3H
0.0 -0.1
R97: C2H4 + H ⇔ C2H3 + H2 R106: H
0.2
Substrate
-
Production rate
Substrate
R106: H
-0.02
e + 2H
R77: CH3 + H + M
0.5
0.00
-
R1: e + H2
0.04
Net production rate
10
Axial position
Axial position [cm]
0.5H2 (metallic surface)
Diffusion D R10-7: 2H2 ⇔ 2H + H2
-0.2
R11-8: H2 + H ⇔3H
-0.3
-0.08 0
2
4
6
8
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Axial position
Axial position [cm]
Fig. 10. Net production balance for H-atom at different couples (pressure and power): (a) 25 hPa/600 W; (b) 100 hPa/2000 W; (c) 270 hPa/4000 W; (d) details of (c) at the near vicinity of the surface. The percentage of methane is kept constant at 5%. The complete chemical kinetics scheme is given in references 6 and 48.
1 dH v s Ts X H js ¼ 1 þ cs X HMax Tg Max 4DH 1 dH v s Ts ¼ 1 þ cs X H1 Tg 1 4DH
ð14Þ
where XH|s and XH1 = XHMax represent the H atom mole fraction at the surface and in the plasma (maximum value), respectively. In Fig. 11a is reported the variation of surface XH as a function of the pressure for different powers obtained. A comparison between experimental and calculated surface H atom densities is presented in Fig. 11b. Again a rather good agreement is observed. A factor from 0.1 for the lower power density to 0.03 for the higher power density is observed between the surface H atom density and the maximum volume H-atom density ([H]s/[H]1 = 0.1 to 0.03). We can appreciate the effect of increasing power and pressure to increase the surface H atom density. The upper values must be compared to the maximal value of H atom density at the surface (6 1017 cm3) predicted by Goodwin et al. for a fully dissociated gas arriving at the stagnation point with an initial mean velocity characterized by a stagnation-point velocity gradient of 105 s1, at two atmospheres. We observe a difference of a factor 30 with our experimental values (1.7 1016/ 6 1017). The microwave cavity based diamond deposition plasma reactor operating at low Peclet number and at pressure up to 0.5 atmospheres is then far to be as efficient as the high speed fully dissociated plasma operating at two atmospheres. For fully disso-
ciated plasma operating at 0.5 atmospheres (the upper pressure value accessible due to the formation of filamentary discharges), we can expect around 3 1016 cm3 H atom density at the surface that represents only 5% of the upper limit predicted by Goodwin. 4. Conclusion The purpose of this paper was to estimate H-atom density in diamond deposition plasma reactors under conditions of high power density, since this parameter is probably the most important one to monitor for producing thick films at relatively high growth rate. After estimating the variation of the electron temperature, the variation of H-atom mole fraction was obtained as the pressure was varied from 14 to 400 hPa and simultaneously the power was increased in the range of 400–4000 W. H atom mole fraction up to 0.6 has been obtained, even if this value must be considered as probably an upper estimation due to the assumptions made and the experimental uncertainties. The actinometry method was seen to be a powerful technique even at high power density. From this analysis, it comes that relatively high surface H-atom densities can be obtained under conditions of very high gas temperature with a gas temperature peak located very close to the surface. An increase in power density coupled to the plasma (high pressure and/or power values) was seen to induce both an increase in the maximum value of the gas temperature and a shortening of the distance of this maximum relatively to the substrate. Growing at fast
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
H surface mole fraction (%)
a
0.010
0.008
400W 600W 800W 1000W 1150W 1250W 1500W 2000W 2500W 3000W 3500W 4000W
0.006 7% CH4
0.004
0.002
0.000 0
100
200
300
400
Pressure (hPa)
b
1
16
H [H]surf (10 ) cm
-3
10
600W 800 W 1000 W 1500 W 2000 W 3000 W 4000 W
0.1
0.01
0
50
100
150
200
250
300
350
400
Pressure (hPa) Fig. 11. (a) Surface H-atom mole fractions as a function of pressure for different power, obtained from actinometry measurements in the plasma bulk. (b) Surface H atom densities deduced from measurements and calculated with the 1D model, for different conditions of pressure and power. Open symbols correspond to calculations. The black line indicates the upper value predicted by Goodwin (see text).
growth rate under conditions of highly dissociated plasmas appears accessible with the microwave cavity based reactors operating up to 0.5 atmospheres, but these will never reach the efficiency obtained for fully dissociated plasma flowing at high speed at two atmospheres. It is worth noting however that, unlike the reactors running at very high flow, microwave cavity based reactors are much easier to monitor in particular on the cleanness point of view that is crucial for growing very high purity diamond. Acknowledgements François Silva and Ovidiu Brinza are thanked for their help in setting up the plasma reactor. This work has been granted by ANR (Agence Nationale de la Recherche) through Project ANR-06BLAN-0173. References [1] A. Gicquel, K. Hassouni, S. Farhat, Y. Breton, C.D. Scott, M. Lefebvre, M. Pealat, Diam. Relat. Mater. 3 (4) (1994) 581. [2] A. Gicquel, K. Hassouni, Y. Breton, M. Chenevier, J.C. Cubertafon, Diam. Relat. Mater. 5 (3–5) (1996) 366. [3] A. Gicquel, M. Chenevier, Y. Breton, M. Petiau, J.P. Booth, K. Hassouni, J. Phys. III 6 (1996) 1167. [4] A. Gicquel, M. Chenevier, K. Hassouni, A. Tserepi, M. Dubus, J. Appl. Phys. 83 (12) (1998) 7504. [5] A. Gicquel, K. Hassouni, G. Lombardi, X. Duten, A. Rousseau, Mater. Res. 6 (2003) 25. [6] K. Hassouni, F. Silva, A. Gicquel, J. Phys. D Appl. Phys. 43 (15) (2010) 153001. [7] G. Lombardi, K. Hassouni, G.D. Stancu, L. Mechold, J. Röpcke, A. Gicquel, J. Appl. Phys. 98 (5) (2005) 053303.
247
[8] G. Lombardi, K. Hassouni, G.D. Stancu, L. Mechold, J. Röpcke, A. Gicquel, Plasma Sources Sci. Technol. 14 (3) (2005) 440. [9] K. Hassouni, O. Leroy, S. Farhat, A. Gicquel, Plasma. Chem. Plasma Process. 18 (3) (1998) 325. [10] K. Hassouni, T.A. Grotjohn, A. Gicquel, J. Appl. Phys. 86 (1) (1999) 134. [11] K. Hassouni, G. Lombardi, X. Duten, G. Haagelar, F. Silva, A. Gicquel, T.A. Grotjohn, M. Capitelli, J. Röpcke, Plasma Sources Sci. Technol. 15 (1) (2006) 117. [12] G. Lombardi, G.D. Stancu, F. Hempel, A. Gicquel, J. Röpcke, Plasma Sources Sci. Technol. 13 (1) (2004) 27. [13] J. Ma, M.N.R. Ashfold, Yu.A. Mankelevich, J. Appl. Phys. 105 (4) (2009) 043302. [14] Yu.A. Mankelevich, M.N.R. Ashfold, J. Ma, Appl. Phys. 104 (11) (2008) 113304. [15] Yu.A. Mankelevich, P.W. May, Single crystal diamond in MW PECVD reactors, Diam. Relat. Mater. 17 (7–10) (2008) 1021. [16] P.W. May, Yu A. Mankelevich, J. Phys. Chem. C 112 (32) (2008) 12432. [17] J.E. Butler, Yu A. Mankelevich, A. Cheesman, J. Ma, M.N.R. Ashfold, J. Phys. Condens. Mat. 21 (36) (2009) 364201. [18] J. Ma, J.C. Richley, D.R.W. Davies, M.N.R. Ashfold, Yu.A. Mankelevich, J. Phys. Chem. A 114 (37) (2010) 10076. [19] J. Ma, A. Cheesman, M.N.R. Ashfold, K.G. Hay, S. Wright, N. Langford, G. Duxbury, Yu.A. Mankelevich, J. Appl. Phys. 106 (3) (2009) 033305. [20] J.R. Ma, C. James, Michael N.R. Ashfold, Yuri A. Mankelevich, Probing the plasma chemistry in a microwave reactor used for diamond chemical vapor deposition by cavity ring down spectroscopy, J. Appl. Phys. 104 (10) (2008) 103–305. [21] T.A. Grotjohn, R. Liske, K. Hassouni, J. Asmussen, Scaling behavior of microwave reactors and discharge size for diamond deposition, Diam. Relat. Mater. 14 (3–7) (2005) 288–291. [22] T.A. Grotjohn, J. Asmussen, S. Sivagnaname, D. Story, A.L. Vikharev, A. Gorbachev, A. Kolysko, Diam. Relat. Mater. 9 (3–6) (2000) 322. [23] K.W. Hemawan, T.A. Grotjohn, D.K. Reinhard, J. Asmussen, Diam. Relat. Mater. 19 (12) (2010) 1446. [24] S.O. Hay, W.C. Roman, M.B. Colket, J. Mater. Res. 5 (11) (1990) 2387. [25] F.G. Celii, P.E. Pehrsson, H.T. Wang, J.E. Butler, Appl. Phys. Lett. 52 (24) (1988) 2043. [26] J.E. Butler, F.G. Celii, D.B. Oakes, L.M. Hanssen, W.A. Carrington, K.A. Snail, High Temp. Sci. 27 (1989) 183. [27] J. Hirmke, A. Glaser, F. Hempel, G.D. Stancu, J. Röpcke, S.M. Rosiwal, R.F. Singer, Vacuum 81 (5) (2007) 619. [28] A. Cheesman, J.A. Smith, M.N.R. Ashfold, N. Langford, S. Wright, G. Duxbury, J. Phys. Chem. A 110 (8) (2006) 2821. [29] E.A. Brinkman, G.A. Raiche, M.S. Brown, J.B. Jeffries, Appl. Phys. B: Lasers Opt. 64 (6) (1997) 689. [30] G.A. Raiche, J.B. Jeffries, Appl. Opt. 32 (24) (1993) 4629. [31] C. Kaminski, P. Ewart, Appl. Phys. B: Lasers Opt. 61 (6) (1995) 585. [32] T. Lang, J. Stiegler, Y. Von Kaenel, E. Blank, Diam. Relat. Mater. 5 (10) (1996) 1171. [33] D.G. Goodwin, J.E. Butler, Theory of diamond chemical vapor deposition, in: G.P.M.A. Prelas, L.K. Bigelow (Eds.), Handbook of Industrial Diamonds and Diamond Films, Marcel Dekker, Inc., NY, 1997, pp. 527–581. [34] Gicquel et al., work under progress. [35] A. Tallaire, J. Achard, F. Silva, A. Gicquel, Physica Status Solidi (a) 202 (11) (2005) 2059–2065. [36] D.G. Goodwin, J. Appl. Phys. 74 (11) (1993) 6888. [37] D.G. Goodwin, J. Appl. Phys. 74 (11) (1993) 6895. [38] J.W. Coburn, M. Chen, J. Appl. Phys. 51 (6) (1980) 3134. [39] K. Hassouni et al., Plasma Sources Sci. Technol. 8 (3) (1999) 494. [40] R.K. Janev, Elementary Process in Hydrogen Plasma, Springer, Berlin, 1987. p. 25. [41] B.L. Preppernau, K. Pearce, A. Tserepi, E. Wurzberg, T.A. Miller, Chem. Phys. 196 (1–2) (1995) 371. [42] J. Bittner, K. Kohse-Höinghaus, U. Meier, Th Just, Chem. Phys. Lett. 143 (6) (1988) 571. [43] J.W.L. Lewis, W.D. Williams, J. Quant. Spectrosc. Radiat. Transfer 16 (1976) 939. [44] A. Catherinot, B. Dubreuil, M. Gand, Phys. Rev. A 18 (3) (1978) 1097. [45] S. Lauer, H. Liebel, F. Vollweiler, O. Wilhelmi, R. Kneip, E. Flemming, H. Schmoranzer, M. Glass-Maujean, J. Phys. B: At. Mol. Opt. Phys. (1998) 3049– 3056. [46] S.J. Harris, Appl. Phys. Lett. 56 (23) (1990) 2298. [47] S.J. Harris, D.G. Goodwin, J. Phys. Chem. 97 (1) (1993) 23. [48] M. Frenklach, H. Wang, Phys. Rev. B 43 (2) (1991) 1520. [49] J.E. Butler, R.L. Woodin, Thin-film diamond growth mechanisms, Philos. Trans. Roy. Soc. London Ser. A – Math. Phys. Eng. Sci. 342 (1664) (1993) 209. [50] D.G. Goodwin, J.E. Butler, Theory of diamond chemical vapor deposition, in: G.P.M.A. Prelas, L.K. Bigelow (Eds.), Handbook of Industrial Diamonds and Diamond Films, Marcel Dekker, Inc., NY, 1997, pp. 527–581. [51] A. Gicquel, F. Silva, C. Rond, N. Derkaoui, O. Brinza, J. Achard, G. Lombardi, A. Tallaire, A. Michau, K. Hassouni, Ultra-fast deposition of diamond by plasma enhanced CVD, in: Comprehensive Hard Materials, Elsevier, 2012, in press. [52] A. Gicquel, K. Hassouni, F. Silva, J. Achard, Curr. Appl. Phys. 1 (6) (2001) 479. [53] L.N. Krasnoperov, I.J. Kalinovski, H.N. Chu, D. Gutman, J. Phys. Chem. 97 (45) (1993) 11787. [54] A. Rousseau, G. Cartry, X. Duten, J. Appl. Phys. 89 (4) (2001) 2074. [55] Y.C. Kim, M. Boudart, Langmuir 7 (12) (1991) 2999. [56] M.H. Gordon, X. Duten, K. Hassouni, A. Gicquel, J. Appl. Phys. 89 (3) (2001) 494.
Contents lists available at SciVerse ScienceDirect
Chemical Physics journal homepage: www.elsevier.com/locate/chemphys
Quantitative analysis of diamond deposition reactor efficiency A. Gicquel a,b,⇑, N. Derkaoui a,b, C. Rond a,b, F. Benedic a,b, G. Cicala c, D. Moneger a,b, K. Hassouni a,b a
Laboratoire des Sciences des Procédés et des Matériaux, UPR3407, CNRS, Université Paris 13, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France Laboratoire d’Excellence Sciences and Engineering for Advanced Materials and devices, PRES Sorbonne Paris Cité, France c CNR-IMIP (Istituto di Metodologie Inorganiche e dei Plasmi), Sezione di Bari, Via G. Amendola 122/D, 70126 Bari, Italy b
a r t i c l e
i n f o
Article history: Available online 6 September 2011 Keywords: Microwave plasma Diamond deposition Emission spectroscopy Actinometry Plasma modelling
a b s t r a c t Optical emission spectroscopy has been used to characterize diamond deposition microwave chemical vapour deposition (MWCVD) plasmas operating at high power density. Electron temperature has been deduced from H atom emission lines while H-atom mole fraction variations have been estimated using actinometry technique, for a wide range of working conditions: pressure 25–400 hPa and MW power 600–4000 W. An increase of the pressure from 14 hPa to 400 hPa with a simultaneous increase in power causes an electron temperature decrease from 17,000 K to 10,000 K and a H atom mole fraction increase from 0.1 to up to 0.6. This last value however must be considered as an upper estimate due to some assumptions made as well as experimental uncertainties. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction At long term, single crystal diamond films with very high purity is believed to outperform silicon in devices such as switches working at voltages of 10 and up to 20 kV. Some key bottlenecks must however be over-passed to reach this era. They concern mostly today the ability to synthesize very high quality bi-polar (intrinsic, n-doped, pdoped and p+ doped) or even uni-polar (intrinsic, p-doped and p+ doped) multilayers all in diamond, to reduce substantially the dislocation density inside the crystals (typically of 104/cm2 for the state of the art), to enlarge the diamond single crystal layers and to grow 100 lm to 1 mm thick films at very high growth rates. Part of these issues, in particular the last one, is based on the capability to produce very energetic and very high purity plasma able to run for long deposition time (for thick films). The goal is to produce a large amount of atomic hydrogen in the plasma that diffuses towards the substrate as well as CH3 radicals at the plasma/surface interface, these species being key for diamond deposition. Microwave plasma reactors, running at pressure typically in the range of 100–400 hPa with some kilowatts power coupled to the plasma, answer pretty well to this purpose. These reactors have been extensively studied for conditions of moderate power density (less than 30 W cm3), in particular by Gicquel’s group in collaboration with different laboratories [1–12], but also by Ashfold and Mankelevich [13–20], as well as Grotjohn et al. [21–23]. However the conditions of very high power density (high pressure and high microwave ⇑ Corresponding author at: Laboratoire des Sciences des Procédés et des Matériaux, UPR3407, CNRS, Université Paris 13, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France. E-mail address: [email protected] (A. Gicquel). 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.08.022
power coupled to the plasma) have not been studied so much. In particular, even if some works have been carried out [6,18], there is still lacks in experimental validations of the simulation codes and basic studies aiming to determine the main parameters (species, flow, . . .) responsible for doping as well as for soot formation which has been observed under conditions of high power density coupled to high methane input, and more recently in presence of diborane in the plasma. In the past, different spectroscopic methods have been employed to monitor the gas phase chemistry and composition in diamond deposition reactors. In particular, absorption spectroscopy and laser induced fluorescence (LIF) spectroscopy have been used due to their capability in accessing ground state species. Thus, ground state H atoms, which is a key factor for CVD diamond deposition, has been studied in microwave plasma reactors at low to moderate power density by Two-photon laser induced fluorescence (TALIF) [2–4] to estimate the temperature and relative mole fraction of H atoms, while ground state molecular hydrogen temperature have been measured through coherent anti-stokes Raman spectroscopy (CARS) spectroscopy [1,2,24]. Concerning carbon containing species, the ultraviolet absorption of CH3 at 216 nm was used for number density measurements firstly in hot filament reactors and later on in plasma reactors. Most recent experimental advances derive from the improvement of laser absorption spectroscopy methods that have allowed accessing to stable hydrocarbon species like CH4, C2H2 as well as transient species such as CH3 radicals through IR absorption using tunable diode laser [8,12,25–27] and quantum cascade laser (QCL) [19,28]. Furthermore, CH3 radicals have also been monitored in microwave reactors using cavity ring-down spectroscopy (CRDS) [20]. Finally, laser induced fluorescence (LIF) observations of CH and C2 radicals
240
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
have been also reported in dc-arcjet plasma for diamond deposition providing gas temperature [29,30] and absolute concentration of C2 [31]. These diagnostics are powerful methods for probing species on their ground electronic states. However the nonflexible and expensive characteristics of these advanced techniques make them unfit for diagnosing industrial reactors, and then comparison between different MW reactors seems hard to be considered. Optical emission spectroscopy (OES) measurements on radiative species can be a powerful technique for accessing plasma characteristics, provided it is coupled with a very detailed analysis of all the electronic excitation processes to obtain ground state density information. Actinometry technique has been demonstrated to be valid in diamond CVD reactor for probing hydrogen atom [4] and then was used to determine the spatially resolved H relative density for low to medium pressure conditions (100 hPa > p > 25 hPa, 2000 W > P > 600 W). Lang et al. also reported results at low pressure conditions (50–100 hPa; 400–880 W) [32], and recently Ma et al. [13] proposed a spatially resolved studies of H relative density for higher pressure conditions (<200 hPa; 1.5 kW). Increasing power and pressure (i.e. power density) enhances drastically CVD diamond growth rates [33,34] and quality [35–37]. Indeed, increasing the MW power density results in a lower electronic temperature but in a higher gas temperature [6,9]. As at high power density (>15 Wcm3, i.e. p > 50 hPa, P > 1000 W), the main Hatom production channel is thermal dissociation [9], as a result: the higher the MW power density, the higher the H density and the more efficient the diamond CVD process. Previous works referred above have been carried out for moderate power density conditions. This paper focused on the study of the plasma phase for high power density growing conditions using actinometry method. Another goal is to analyze the validity of this technique for H atom at high pressure/power conditions by comparing experimental and simulated results. Variations of both electron temperature and H-atom density as a function of the power density, monitored by the couple (pressure, microwave power coupled to the plasma) will be discussed. This paper constitutes a first part of a larger program aiming to put forward our knowledge of diamond deposition reactor operation, when running at high power density.
relatively to the plug-in power that is lower due to the Joule effect energy loss. This has been made in a bell jar reactor operating at low power density evidencing that more than 90% of power was coupled to the plasma [56]. Under conditions of high power density this is obviously not the case as evidenced by the observed strong heating of the microwave guides and quartz windows. This necessarily leads to errors in defining the average power density, expressed in W cm3. As a consequence, the experimental conditions of (pressure-MP power) couple will be most of the time specified rather than the power density. In the frame of this study, large ranges of pressure (25–400 hPa) and MW power (600–4000 W) were used, focusing our attention on high power density conditions. It is worth noting that the results obtained previously at low pressure and power in a bell jar reactor are reported in this paper. The link between these sets of experimental results is provided through calibrations. 2.2. OES measurements A scheme of the MW reactor and the OES set-up is shown in Fig. 1. The steel cavity contains three optical fused silica windows. An Acton 2500i spectrometer equipped with an ICCD camera was used to perform emission spectroscopy. Most of the measurements have been carried out using a 1800 g/mm grating blazed at 500 nm, except for Hb (n = 4) spectra obtained with a 2400 g/mm holographic visible grating. The light emitted from the plasma was collected by an afocal lens system and transported via a 1 mm optical fibre core to the entrance slit (10 lm) of the monochromator. This device enables a spatial resolution of 1 mm and a spectral resolution of 0.03 nm. The optical system was mounted on computer controlled translation stages, allowing axial and radial measurements. Emission intensity, averaged on a line of sight, is measured at 90° to the axis of the reactor. At a given location in the plasma, as the plasma volume is kept as much as possible constant, the line-of-sight averaged emission intensities are always measured within approximately the same plasma volume. Spectra of Ha (k = 656.5 nm), Hb (k = 486.1 nm), and 4p ? 4s argon transition (transition 2p1 ? 1s2 at k = 750.3 nm) were recorded systematically (Fig. 2a). Table 1 gives the different transitions used.
2. Experimental set-up and diagnostics 2.1. Microwave reactor The microwave diamond deposition reactor, which was described elsewhere [35], is a water-cooled stainless steel resonant cavity that operates at moderate pressure and dedicated to high power density operations (Fig. 1). The discharge is generated by a 2.45 GHz MW generator delivering a maximum power of 6 kW along a rectangular waveguide up to a cylindrical chamber. At the centre of this chamber, a 5 cm in diameter substrate holder is supporting a either polycrystalline or single crystal diamond substrate. Both are immersed in a close to hemispheric plasma emerging from MW activation of the feed gas. The gas consists in a mixture of CH4 (0–4%) and Ar (3–4%) diluted in hydrogen and supplied by a total flow rate range of 100–500 sccm. Substrate temperature, monitored using a monochromatric IR pyrometer, can be varied from 620 °C to 915 °C, independently from the plasma conditions. For this specific study, it was maintained at 850 °C. The total pressure in the reactor chamber was adjusted in order to keep as much as possible constant the plasma volume (the dimension of which reminding anyway difficult to estimate). The goal of this procedure is to maintain the ratio of the power coupled to the plasma over the total density constant. However, we cannot report the estimation of the input power fraction really coupled to the plasma
2.2.1. Actinometry method Actinometry was introduced in the early 80’s [38] in order to estimate relative densities of a ground state species from OES measurements. The principle and the validation of the method applied to H-atom relative density measurements has been thoroughly described previously [1,4] and then by Ma et al. [13]. Briefly, actinometry requires the introduction of a small amount of an inert gas (here argon) to the mixture, which constitutes the actinometer. The emission intensity ratio (probed species over actinometer) is proportional to the species electronic ground state relative concentration, provided that (i) the two species are excited from their electronic ground state by a single electron impact; (ii) the excitation cross section of these processes are similar (same energy threshold, proportional for the considered electron energy range); (iii) radiative de-excitation processes are predominant. Quenching processes have to be taken into account for high pressure conditions. Argon has been chosen as actinometer to study the relative density of H atom in diamond CVD plasma, since its excited state (4p) is produced by direct electron impact processes from the 3p6 ground state under the conditions studied here, the excitation cross section of which being similar in shape as that of H(n = 3). The main processes involved in the production and loss of H(n = 3) and Ar(4p) (sublevel 2p1) have been widely studied and presented in [4]. As well
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
241
Fig. 1. MW reactor scheme and OES set-up.
the relationship linking H-atom mole fraction to emission intensity measurements has been established: Ar
½H xH k ¼ ¼ F eHa ½Ar xAr ke Ar
mAr Q I =I mHa T H Ar
ð1Þ
Ha
where ke and ke are excitation rate constants for the transition Ar(3p) ? Ar(4p) and H(n = 1) ? H(n = 3); mi is the de-excitation frequency of species i; xi is the mole fraction of species i; QT is the term relative to radiative and quenching processes and F is an optical device factor. Giving the cross sections (r) in Å2, the gas temperature (T) in K, the pressure (P) in hPa and xH2 the molecular hydrogen mole fraction, QT is equal to [4]:
QT ¼
1 þ PT 1=2 ½0132rHa=H2 xH2 þ 0152rHa=H ð1 xH2 Þ
ð2Þ
1 þ PT 1=2 ½0162rAr =H2 xH2 þ 0226rAr =H ð1 xH2 Þ Ar
Ha
The estimation of the excitation rate constants ke and ke needs the knowledge of the electron temperature that, in these kinds of plasma, cannot be measured by Langmuir probe due to the highly collisional character at these pressures. In the plasmas studied here, the electron energy distribution function is characterized by two sets of electrons (the hot electrons with an energy above 12 eV and the cold electrons with an energy below 8 eV) [6,39]. Each group presents a Boltzmann distribution characterized by an electron temperature, the cold electron having a temperature higher 10,000–20,000 K than the hot electrons 6000–10,000 K. As a matter of fact, the electron energy distribution function of the hot electrons drops faster than that of the cold electrons. From the analysis of the electron distribution and the adequacy with the main processes occurring in the plasma, it was deduced that the average energy heei based on the set of the colder electrons was a relevant parameter to use. While the gas heating leading to very high gas temperature is driven by the energy of around 1 eV, it is not the case for direct electron impact electronic excitation from ground state, in particular for atomic hydrogen and argon. These processes require electrons with energy higher than 12 eV that is located at the frontier of the two sets of electrons. As a consequence, they are driven either by the hottest electrons of the cold electron Maxwellian distribution or by the coldest electrons of the hot electrons distribution function. Taking into consideration the relative density of these two sets of electrons, we have based our method on the estimation of the electron temperature characterizing the set of the colder electrons.
In Ref. [4], the processes of production of both Ar(4p) and H(n = 3) have been established. For power density higher than 9 W cm3 (25 hPa, 600 W) the direct electron impact process is responsible for the electronic excitation of both H(n = 3) and Ar(4p). As far as H(n = 4) is concerned, the same conclusion can be stated since the different mechanisms of production of this electronic state is similar to that of H(n = 3). One additional question however must be raised for condition of very high pressure; the possibility that self absorption processes may participate to populate the electronic excitated states n = 3 and n = 4 of atomic hydrogen from overpopulated level H(n = 2). Unlike the Lyman a radiation (in the VUV range) is assumed to be entirely absorbed by the H(n = 1) atoms (optically thick plasma) in the LSPM 0 D collisional radiative model, the Balmer radiations are assumed not to be reabsorbed (the plasma is considered for these transitions optically thin) [13]. This assumption is supported on the one hand by the ratio value of the H(n = 2)/H(n = 1) evaluated both by us and by the Ashfold group [13,14] at around 108. On the other hand, very little broadening is observed in the Ha emission intensity spectra as the pressure and power are increased, as shown in Fig. 2b. This can be attributed to the Doppler effect but not to a change in the production mechanism of this state. 2.2.2. Electron temperature analysis The estimation of [H] relative concentration through actinometry method is based on the knowledge of both the electronic excitation cross sections of the species studied and the electron temperature. For estimating the electron temperature, we have used the emission intensity ratio of two hydrogen lines. The procedure is valid upon provided that the excited states are populated from their ground state through a direct electron impact. This aspect has been established in the previous section. Electron temperature is linked to the emission intensity ratio by the relation: Ha
I Ha k ¼ F eHb IHb ke Ha
m656 Q m486 T;H Hb
ð3Þ
where ke and ke are excitation rate constants for the transition H(n = 1) ? H(n = 3) and H(n = 1) ? H(n = 4), respectively [40]; m656 and m486 are the de-excitation frequency for H(n = 3) and H(n = 4); F is an optical device factor. Finally QT,H is the term relative to radiative and quenching processes which can be expressed as:
242
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
a
Wavelenghts (nm) 740
745
750
755 80
50000
150 mbar - 2500 W 250 mbar - 3500 W
70
Ar750
Relative intensity (a.u.)
40000
60
50
30000
40 20000
30
20
Hα
10000
Relative intensity (a.u.)
735
10
0
0 652
656
660
664
668
Wavelenghts (nm)
b Hα emission intensity (normalized)
1.0
40 mbar 800 W 70 mbar 1500 W 200 mbar 3000 W 270 mbar 4000 W 400 mbar 3000 W
0.8
0.6
0.4
0.2
0.0
656,10
656,15
656,20
656,25
656,30
656,35
656,40
656,45
656,50
Wavelengths (nm) Fig. 2. (a) Optical emission spectra of Ha (656.3 nm) and Ar750 (750.4 nm) for two experimental conditions of pressure/MW power (note that the scales for Ha and Ar750 are indicated respectively on the bottom left corner and on the upper right corner); (b) Ha profiles as a function of different pressure and power couples.
Q T;H ¼
1 þ PT 1=2 ½0132rHa=H2 xH2 þ 0152rHa=H ð1 xH2 Þ 1 þ PT 1=2 ½0426rHb=H2 xH2 þ 0492rHb=H ð1 xH2 Þ
ð4Þ
where pressure is expressed in hPa, rHa=H2 and rHa/H (in Å2) are the quenching cross sections of Ha by the H2 molecules and by the H atoms respectively, which are given in [41,42] and [4], and rHb=H2 and rHb/H (in Å2) are the quenching cross sections of Hb by the H2 molecules and by the H atoms respectively. No data concerning the quenching cross sections of Hb by the H2 molecules, under the conditions of pressure studied here could be found, although Lewis et al. [43], Catherinot et al. [44] and Glass-Maujean et al. [45] provide values for H(n = 3) and H(n = 4) states at much lower pressures (less than 2 hPa). Due to the strong pressure dependence of the quenching cross sections observed by these authors, we have decided not to take into account for the quenching for the excited states. The obvious consequence is that we will only access to an estimate of the electron temperature and its variation as a function of the pressure. It is worth noting that the quenching effect of carbon containing species has not also been taken into account, since
Table 1 Species, transition wavelengths, upper and lower level assignments, and energies for tracers monitored in the OES study. Species
k (nm)
Upper level
Energy (eV)
Lower level
Energy (eV)
Ha Hb Ar750
656.3 486.1 750.4
n=3 n=4 2p1
12.10 12.75 13.48
n=2 n=2 1s2
10.20 10.20 11.86
no more that 7% and most of the time 4% of methane was introduced in the feed gas.
3. Experimental results 3.1. Positioning of the problem Under medium pressure microwave diamond deposition reactor, as it is largely accepted by the community, H atoms and CH3
243
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
kðTsÞ½CH3 s ½Hs
ð5Þ
5109 þ ½Hs
where k(Ts) = 1.8 1011 at Ts = 1200 K and, [H]s and [CH3]s are the concentrations of surface H-atom and CH3-radical (in mol cm3) respectively. Transforming Eq. (5), it comes:
Growth rate ¼ kðTsÞ½CH3 s
5:109 1þ ½Hs
!1 ð6Þ
Eq. (6) clearly shows that the higher [H]s the higher the growth rate. A maximum value of 106 mol cm3 has been predicted by Goodwin for fully dissociated plasma flowing at very high speed and at two atmospheres. We will estimate in this paper how the type of plasma studied here (2.45 GHz cavity based reactors working at low Peclet number) are positioned relatively to this maximum value. In addition, based on calculations, we have established [34,51] that surface CH3 radical density varies linearly with the H-atom density in the plasma bulk at high power density (Fig. 3). Then we can state that, for a given CH4 percentage introduced in the discharge and a given location of its injection, the growth rate will be an only function of H-atom density produced into the plasma. For very high energetic condition, an almost linear variation may even be expected. This statement strengthens the fact that studying a diamond deposition reactor implies first to explicit the spatial H atom production and loss terms as a function of the plasma conditions. This is the goal of this paper.
One of the best ways to increase H atom density and then growth rates is to increase the power density of the plasma. This can be done either by increasing simultaneously pressure and power keeping constant the plasma volume or by increasing only pressure while keeping constant the power (in this latter case the plasma volume decreases). The emission intensity ratio of Ha and Hb lines is a relevant measurement of the electron temperature provided that a calibration is available. This latter has been obtained from electron temperature calculated in [52] for the following couple of power and pressure (1000 W and 50 hPa; 15 W cm3). Experimental axial distributions of the electron temperature for different conditions of power and pressure have been obtained (Fig. 4a and b). A rather good agreement between experimental and calculated results can be observed in Fig. 5, although as discussed above the quenching cross sections of the H atom excited states were not taken into account. A decrease in the electron temperature from 16,000 K to around 11,000 K is observed as the pressure is increased from 25 hPa to 270 Pa, and simultaneously the power is increased from 600 W to 4000 W. It is worth noting that, within the error bar that can be estimated at ±1000 K, at 400 hPa, 3000 W and 7% of CH4, the
a 14000
6000
0.0
0.5
1.0
1.5
2.0
0.6 0.4
2.5
3.0
3.5
4.0
Axial position [cm] 20000
Actinometry experiments Calculations 1D model
16000 14000 12000 10000
Substrate
Electron temperature [K]
-3 14
8000
18000
1.2
[CH3]surf (.10 cm )
10000
2000
1.4
0.8
12000
4000
b
1.0
Actinometry experiments Calculations 1D model
Substrate
Growth rate ¼
3.2. Influence of microwave power density on the H atom density in the plasma bulk
Electron temperature [K]
radical constitute the main governing species for growing polycrystalline and single crystal diamond layers. The first diamond growth model proposed by Harris, was then improved by different authors [36,37,46–49] and a very complete review paper of diamond growth can be found in references [17,50]. Although it only applies to growth on (1 0 0) faces, the simplified model is clearly based on the key role of CH3 radicals and H atoms. From this mechanism, the authors stated on a very simple growth law valid for concentrations of the CH3 and H-atom in the range of [3 1010, 105] mol cm3 and [1011, 106] mol cm3 respectively [36]:
8000 6000 4000
0.2 2000 0.0
0.0 0
5
10
15
20 16
25
-3
plasma [H]max (.10 cm ) Fig. 3. Variation of the surface CH3-radical density as a function of the plasma bulk H-atom density. The pressure and power couples were varied from 25 hPa/600 W to 270 hPa/4000 W. Percentage of CH4 added in the feed gas: 4% [34,48].
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Axial position [cm] Fig. 4. Simulated (red diamond) and experimental (black square) electron temperature profiles for two power densities (couples (pressure, power)): (a) 110 hPa/ 2500 W, (b) 200 hPa/3000 W. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
a
600 W 800 W 1000 W 1250 W 1500 W 2000 W 2500 W 3000 W 3500 W 4000 W Calculation
16000
14000
0.35
Actinometry experiments Calculations 1D model
0.30
H mole fraction
Electron temperature (K)
18000
12000
0.25 0.20 0.15
Substrate
244
0.10
7% CH4
0.05
10000 0
100
200
300
400
0.00
500
0.0
0.5
1.0
Pressure (hPa)
1.5
2.0
2.5
3.0
3.5
4.0
Axial position [cm]
Fig. 5. Electron temperature fractions as a function of pressure for different powers, obtained from the measurement of the ratio IH/IHb. %CH4 = 4% except for one condition (indicated onto the figure).
b
0.35
Actinometry experiments Calculations 1D model
3.3. Estimation of the H atom density at the surface From the spatial distributions of XH (H-atom mole fraction) shown in Fig. 7a and b, the mass boundary layer thicknesses, corresponding to characteristic length scales for diffusion, can be defined locally at the surface by:
dH ¼
X H1 X H0 ðdX H =dzÞjz¼0
ð7Þ
1.0
0.8
H mole fraction
7% CH4 0.6 600 W 800 W 1000 W 1250 W 1500 W 2000 W 2500 W 3000 W 3500 W 4000 W Calculation
0.4
0.2
0.0
0
100
200
300
400
500
Pressure (hPa) Fig. 6. Maximal plasma H-atom mole fraction as a function of pressure for different powers, obtained from actinometry measurements.
0.25 0.20 0.15
Substrate
electron temperature is equal to that obtained at 270 hPa, 4000 W and 4% CH4. The variation of the H mole fraction in the plasma bulk as a function of the pressure and for different powers coupled to the plasma is shown is Fig. 6. These measurements are deduced from the emission intensity ratio of the Ha line over that of the 750 nm argon line using Eq. (1), and after calibration made using the lower power density that provides H atoms from thermal dissociation, i.e. 1000 W and 50 hPa. Results show a strong increase in the H-atom mole fraction: it rises from 0.01 at 25 hPa and 600 W up to around 0.5 at 270 hPa and 4000 W. At 300 hPa and 3000 W, it reaches 0.6 ± 0.1, evidencing the strong effect of pressure.
H mole fraction
0.30
0.10 0.05 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Axial position [cm] Fig. 7. Experimental and calculated spatial distribution of H-atom mole fractions for two power densities (couples (pressure, power)): (a) 110 hPa/2500 W, (b) 200 hPa/3000 W.
The experimental values that appear higher than the calculated ones, give a variation from 16.8 mm at 25 hPa and 600 W, to 9.7 mm at 3 kW and 200 hPa. The decrease in dH as a function of the power density (increase in power and pressure) is attributed to that of the thermal boundary layer thickness dT. As a matter of fact, since molecular hydrogen dissociation is controlled by thermal processes, the H atom mole fraction distribution is directly correlated to that of the gas temperature. Since in addition gas temperature is driven by the energy transfer from the electrons, it depends on the location where the microwave energy is deposited into the plasma. As shown from the measurements of the emission argon line intensity profile (IAr750,4), the maximum of IAr750,4 is displaced towards the surface as the pressure and power increases, evidencing that the higher the power density, the closer to the surface, the power is absorbed (Fig. 8). The good agreement between the electron temperature (Te) axial profiles obtained from the emission intensity ratio IHa/IHb and the calculated axial profiles of electron temperature for different couples pressure and power, confirms the slight increase in the absorbed power in the nearest vicinity of the surface as the power density is increased (Fig. 4a and b). In addition, the decrease in dT is also attributed to the decrease of the thermal diffusivity at high power density, i.e. high pressure (Fig. 9). The spatial net H-atom production yields for different reactions and as a function of the power density (pressure/power) are shown in Fig. 10. As already discussed in references [6,51] where the
245
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
DH ð@X H =@zÞ ¼ RSH
2000W, 100 hPa 3000W, 200 hPa
7000000
where RSH is the total H-atom surface consumption reaction rate. At steady state and without any convective flux (stagnation point condition), it comes:
6000000 5000000
Intensité Ar7
ð9Þ
DH ð@ 2 X H =@z2 Þ þ RH ¼ 0
ð10Þ
4000000 3000000 2000000 1000000 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Position axiales [cm] Fig. 8. IAr750,4 emission intensity axial profiles for two power/pressure sets.
chemical kinetics model is given, the thermal dissociation of molecular hydrogen clearly dominates at high power density. Two processes are responsible for the production of H atoms: H2 + H2 ? 2H + H2, and H2 + H ? 3H. Under conditions of high Hatom density the second process dominates. At 9 W cm3 (25 hPa/600 W) (Fig. 10a), atomic hydrogen is mainly produced by electron collisional dissociation process, the gas temperature being not high enough to ensure high molecular hydrogen vibrational excitation, and the consequent thermal dissociation due to successive inelastic collisions. At 270 hPa/4000 W (Fig. 10c and d), molecular hydrogen electronic dissociation is totally inefficient versus the thermal dissociation. Due to the low mass Peclet number (PeM = 0.1), in these systems, diffusion towards locations of lower H-atom density ensures an efficient transport of H-atom through the surface boundary layer (dH thickness), where they recombine. Once the H atoms are produced, the H atom spatial evolution is given by the continuity equation. In one dimension, it is written as it follows:
uð@X H =@zÞ þ dX H =dt ¼ DH ð@ 2 X H =@z2 Þ þ RH
ð8Þ
where u is the gas velocity, XH the H-atom mole fraction, and RH the H-atom loss rate due to reaction in volume. The associated boundary condition is:
To solve this problem, we need evaluating the respective contributions of volume reactions and diffusion process to the H-atom loss rate. Although the considered pressures are somewhat high, whatever it is, there is no contribution of the volume reactions. Even at 270 hPa, the volume recombination is un-significant (Fig. 10c and d). This means that once atomic hydrogen is produced, it is free to travel into the gas phase until the reactor walls or the diamond substrate. At low power density, the H-atom density is low and the reactor metallic walls recombination reaction is seen to contribute to the consumption of H atoms (reaction R106 in Fig. 10a). At high Hatom density (high power density) this process becomes negligible (Fig. 10d). The diffusion process, driven by the high H-atom density gradient at the plasma/surface interface, is the only process responsible for extracting H atoms from the gas phase. The H atom consumption at the surface acts as a well for H-atom and diffusion constitutes its supplier. It is worth noting that in addition to the diamond surface recombination process, recombination on the reactor walls is also taken into account in the calculations (as a radial diffusion loss). This channel is however much less important than diamond recombination due to the low temperature of the walls that are water cooled.
Finally; the continuity equation becomes : DH ð@ 2 X H =@z2 Þ ¼0
ð11Þ
with the boundary condition : DH ð@X H =@zÞ ¼ RSH
ð9Þ
At the diamond surface, the H atoms recombine and/or participate to surface reactions, such as abstraction for instance. In principle, one should identify the main processes, together with their reaction rates to obtain an expression for RHS. However, using the global parameter cH, the H-atom recombination coefficient allows one simulating all the processes with a single parameter. cH has been determined by different authors [36,37,53,54] on diamond surface, and Goodwin proposed the following expression as a function of the surface temperature:
cH ¼ 4104 þ 1:95 expð3025=TÞ
ð12Þ 3
0.35
DH/H2
2
Diffusion coefficient (m /s)
0.30
DCH3/H2 0.25 0.20 0.15 0.10 0.05 0.00 0
50
100
150
200
250
300
Pressure (hPa) Fig. 9. H-atom and CH3 radical diffusion coefficients as a function of the pressure. Power is simultaneously increased from 600 W to 4000 W as pressure is increased from 25 hPa to 270 hPa.
At 1100 K, cH = 0.12. In addition cHis generally taken at 10 –104 for recombination on quartz surfaces [55], and cH has been taken at 102 for recombination on the water cooled stainless steel walls. Since diffusion is responsible for the H-atom transport to the surface, the surface H-atom mole fraction is linearly related to its maximum value into the plasma volume, this latter being a function of the maximum gas temperature reached into the plasma. Also, the location of the maximum of H-atom mole fraction is defined by the location where Tg is maximal. The higher the power density is, the stiffer the H-atom mole fraction gradient and the higher the atomic hydrogen flux towards the surface are. Since the H-atom surface balance equation will express that the H-atom flux to the surface is equal to the surface consumption of the Hatom at the surface (that is a strong function of the surface temperature), we can state that the higher the flux, the higher the surface H-atom density. Eqs. (11) and (12) allow us obtaining the H-atom mole fraction (and density) at the surface:
v ~ ns ~ Ds r njwall ¼ RSH ¼ cs s nsw for H-atoms 4
Written in 1 dimension, it comes:
ð13Þ
246
c
0.0020
1.2
0.0015
1.0
0.0010
0.8
R85: CH4 + H
CH4 + M
CH3 + H2
R90: C2H + H2 ⇔ C2H2 + H
-
-
R1: e + H2
e + 2H
R77: CH3 + H + M
-0.0005
R85: CH4 + H
CH4 + M
CH3 + H2
R93: C2H2 + H + M ⇔ C2H3 + M
-0.0010
R97: C2H4 + H ⇔ C2H3 + H2
-0.0015
Diffusion D R10-7: 2H2 ⇔ 2H + H2
R106: H
0.6 0.4
R93: C2H2 + H + M ⇔ C2H3 + M
Substrate
0.0000
-
e + 2H
R92: C2H + H + M ⇔ C2H2 + M
Production rate
0.0005
-
R1: e + H2
R77: CH3 + H + M
Substrate
Net production rate
a
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
R94: C2H3 + H ⇔ C2H2 + H2 R97: C2H4 + H ⇔ C2H3 + H2 R106: H
0.5H2 (metallic surface)
Diffusion D R10-7: 2H2 ⇔ 2H + H2 R11-8: H2 + H ⇔3H
0.2 0.0
0.5H2 (metallic surface)
-0.2
R11-8: H2 + H ⇔3H
-0.0020 0
2
4
6
8
0
10
2
4
6
8
b
d
-
R85: CH4 + H
CH4 + M
CH3 + H2
R90: C2H + H2 ⇔ C2H2 + H R92: C2H + H + M ⇔ C2H2 + M
0.4
R93: C2H2 + H + M ⇔ C2H3 + M
0.02
R94: C2H3 + H ⇔ C2H2 + H2
0.3
R97: C2H4 + H ⇔ C2H3 + H2
-
R1: e + H2
e + 2H
R77: CH3 + H + M R85: CH4 + H
CH4 + M
CH3 + H2
R90: C2H + H2 ⇔ C2H2 + H R92: C2H + H + M ⇔ C2H2 + M R93: C2H2 + H + M ⇔ C2H3 + M
-0.04
R94: C2H3 + H ⇔ C2H2 + H2
-0.06
0.1
0.5H2 (metallic surface)
Diffusion D R10-7: 2H2 ⇔ 2H + H2 R11-8: H2 + H ⇔3H
0.0 -0.1
R97: C2H4 + H ⇔ C2H3 + H2 R106: H
0.2
Substrate
-
Production rate
Substrate
R106: H
-0.02
e + 2H
R77: CH3 + H + M
0.5
0.00
-
R1: e + H2
0.04
Net production rate
10
Axial position
Axial position [cm]
0.5H2 (metallic surface)
Diffusion D R10-7: 2H2 ⇔ 2H + H2
-0.2
R11-8: H2 + H ⇔3H
-0.3
-0.08 0
2
4
6
8
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Axial position
Axial position [cm]
Fig. 10. Net production balance for H-atom at different couples (pressure and power): (a) 25 hPa/600 W; (b) 100 hPa/2000 W; (c) 270 hPa/4000 W; (d) details of (c) at the near vicinity of the surface. The percentage of methane is kept constant at 5%. The complete chemical kinetics scheme is given in references 6 and 48.
1 dH v s Ts X H js ¼ 1 þ cs X HMax Tg Max 4DH 1 dH v s Ts ¼ 1 þ cs X H1 Tg 1 4DH
ð14Þ
where XH|s and XH1 = XHMax represent the H atom mole fraction at the surface and in the plasma (maximum value), respectively. In Fig. 11a is reported the variation of surface XH as a function of the pressure for different powers obtained. A comparison between experimental and calculated surface H atom densities is presented in Fig. 11b. Again a rather good agreement is observed. A factor from 0.1 for the lower power density to 0.03 for the higher power density is observed between the surface H atom density and the maximum volume H-atom density ([H]s/[H]1 = 0.1 to 0.03). We can appreciate the effect of increasing power and pressure to increase the surface H atom density. The upper values must be compared to the maximal value of H atom density at the surface (6 1017 cm3) predicted by Goodwin et al. for a fully dissociated gas arriving at the stagnation point with an initial mean velocity characterized by a stagnation-point velocity gradient of 105 s1, at two atmospheres. We observe a difference of a factor 30 with our experimental values (1.7 1016/ 6 1017). The microwave cavity based diamond deposition plasma reactor operating at low Peclet number and at pressure up to 0.5 atmospheres is then far to be as efficient as the high speed fully dissociated plasma operating at two atmospheres. For fully disso-
ciated plasma operating at 0.5 atmospheres (the upper pressure value accessible due to the formation of filamentary discharges), we can expect around 3 1016 cm3 H atom density at the surface that represents only 5% of the upper limit predicted by Goodwin. 4. Conclusion The purpose of this paper was to estimate H-atom density in diamond deposition plasma reactors under conditions of high power density, since this parameter is probably the most important one to monitor for producing thick films at relatively high growth rate. After estimating the variation of the electron temperature, the variation of H-atom mole fraction was obtained as the pressure was varied from 14 to 400 hPa and simultaneously the power was increased in the range of 400–4000 W. H atom mole fraction up to 0.6 has been obtained, even if this value must be considered as probably an upper estimation due to the assumptions made and the experimental uncertainties. The actinometry method was seen to be a powerful technique even at high power density. From this analysis, it comes that relatively high surface H-atom densities can be obtained under conditions of very high gas temperature with a gas temperature peak located very close to the surface. An increase in power density coupled to the plasma (high pressure and/or power values) was seen to induce both an increase in the maximum value of the gas temperature and a shortening of the distance of this maximum relatively to the substrate. Growing at fast
A. Gicquel et al. / Chemical Physics 398 (2012) 239–247
H surface mole fraction (%)
a
0.010
0.008
400W 600W 800W 1000W 1150W 1250W 1500W 2000W 2500W 3000W 3500W 4000W
0.006 7% CH4
0.004
0.002
0.000 0
100
200
300
400
Pressure (hPa)
b
1
16
H [H]surf (10 ) cm
-3
10
600W 800 W 1000 W 1500 W 2000 W 3000 W 4000 W
0.1
0.01
0
50
100
150
200
250
300
350
400
Pressure (hPa) Fig. 11. (a) Surface H-atom mole fractions as a function of pressure for different power, obtained from actinometry measurements in the plasma bulk. (b) Surface H atom densities deduced from measurements and calculated with the 1D model, for different conditions of pressure and power. Open symbols correspond to calculations. The black line indicates the upper value predicted by Goodwin (see text).
growth rate under conditions of highly dissociated plasmas appears accessible with the microwave cavity based reactors operating up to 0.5 atmospheres, but these will never reach the efficiency obtained for fully dissociated plasma flowing at high speed at two atmospheres. It is worth noting however that, unlike the reactors running at very high flow, microwave cavity based reactors are much easier to monitor in particular on the cleanness point of view that is crucial for growing very high purity diamond. Acknowledgements François Silva and Ovidiu Brinza are thanked for their help in setting up the plasma reactor. This work has been granted by ANR (Agence Nationale de la Recherche) through Project ANR-06BLAN-0173. References [1] A. Gicquel, K. Hassouni, S. Farhat, Y. Breton, C.D. Scott, M. Lefebvre, M. Pealat, Diam. Relat. Mater. 3 (4) (1994) 581. [2] A. Gicquel, K. Hassouni, Y. Breton, M. Chenevier, J.C. Cubertafon, Diam. Relat. Mater. 5 (3–5) (1996) 366. [3] A. Gicquel, M. Chenevier, Y. Breton, M. Petiau, J.P. Booth, K. Hassouni, J. Phys. III 6 (1996) 1167. [4] A. Gicquel, M. Chenevier, K. Hassouni, A. Tserepi, M. Dubus, J. Appl. Phys. 83 (12) (1998) 7504. [5] A. Gicquel, K. Hassouni, G. Lombardi, X. Duten, A. Rousseau, Mater. Res. 6 (2003) 25. [6] K. Hassouni, F. Silva, A. Gicquel, J. Phys. D Appl. Phys. 43 (15) (2010) 153001. [7] G. Lombardi, K. Hassouni, G.D. Stancu, L. Mechold, J. Röpcke, A. Gicquel, J. Appl. Phys. 98 (5) (2005) 053303.
247
[8] G. Lombardi, K. Hassouni, G.D. Stancu, L. Mechold, J. Röpcke, A. Gicquel, Plasma Sources Sci. Technol. 14 (3) (2005) 440. [9] K. Hassouni, O. Leroy, S. Farhat, A. Gicquel, Plasma. Chem. Plasma Process. 18 (3) (1998) 325. [10] K. Hassouni, T.A. Grotjohn, A. Gicquel, J. Appl. Phys. 86 (1) (1999) 134. [11] K. Hassouni, G. Lombardi, X. Duten, G. Haagelar, F. Silva, A. Gicquel, T.A. Grotjohn, M. Capitelli, J. Röpcke, Plasma Sources Sci. Technol. 15 (1) (2006) 117. [12] G. Lombardi, G.D. Stancu, F. Hempel, A. Gicquel, J. Röpcke, Plasma Sources Sci. Technol. 13 (1) (2004) 27. [13] J. Ma, M.N.R. Ashfold, Yu.A. Mankelevich, J. Appl. Phys. 105 (4) (2009) 043302. [14] Yu.A. Mankelevich, M.N.R. Ashfold, J. Ma, Appl. Phys. 104 (11) (2008) 113304. [15] Yu.A. Mankelevich, P.W. May, Single crystal diamond in MW PECVD reactors, Diam. Relat. Mater. 17 (7–10) (2008) 1021. [16] P.W. May, Yu A. Mankelevich, J. Phys. Chem. C 112 (32) (2008) 12432. [17] J.E. Butler, Yu A. Mankelevich, A. Cheesman, J. Ma, M.N.R. Ashfold, J. Phys. Condens. Mat. 21 (36) (2009) 364201. [18] J. Ma, J.C. Richley, D.R.W. Davies, M.N.R. Ashfold, Yu.A. Mankelevich, J. Phys. Chem. A 114 (37) (2010) 10076. [19] J. Ma, A. Cheesman, M.N.R. Ashfold, K.G. Hay, S. Wright, N. Langford, G. Duxbury, Yu.A. Mankelevich, J. Appl. Phys. 106 (3) (2009) 033305. [20] J.R. Ma, C. James, Michael N.R. Ashfold, Yuri A. Mankelevich, Probing the plasma chemistry in a microwave reactor used for diamond chemical vapor deposition by cavity ring down spectroscopy, J. Appl. Phys. 104 (10) (2008) 103–305. [21] T.A. Grotjohn, R. Liske, K. Hassouni, J. Asmussen, Scaling behavior of microwave reactors and discharge size for diamond deposition, Diam. Relat. Mater. 14 (3–7) (2005) 288–291. [22] T.A. Grotjohn, J. Asmussen, S. Sivagnaname, D. Story, A.L. Vikharev, A. Gorbachev, A. Kolysko, Diam. Relat. Mater. 9 (3–6) (2000) 322. [23] K.W. Hemawan, T.A. Grotjohn, D.K. Reinhard, J. Asmussen, Diam. Relat. Mater. 19 (12) (2010) 1446. [24] S.O. Hay, W.C. Roman, M.B. Colket, J. Mater. Res. 5 (11) (1990) 2387. [25] F.G. Celii, P.E. Pehrsson, H.T. Wang, J.E. Butler, Appl. Phys. Lett. 52 (24) (1988) 2043. [26] J.E. Butler, F.G. Celii, D.B. Oakes, L.M. Hanssen, W.A. Carrington, K.A. Snail, High Temp. Sci. 27 (1989) 183. [27] J. Hirmke, A. Glaser, F. Hempel, G.D. Stancu, J. Röpcke, S.M. Rosiwal, R.F. Singer, Vacuum 81 (5) (2007) 619. [28] A. Cheesman, J.A. Smith, M.N.R. Ashfold, N. Langford, S. Wright, G. Duxbury, J. Phys. Chem. A 110 (8) (2006) 2821. [29] E.A. Brinkman, G.A. Raiche, M.S. Brown, J.B. Jeffries, Appl. Phys. B: Lasers Opt. 64 (6) (1997) 689. [30] G.A. Raiche, J.B. Jeffries, Appl. Opt. 32 (24) (1993) 4629. [31] C. Kaminski, P. Ewart, Appl. Phys. B: Lasers Opt. 61 (6) (1995) 585. [32] T. Lang, J. Stiegler, Y. Von Kaenel, E. Blank, Diam. Relat. Mater. 5 (10) (1996) 1171. [33] D.G. Goodwin, J.E. Butler, Theory of diamond chemical vapor deposition, in: G.P.M.A. Prelas, L.K. Bigelow (Eds.), Handbook of Industrial Diamonds and Diamond Films, Marcel Dekker, Inc., NY, 1997, pp. 527–581. [34] Gicquel et al., work under progress. [35] A. Tallaire, J. Achard, F. Silva, A. Gicquel, Physica Status Solidi (a) 202 (11) (2005) 2059–2065. [36] D.G. Goodwin, J. Appl. Phys. 74 (11) (1993) 6888. [37] D.G. Goodwin, J. Appl. Phys. 74 (11) (1993) 6895. [38] J.W. Coburn, M. Chen, J. Appl. Phys. 51 (6) (1980) 3134. [39] K. Hassouni et al., Plasma Sources Sci. Technol. 8 (3) (1999) 494. [40] R.K. Janev, Elementary Process in Hydrogen Plasma, Springer, Berlin, 1987. p. 25. [41] B.L. Preppernau, K. Pearce, A. Tserepi, E. Wurzberg, T.A. Miller, Chem. Phys. 196 (1–2) (1995) 371. [42] J. Bittner, K. Kohse-Höinghaus, U. Meier, Th Just, Chem. Phys. Lett. 143 (6) (1988) 571. [43] J.W.L. Lewis, W.D. Williams, J. Quant. Spectrosc. Radiat. Transfer 16 (1976) 939. [44] A. Catherinot, B. Dubreuil, M. Gand, Phys. Rev. A 18 (3) (1978) 1097. [45] S. Lauer, H. Liebel, F. Vollweiler, O. Wilhelmi, R. Kneip, E. Flemming, H. Schmoranzer, M. Glass-Maujean, J. Phys. B: At. Mol. Opt. Phys. (1998) 3049– 3056. [46] S.J. Harris, Appl. Phys. Lett. 56 (23) (1990) 2298. [47] S.J. Harris, D.G. Goodwin, J. Phys. Chem. 97 (1) (1993) 23. [48] M. Frenklach, H. Wang, Phys. Rev. B 43 (2) (1991) 1520. [49] J.E. Butler, R.L. Woodin, Thin-film diamond growth mechanisms, Philos. Trans. Roy. Soc. London Ser. A – Math. Phys. Eng. Sci. 342 (1664) (1993) 209. [50] D.G. Goodwin, J.E. Butler, Theory of diamond chemical vapor deposition, in: G.P.M.A. Prelas, L.K. Bigelow (Eds.), Handbook of Industrial Diamonds and Diamond Films, Marcel Dekker, Inc., NY, 1997, pp. 527–581. [51] A. Gicquel, F. Silva, C. Rond, N. Derkaoui, O. Brinza, J. Achard, G. Lombardi, A. Tallaire, A. Michau, K. Hassouni, Ultra-fast deposition of diamond by plasma enhanced CVD, in: Comprehensive Hard Materials, Elsevier, 2012, in press. [52] A. Gicquel, K. Hassouni, F. Silva, J. Achard, Curr. Appl. Phys. 1 (6) (2001) 479. [53] L.N. Krasnoperov, I.J. Kalinovski, H.N. Chu, D. Gutman, J. Phys. Chem. 97 (45) (1993) 11787. [54] A. Rousseau, G. Cartry, X. Duten, J. Appl. Phys. 89 (4) (2001) 2074. [55] Y.C. Kim, M. Boudart, Langmuir 7 (12) (1991) 2999. [56] M.H. Gordon, X. Duten, K. Hassouni, A. Gicquel, J. Appl. Phys. 89 (3) (2001) 494.