M Mao

A Bogaerts

Investigating the plasma chemistry for the synthesis of carbon nanotubes/nanofibers in an inductively coupled plasma enhanced CVD system: the effect of processing parameters

Investigating the plasma chemistry for the synthesis of carbon nanotubes/nanofibres in an inductively coupled plasma-enhanced CVD system: the effect of processing parameters M Mao, A Bogaerts

To cite this version:

M Mao, A Bogaerts. Investigating the plasma chemistry for the synthesis of carbon nanotubes/nanofibres in an inductively coupled plasma-enhanced CVD system: the effect of processing parameters. Journal of Physics D: Applied Physics, 2010, 43 (31), pp.315203. 10.1088/0022-3727/43/31/315203. hal-00569665

Introduction

In the past decades, carbon nanotubes and nanofibers (CNTs/CNFs) became the subject of many investigations, encouraged by their unique electronic and mechanical properties [1]. A large number of potential applications has been considered including nanoelectronics [2], hydrogen storage [3], and field emission devices [4]. Most of these applications are, however, still under development and no significant commercial product using CNTs/CNFs can be found on the market at present [5].

CNTs/CNFs can be synthesized by several methods, such as arc discharges, laser ablation, thermal chemical vapour deposition, and plasma enhanced chemical vapour deposition (PECVD). Compared to other growth techniques, PECVD has become a very promising method because vertically aligned CNTs/CNFs can be grown at relatively low temperature. Moreover the radius and length of the CNTs/CNFs can be controlled over a wide range [6].

A variety of plasma sources have been reported in the literature for CNT/CNF growth [7][8][9][10][11][12][13][14][15][16][17][18][START_REF] Wei | Study of Growth of Vertically-Aligned Carbon Nanofibers by Plasma Enhanced Chemical Vapor Deposition-Growth Mechanism and Field Emission[END_REF][START_REF] Lin | [END_REF][21][START_REF] Yang | Low temperature growth of single-walled carbon nanotubes by PECVD[END_REF][START_REF] Denysenko | [END_REF][24], such as direct current (dc) glow discharges [7][8][9][10], microwave discharges (MW) [11,12], radio-frequency capacitively coupled plasmas (RF-CCP) [13][14][15]and RF inductively coupled plasmas (RF-ICP) [16][17][18][START_REF] Wei | Study of Growth of Vertically-Aligned Carbon Nanofibers by Plasma Enhanced Chemical Vapor Deposition-Growth Mechanism and Field Emission[END_REF][START_REF] Lin | [END_REF][21][START_REF] Yang | Low temperature growth of single-walled carbon nanotubes by PECVD[END_REF][START_REF] Denysenko | [END_REF][24]. A wide range of operating conditions was reported for the CNT/CNF growth by PECVD. However, for a specific PECVD system, CNTs/CNFs can only be synthesized in some particular conditions. In order to investigate and optimize the suitable growth conditions, some parametric studies have been performed in the past decades.

A series of systematic studies was performed by Milne and coworkers [7][8][9] on the CNT growth process conditions by dc-PECVD, using a C 2 H 2 /NH 3 gas mixture. The growth properties (such as growth rate, diameter, length and density of the CNTs) were studied as a function of the Ni catalyst layer thickness (0.5~9 nm), bias voltage (0~-600V), deposition temperature (550~900°C), C 2 H 2 :NH 3 ratio (where the molar fraction of C 2 H 2 varied from 20% to 75%) and pressure (0.2~10Torr) [7]. They found that the diameter and length of the CNTs exhibited a linear dependence on the Ni initial thickness, while the density of the CNTs showed a maximum at 2 nm thickness of Ni. The electric field above the substrate Confidential: not for distribution. Submitted to IOP Publishing for peer review 25 June 2010 determined the alignment of the CNTs. It was found that CNTs were perfectly aligned with uniform diameter and length at electric field 0.15V/µm (-600V). They also found that the length of the CNTs increased linearly with growth time and pressure, but showed a maximum at 30% C 2 H 2 in the C 2 H 2 :NH 3 gas mixture. The study of deposition temperature showed that the growth rate initially increased with the substrate temperature and then decreased at temperatures above 700°C [7]. The plasma composition under the same conditions was also analyzed by mass spectrometry [8]. H 2 , N 2 and HCN were detected as the major neutral species beside NH 3 and C 2 H 2 , and the dominant ions were NH 3 + , C 2 H 2 + , NH 2 + , NH 4 + , HCN + and C 2 H + . A variation of the fraction of C 2 H 2 in the C 2 H 2 :NH 3 plasma was performed in order to find out the reason why optimal growth occurred at around 20% C 2 H 2 . Their results show that H 2 was derived from NH 3 at low C 2 H 2 fraction and from C 2 H 2 at high C 2 H 2 fraction, which resulted in a minimum in H 2 generation at around 23% C 2 H 2 . The role of NH 3 was found to suppress C 2 H 2 decomposition and encourage CNT formation. C 2 H 2 was found the dominant precursor for CNT formation. Finally, four key factors determining the properties of CNTs by dc-PECVD were also investigated by this group, including the presence of plasma during deposition, the ratio of feedstock gas to etchant gas, the plasma power and the strength of the electric field [9]. They found that the presence of plasma during the deposition process enabled deposition to take place at lower temperatures, facilitating the use of substrates which would otherwise be damaged. The ratio of carbon feedstock gas to etchant gas was important for controlling the shape of the deposited CNTs. It was also shown that a higher plasma power resulted in a lower growth rate, whereas a higher electric field caused a higher amount of ionization in the plasma, which resulted in a higher growth rate. Hash developed a one-dimensional model to investigate the plasma chemistry for the growth of CNTs/CNFs by dc-PECVD [10]. The effect of dc power was studied in the paper. Their results showed that the plasma played a significant role in determining the gas-phase species impinging on the catalyst. It was demonstrated that the feedstock gases (C 2 H 2 /NH 3 in the case under study) were efficiently dissociated at higher plasma power, which resulted in a decrease of the growth precursor (C 2 H 2 ) and hence in a decreased growth rate.

The synthesis of CNTs/CNFs by MW-PECVD has been reported by several groups [11,12]. Matthew et al. [11] carried out a parametric study of the synthesis conditions for high-quality single-walled carbon nanotubes (SWCNTs) in a MW-PECVD system. A H 2 /CH 4 mixture and an MgO-supported bimetallic Mo/Co catalyst were used in this study. Reaction parameters including temperature (580~823°C), H 2 :CH 4 ratio (50:2, 50:5, 50:10 and 30:10), plasma power (130~500W), and synthesis time (1~180 min) were examined to assess their influence on the SWCNT growth. Significant differences between the temperature of the catalytic surface and the heated susceptor were observed. The optimum temperature was found as 770°C at the catalytic surface. The volumetric flow rate of hydrogen to methane was found to be optimal at a ratio of 50:10. An enhancement of the SWCNT density was observed with higher plasma power. The authors concluded that the synthesis of SWCNTs could be better controlled by these synthesis parameters in the MW-PECVD system. Wang and co-workers [12] reported a study on growing few-walled CNTs in a MW-PECVD system, where a gas mixture of C 2 H 2 /NH 3 and catalyst of polystyrene-block-polyferrocenylethylmethylsilane were used. The effects of growth temperature (600~885°C), growth pressure (20~30 Torr), and precursor gas ratio (15~75/150) on the growth of CNTs were investigated. The study showed that the diameter of the CNTs increased when temperature decreased. Moreover, a higher growth pressure resulted in better CNT growth. Finally, it was shown that the longest CNTs with the highest density were observed for the smallest gas ratio of C 2 H 2 /NH 3 (15/150).

Okita and co-workers performed some studies on synthesizing CNTs in an RF-CCP system. A 1D-fluid model was used to reveal the plasma chemistry behind the CNT growth [13][14][15], for a CH 4 /H 2 gas mixture with total flux of 30 sccm, a growth pressure of 1~10 Torr, an input power of 100 W, and the substrate heated to 650°C. The amount of carbon deposited on the substrate was calculated both from experimental results and 1D-fluid simulations and reasonable agreement was reached [13]. It was suggested that the positive ions, as well as CH 3 and C 2 H 5 were the main species that fulfil the role of supplying carbon to the substrate. The effect of hydrogen on the CNT formation was investigated as well as the influence of the gas mixture ratio of CH 4 /H 2 [14]. An optimal gas ratio of 27/3 (CH 4 /H 2 ) was found for obtaining thin CNTs with a high number density. It was confirmed that MWCNTs were not etched by a H 2 plasma. The pressure dependence on the CNT growth was analyzed using a 1D-fluid model in [15]. It was found that non-radical neutrals heavier than CH 4 were greatly generated, and their fluxes tended to increase with increasing gas pressure, while the fluxes of positive ions were decreasing. These results suggested that non-radical neutrals played an important role as CNT precursors as well as the radicals.

PECVD based on ICP systems became recently more and more attractive for the synthesis of CNTs/CNFs, because of their simple geometry, the independently controlled bias power and because they are widely used in the semiconductor industry. In order to scale up the growth conditions for CNTs/CNFs in ICP-PECVD, several parametric studies have been carried out by Meyyappan and coworkers [16][17][18] and by Tsai and coworkers [START_REF] Wei | Study of Growth of Vertically-Aligned Carbon Nanofibers by Plasma Enhanced Chemical Vapor Deposition-Growth Mechanism and Field Emission[END_REF][START_REF] Lin | [END_REF][21][START_REF] Yang | Low temperature growth of single-walled carbon nanotubes by PECVD[END_REF] for different types of ICP reactors. A detailed parametric study varying inductive power (0~200W), pressure (0.5~20 Torr), temperature (700~800°C), gas composition (1~20% of CH 4 ), catalyst thickness (1~40nm), and power to substrate (0~120W) was undertaken in [16][17][18] for a planar-type ICP-PECVD system, with the RF-coil situated on top of the reactor. A CH 4 /H 2 gas mixture and Al/Fe catalysts were used to grow CNTs. Emission spectroscopy and a global model were applied to characterize the plasma under study. The results showed that both MWCNTs and MWCNFs were synthesized, and the power applied on the substrate seemed to play the key role in the transition from MWCNTs to MWCNFs. Indeed, MWCNTs were grown in the lower capacitive power region (0~20W), while MWCNFs were predominantly grown in the higher capacitive region (more than 50W). The study on dilution of argon indicated that the reduction of H atoms in the plasma caused the transition from MWCNF growth to MWCNT growth. The 0-D model was shown to generate global scaling laws of plasma properties with process variables, which are the main characterics of the bulk plasma. However, CNTs/CNFs are grown in the plasma sheath on the substrate surface, where the plasma properties are different from the plasma bulk; therefore a more detailed two-dimensional model will be of interest in order to describe the plasma in a more accurate way. Wei et al. [START_REF] Wei | Study of Growth of Vertically-Aligned Carbon Nanofibers by Plasma Enhanced Chemical Vapor Deposition-Growth Mechanism and Field Emission[END_REF][START_REF] Lin | [END_REF][21] reported a parametric study on the growth of vertically aligned CNFs by a solenoidtype ICP-PECVD system. A mixture of C 2 H 2 and H 2 was used, where C 2 H 2 provided the carbon source for the CNF growth, and H 2 was applied to keep the Ni catalyst active. The influence of process parameters such as ICP source power (200~1800W), growth time (3~20 min), dc bias (-100~-600V), pressure (7.9~54 mTorr), substrate temperature (400~650°C) and gas mixture ratios (H 2 :C 2 H 2 varying from 1:2 to 4:2), on the CNF formation was analyzed. The plasma composition was detected by mass spectrometry. It was shown that the CNF density decreased with ICP power, dc bias, and growth time. It was proposed that the ion-assisted etching effect by atomic hydrogen resulted in the detachment of CNFs even with low electric field in the plasma sheath. Yang [START_REF] Yang | Low temperature growth of single-walled carbon nanotubes by PECVD[END_REF] studied the influence of process parameters on the synthesis of SWCNTs in an ICP-PECVD system. The gas mixture of CH 4 /H 2 with two different catalysts (Fe and Ni) was tested. The operating pressure was fixed as 1Torr. He found that CNTs can grow both with Fe and Ni catalyst for the conditions under study. The substrate heating temperature affected the carbon supply to the catalyst and the diffusion of carbon on the surface and in the bulk of the catalyst. A lower substrate heating temperature was found to suppress the excess of carbon supply. It was also observed that CH 4 decomposed more easily under higher ICP power to generate unsaturated hydrocarbon radicals; the latter can more easily resolve carbon for CNT growth. Therefore the author suggested that SWCNTs would be synthesized with lower ICP power. From the literature review above, it appears that CNTs/CNFs could be synthesized under either moderate pressure (1~10 Torr) or low pressure (10s of mTorr) in a PECVD system. Both methane (CH 4 ) and acetylene (C 2 H 2 ) are popular feedstock gases for the carbon source, whereas a dilution by H 2 and NH 3 is often used to obtain hydrogen-rich plasmas, in order to produce 'clean' CNTs/CNFs. Most of the above works focus on how to grow CNTs/CNFs in low-temperature PECVD, whereas the role of the plasma and the key precursors for CNT growth still remain a bit unclear. In order to obtain a good insight in the plasmas used for CNT/CNF growth, some modelling efforts have been attempted in the past decades, for DC discharges [10], CCP discharges [15] (see also above) and for ICP systems [START_REF] Denysenko | [END_REF][24]. Denysenko et al. [START_REF] Denysenko | [END_REF] performed detailed numerical simulations with a global model for depositing vertically aligned carbon nanostructures in an ICP-PECVD system. A gas mixture of Ar/CH 4 /H 2 was used in their study. The densities and fluxes of radicals and charged species as well as the effective electron temperature, and methane conversion factor were calculated under various conditions. Their results showed that the deposited cation fluxes generally exceed those of the radical neutrals. The conversion rates of methane and hydrogen were found very high (~99%) in their study. Furthermore, Ostrikov et al. [24] reported a two-dimensional simulation of nanoassembly precursor species in an inductive Ar/H 2 /C 2 H 2 plasma. The number density and fluxes of the main building blocks and surface preparation species involved in the nanoassembly of carbon-based nanopatterns were calculated in their study. They showed that the nanopattern quality might be affected by the process parameters and the non-uniformity of the surface fluxes of each particular species. Moreover, the growth kinetics of carbon nanotubes/nanofibers in hydrocarbon plasma have been studied by Ostrikov and coworkers [25][26][27][28]. The ion-induced dissociation of hydrocarbons, the interaction of adsorbed species with incoming hydrogen atoms, and the dissociation of hydrocarbon ions were included in the model [25][26][27]. They found that surface diffusion of carbon adatoms produced on the catalyst particle via ion-induced dissociation of a hydrocarbon precursor plays an important role in CNF growth at low process temperatures. The catalyst size effects on the growth of SWCNT were also analyzed in [28]. The results indicated that wide-sheath plasma systems feature growth rates up to two orders of magnitude higher than in neutral systems. Some other models for the catalytic growth of carbon nanotubes were developed by Lysaght and Chiu(for CVD) [29][30] and by Naha and Puri [31]. The latter model is more detailed and generally applicable. It consists of several mechanisms including (a) impingement of carbon atoms from the predominant carbon-containing species in the ambient, (b) their adsorption and desorption at the catalystgaseous hydrocarbon interface, (c) surface and bulk diffusions, (d) nucleation and (e) separation of solid undissolved carbon in nanostructured form. Their results showed that an increase in either the temperature or feedstock partial pressure leads to an increasing CNT growth rate and terminal length. However, the plasma condition for CNT/CNF growth was not included in their model. We have applied the 2D Hybrid Plasma Equipment Model (HPEM) [32][33][34][35][36][37][38] to investigate the plasma chemistry for a CNT-PECVD system. An ICP reactor, more specifically, a transformer coupled plasma (TCP) reactor [16,39] is considered. In a previous paper [40], the effects of different gas mixtures on the plasma chemistry for CNT/CNF growth have been studied. Four kinds of feedstock gas mixtures (i. e., CH 4 /H 2 , CH 4 /NH 3 , C 2 H 2 /H 2 , and C 2 H 2 /NH 3 ) were considered for two different pressures: 50 mTorr and 1 Torr, corresponding to the low and moderate pressure range investigated in the experiments. In the present work, a detailed parametric study is carried out to investigate the effect of gas mixture ratios, ICP power, operating pressure, bias power and substrate heating temperature. Our aim is to find out the influence of these processing parameters on the plasma characteristics, especially near the surface of the substrate, used for the synthesis of CNTs/CNFs.

Description of the model

The Hybrid Plasma Equipment Model (HPEM), which has been developed at the University of Illinois by Kushner and coworkers [32][33][34][35][36][37][38] is used in our study. It addresses the plasma physics and chemistry in a modular way. The main modules are the Electromagnetic Module (EMM), Electron Energy Transport Module (EETM), and Fluid Kinetics Module (FKM). The EMM calculates the electromagnetic fields within a given reactor volume by solving Maxwell equations. These fields are used as inputs in the EETM, where the electron density, electron temperature, electron energy distribution function and electron impact reaction rates are computed with a Monte Carlo procedure or with the Boltzmann equation. The electron impact reaction rates are used as input in the FKM where the densities and fluxes of the various plasma species (i.e. heavy particles and electrons) are computed with continuity equations, and the electrostatic field with Poisson's equation. This electrostatic field is used as input again in the EMM, and this cycle is iterated until convergence is reached. Four different gas mixtures, i.e., CH 4 /H 2 , CH 4 /NH 3 , C 2 H 2 /H 2 , and C 2 H 2 /NH 3 are investigated. In the CH 4 /H 2 plasma, 33 species (electrons, ions, radicals and background neutrals) along with 58 electron impact reactions, 115 ion-neutral reactions, and 45 neutral-neutral reactions are taken into account in our model. For the C 2 H 2 /H 2 plasma, 48 different species are considered, which take part in 105 reactions involving 31 electron-impact reactions, 29 neutral-neutral reactions and 45 ion-neutral reactions. When NH 3 is used as dilution gas instead of H 2 , an extra number of 22 species, 43 electron-impact reactions, 48 ion-neutral reactions and 67 neutral-neutral reactions were added to the model. All details about this plasma chemistry can be found in our previous paper [40].

Finally, a sticking model, where the deposition of species at the wall is described, is applied to treat the plasma-wall interactions. The sticking coefficients assumed for the different radicals can also be found in [40]. For the ions a sticking coefficient of 1 is assumed, because they will be neutralized. For the molecules, a sticking coefficient of 0 is used, as they are considered to be reflected at the walls.

It should be realized that this model does not yet provide a full description of the CNT growth, because it is limited to the plasma chemistry and does not include the actual growth processes of the CNT. Carbon drains to the CNT surface and generation of hydrogen and other fragments and their backflow are not considered. Only sticking coefficients of the various plasma species at the surface are taken into account. This might influence the plasma chemistry calculations to some extent. On the other hand, the plasma volume is much larger than the substrate surface, so that the effect on the overall plasma chemical composition is probably not so big. In a future work, we would like to include the effect of the surface processes to our plasma chemistry model, to obtain a more complete description of the PE-CVD growth process of CNTs."

Results and discussion

Operating conditions

The standard calculations were performed for a gas mixture of CH 4 /H 2 at a pressure of 50 mTorr, in a gas ratio of 20% CH 4 and 80% H 2 . Other operating conditions are: 100 sccm total gas flow rate, 300 W source power, 30W bias power at the substrate electrode and an operating frequency of 13.56 MHz applied to the coil and to the substrate electrode. The substrate is heated to 550 °C. These are typical operating conditions for CNT growth under low pressures, as was illustrated in the introduction. The parameter study focused on the effect of gas mixture ratios, ICP power, operating pressure, bias power and substrate heating temperature, on the plasma chemistry used for CNT/CNF growth. It should be noted that when one parameter is changed, the others are kept as the standard condition. The reactor geometry under study is a TCP reactor, which is often used for CNT growth [11,16,39]. It is schematically illustrated in Figure 1.

Effect of gas mixture ratios

For this study, four different gas mixtures, i.e. CH 4 /H 2 , CH 4 /NH 3 , C 2 H 2 /H 2 and C 2 H 2 /NH 3 , are taken into account, where CH 4 and C 2 H 2 are the deposition gases and H 2 and NH 3 are the etchant gases. The fraction of deposition gas (CH 4 or C 2 H 2 ) in the gas mixture is varied from 0 to 100. As it was discussed in the literature [5,17], the carbon sources for CNT/CNF growth are determined by the species impinging on the substrate and the decomposition activity on the catalyst surface. Therefore the fluxes of different species arriving at the substrate surface were calculated at the different ratios of gas mixtures under study.

a. Methane-hydrogen plasma (CH 4 /H 2 )

The calculated fluxes of the various neutrals and ions bombarding the substrate in the CH 4 /H 2 mixture, averaged over the radial position on the substrate, are plotted as a function of CH 4 gas fraction in figure 2. It is clear from figure 2(a) that C 2 H 2 , C 2 H 4 and C 2 H 6 are the dominant molecules regardless of the gas mixture ratios, besides the feedstock gases CH 4 and H 2 . The fluxes of these molecules first increase quickly before the fraction of CH 4 reaches 20%, and then, more slightly when the fraction of CH 4 is further enhanced. The primary radicals are H and CH 3 at all mixture ratios. The H flux decreases gradually as the H 2 gas fraction decreases, while the CH 3 flux shows the same trend as the background gas CH 4 . It is also clear that the fluxes of C and C 2 are the lowest of all radicals. These observations confirm that the carbon source for CNT/CNF growth mainly arises from the decomposition of hydrocarbon molecules on the surface of the catalyst [41]. Of course, this conclusion is only made based on the fluxes of the plasma species to the substrate, and does not take into account the surface processes, i.e., the reaction rate coefficients at the surface. Indeed, it could be that the small flux of C 2 is compensated by higher reaction rates at the surface. As mentioned above, we plan to include these processes in our future work. It is observed from figure 2 Figure 2 Calculated radially-averaged fluxes of (a) neutrals and (b) ions bombarding the substrate as a function of CH4 fraction in a CH4/ H2 gas mixture at a pressure of 50 mTorr. The operating conditions are: 100 sccm total gas flow rate, 300W source power, 30W bias power at the substrate and 13.56 MHz operating frequency at the coil and at the substrate electrode. The substrate is heated to 550 °C.

It was reported that the unsaturated hydrocarbons such as C 2 H 2 and C 2 H 4 , have a higher reactivity than CH 4 on the transition metal clusters [41]. Moreover C 2 H 2 and C 2 H 4 decompose more easily at the catalyst surface than CH 4 at lower temperature [41]. Furthermore, C 2 H 2 [42]and C 2 H 4 [43] have been reported as key precursors for the efficient growth of SWCNTs by CVD. Bell et al. [8] also confirmed that C 2 H 2 was the dominant precursor for CNT formation in a C 2 H 2 /NH 3 plasma. Therefore it is well possible that C 2 H 2 and C 2 H 4 are the major precursors for CNT/CNF growth in the CH 4 /H 2 plasma. The large amount of atomic hydrogen, on the other hand, plays a key role in the dehydrogenation of the adsorbed hydrocarbons, enhancing the surface diffusion of carbon, and etching amorphous carbon [41]. Finally, the CH 3 radicals are probably responsible for the amorphous carbon fraction in the CNTs [13]. concentrations. In the left region to the dashed line, the fluxes of atomic hydrogen by far exceed the fluxes of the carbon source both for CNTs/CNFs as well as for an amorphous film. We expect that this will lead to "clean" conditions for CNT/CNF growth, as the amorphous phase, which might be present in the growing tube, will be etched away by the H-flux and moreover, the carbon supply for CNT/CNF growth is also well controlled. In [11] it was also concluded, albeit for a MW-PECVD system, that an optimal ratio of H 2 /CH 4 was obtained at 50:10, hence corresponding to less than 20% CH 4 in the gas mixture.

0
b. Methane-ammonia plasma (CH 4 /NH 3 ) When NH 3 is applied as the dilution gas instead of H 2 , some new species appear in the plasma as was mentioned in section 2 (see [40] for all details). For the sake of clarity, we define the same species both in the CH 4 /H 2 plasma and in the CH 4 /NH 3 plasma as "original species". The new species are called "extra species". The fluxes of the original species exhibit the same trends as in the CH 4 /H 2 plasma; therefore they are not shown here again. The fluxes of the new species are displayed in figure 4 for the neutrals (a) and the ions (b). We found that H 2 is again the most dominant species, in spite of the fact that it is now not one of the feedstock gases, and it drops slightly at high fraction of CH 4 . Apart from the hydrocarbons C 2 H 2 , C 2 H 4 and C 2 H 6 , now also N 2 and HCN become predominant molecules beside the feedstock gases CH 4 and NH 3 . With respect to the radicals, atomic hydrogen (H) is again the most important species followed by CH 3 , N, N 2 H, and NH 2 . It is interesting that H and H 2 follow the same trend as NH 3 , i.e., they drop when the gas fraction of CH 4 increases. This indicates that H and H 2 are mainly generated by decomposition of NH 3 at the conditions under study. Also a lot of HCN is observed in our results, which first increases and then drops as a function of CH 4 fraction. We also found that HCN is mainly formed in the bulk plasma region, which is consistent with Hash's results [44]. It is shown in figure 4(b), that the total ion flux again remains almost constant as a function of CH 4 fraction. However, NH 4 + now become the predominant ion when NH 3 is used as the additive. It is apparent that NH 4 + , NH 3 + , and NH 2 + do not drop significantly, and even rise (in the case of NH 3 + ) upon increase of CH 4 , or decrease of the NH 3 fraction. This indicates that NH 3 is more efficiently ionized at lower NH 3 fraction. The decomposition rates (DR) of the feedstock gas molecules as a function of CH 4 gas fraction in both CH 4 /H 2 and CH 4 /NH 3 are depicted in figure 5. Note that a DR of 1 indicates 100% decomposition. (c,d) ions bombarding the substrate as a function of C2H2 gas fraction for a C2H2/ H2 gas mixture. The other operating conditions are the same as in figure 2.

It is stated that hydrocarbon ions play a key role in the formation of amorphous carbon films [45]. At conditions with low C 2 H 2 fraction, most hydrocarbon ions show a relatively low flux as is clear from figure 6 (c,d), which would efficiently suppress the amorphous carbon growth. This could explain why "clean" CNTs/CNFs are typically grown under H 2 -rich conditions [8,[START_REF] Lin | [END_REF]. Indeed, it was observed that the CNF growth rate decreased while the amorphous carbon film deposition increased with rising C 2 H 2 fraction, both in a C 2 H 2 /H 2 mixture [START_REF] Lin | [END_REF] and in a C 2 H 2 /NH 3 mixture [8]. d. Acetylene-ammonia plasma (C 2 H 2 /NH 3 ) When NH 3 is used as the dilution gas (see figure 7), N 2 , N 2 H 2 and NH 4 + are found to be dominant neutrals and ions, respectively, similar to the CH 4 /NH 3 plasma. Similar observations were made in [8]. The species N 2 H and NH 2 become very important (see figure 7 (a)). However, unlike in the CH 4 /NH 3 plasma, the flux of HCN is not significant at all. This is because HCN is generated from the reaction between CH x (x= 2, 3, 4) and N atoms, and the lower density of CH x (x= 2, 3, 4) in the C 2 H 2 plasma leads to a lower formation of HCN. It was reported [46] that the presence of N 2 can enhance carbon diffusion into the catalysts. Indeed, the bombardment energy of ions in a nitrogen plasma is greater than in a hydrogen plasma, which can keep the front catalyst surface clean and actively prolong surface passivation to enhance carbon bulk diffusion [46]. Our results show that the N 2 flux is predominant beside the NH 3 flux, especially for a low C 2 H 2 fraction(less than 20%). Hence, this might explain why in many papers [7][8][9]12] the C 2 H 2 /NH 3 mixture is used for CNT/CNF growth rather than the C 2 H 2 /H 2 plasma. The DRs of the background gas molecules in the C 2 H 2 -containing plasmas are displayed in figure 8 It is also observed that H 2 shows a very low DR at high fraction of H 2 in the mixture (see figure 8(a)). Furthermore, negative values of the DR are observed at C 2 H 2 -rich conditions. Different from the H 2 gas additive, the DR of NH 3 shows a similar trend as the C 2 H 2 DR. Indeed, the DR of NH 3 decreases with increasing C 2 H 2 gas fraction, which leads to a decline of the atomic hydrogen at high fraction of C 2 H 2 . Moreover, the excess of heavy hydrocarbon ions is also found in this region. Therefore, we expect that an amorphous carbon film will be formed, which cannot easily be etched away because of the low amount of etching H atoms, and this will suppress the growth of CNTs/CNFs. Indeed, most experiments in the literature were performed at C 2 H 2 fraction below 20% [7,12]. The influence of the C 2 H 2 :NH 3 ratio on the structure of CNTs synthesized by dc-PECVD has been reported by Chhowalla et al. [7]. They found that CNTs could be formed for C 2 H 2 fraction from 5% to 30%. Above 30% C 2 H 2 , the CNTs became obelisklike and then turned to a tip structure with even higher C 2 H 2 fraction. Also in [12] for a MW-PECVD system, the longest CNTs with the highest density were obtained for the smallest C 2 H 2 /NH 3 gas ratio (15/150), corresponding to around 10% of C 2 H 2 .

In the following sections, the effects of ICP power, operating pressure, bias power and substrate heating temperature on the plasma chemistry for CNT/CNF growth will be analyzed, considering only the CH 4 /H 2 gas mixture.

Effect of ICP power

The fluxes of species on the substrate as a function of ICP power are plotted in figure 9(a) for the neutrals and in figure 9(b) for the ions. A higher ICP power will give rise to increased dissociation and ionization of the molecules, which results in a decreasing flux of the molecules (CH

Figure 9 Calculated radially-averaged fluxes of (a) neutrals and (b) ions bombarding the substrate as a function of ICP power for a CH4/ H2 gas mixture at a pressure of 50 mTorr with gas ratio of 20:80. The other operating conditions are the same as in figure 2.

It is indeed observed from figure 10 that the ratio of etchant (H) to depositing carbon sources both for CNTs (C 2 H 2 + C 2 H 4 ) and for an amorphous carbon film (CH 3 ) increases drastically when the ICP power is enhanced from 500W to 1000W. This indicates that the etching effect by atomic hydrogen is significant in the high ICP power region. Therefore, this suggests that a relatively "clean" condition for the formation of CNTs/CNFs could be achieved at higher ICP power, which is indeed reported by Lin et al. [START_REF] Lin | [END_REF]. Indeed, they found that more amorphous carbon film was deposited on the surface of the CNFs and the substrate for 250W ICP power than in the 750W case [START_REF] Lin | [END_REF]. Figure 10 Ratio of etchant (H) to the carbon source for CNTs (C2H2 + C2H4) and for an amorphous carbon film (CH3) as a function of ICP power for the CH4/H2 mixture at the same operating conditions as in figure 9.

The influence of ICP power on the DR of the background gas molecules is displayed in figure 11. Both DRs rise nearly linearly with ICP power for the reason explained above. The DR of CH 4 is around 0.2 at 50W and increases to almost 0.96 at 1000W. Again, this suggests that a higher ICP power is beneficial for CNT/CNF growth, as the CH 4 molecules do not efficiently decompose at the catalyst surface; therefore the decomposition needs to take place already in the plasma. The DR of H 2 is only 0.05 at 50W and increases to 0.22 at 1000W. Although the DR of H 2 becomes higher at 1000W, almost no change was observed for the flux of H 2 on the substrate, because the loss of H 2 caused by decomposition is compensated by new H 2 created by decomposition of CH 4 . The other operating conditions are the same as in figure 9.

Effect of gas pressure

The fluxes of the different neutral species to the substrate as a function of pressure are plotted in figure 12. It is found that the feedstock gases H 2 and CH 4 increase with pressure as expected, while the radicals C, CH, CH 2 , C 2 , C 2 H and C 2 H 3 decrease at higher pressure. The other neutrals remain virtually unchanged. As was illustrated in [40], most of the ion fluxes drop at increasing pressure; hence the total ion flux also shows a decreasing trend as a function of pressure. This is because the electrons lose their energy faster at higher pressure, which leads to a decrease of ionization, and hence results in a drop of the ion fluxes with increasing pressure.

Figure 12 Calculated radially-averaged fluxes of the various neutrals bombarding the substrate as a function of gas pressure for a CH4/ H2 gas mixture with gas ratio of 20:80. The other operating conditions are the same as in figure 2.

The ratios of etching species (H) to the carbon source for CNTs (C 2 H 2 + C 2 H 4 ) and to the carbon source for an amorphous carbon film (CH 3 ) are plotted in figure 13. It is clear that a larger ratio of H flux to CH 3 flux is found at high pressure, while the ratio of H flux to C 2 H 2 and C 2 H 4 drops dramatically first and then levels off at 100 mTorr. This indicates that CNTs/CNFs could be synthesized with less amorphous carbon pollution at higher pressure. In addition, the lower DR of CH 4 at higher pressure, as illustrated in figure 14, implies that the carbon supply for CNTs/CNFs could be limited at higher pressure. This could explain why SWCNTs are always synthesized at higher pressures (i.e., in the order of 1 Torr) by an ICP-PECVD system, as reported in [START_REF] Yang | Low temperature growth of single-walled carbon nanotubes by PECVD[END_REF], where the carbon source for growth can be well controlled.

Effect of bias power

In the ICP, the power is mainly deposited in the region below the quartz windows, and it decomposes the feedstock gases to create a large number of radicals and ions. Therefore the fluxes of the various species to the substrate are mainly determined by the ICP power, gas pressure, and gas mixture ratios. The bias power is often applied on the substrate in order to grow aligned CNTs/CNTs [7,16,44,48]. Indeed, it was found that local electric fields are built up near the substrate surface, and control the growth direction of CNTs/CNFs [7,16,44,48]. Therefore, it is of interest to look in more detail at the DC bias voltage formed in front of the substrate, as well as to the sheath electric field which arises from this DC bias voltage. The DC bias voltage and sheath electric field in front of the substrate surface are plotted as a function of bias power in figure 15. The bias voltage sharply decreases from 0 to -230V when the bias power changes from 0 to 100W. When the power is further increased to 1000W, the change in DC bias voltage is only 56V (i.e., until -286V at 1000W). These calculated results are consistent with the observations reported by Lin et al. [START_REF] Lin | [END_REF]. Indeed, they found that the RF peak voltage changed from around 300 Vrms to 450 Vrms (corresponding to a bias voltage changing from -212V to -318V) when the bias power increased from 300W to 500W. The increase of DC bias voltage as a function of bias power indicates that more energetic ions will bombard the substrate with high bias power. The bombardment of more energetic ions will probably result in a higher surface temperature and hence lead to a higher CNT/CNF growth rate. In addition, the high-energy ions will promote the ion-enhanced etching of amorphous carbon by atomic hydrogen to improve the surface diffusion of carbon on the catalytic nanoparticles. Indeed, Lin et al. [START_REF] Lin | [END_REF] reported that the growth rate of CNFs increased significantly with the bias power.

The sheath electric field in front of the substrate changes from 0.034V/µm without any bias power to 0.133 V/ µm at a bias power of 1000W in our simulation. In [21] it was reported that the sheath electric field is in the range of ~0.01-0.06 V/µm in an ICP-PECVD system at low pressure of 17~50 mTorr. Somewhat higher values of ~0.1-0.15 V/µm are reported by Chhowalla [7] and Bower and Zhu [49] for pressures in the order of Torr. These values are consistent with our results, which suggest that the conditions in our study are indeed suitable for CNT/CNF growth. Moreover, the higher electric field in the plasma sheath at higher bias power will probably result in better aligned CNTs/CNFs.

Effect of substrate temperature

It is well known that CNTs/CNFs are typically grown at some elevated temperature of the substrate containing the metal catalysts, in the order of 550°C-800°C [5,11,17]. Therefore, we want to investigate the effects of the elevated substrate temperature on the plasma chemistry and plasma behavior.

In order to calculate the gas temperature distribution, the full momentum equation plus energy equation for all heavy species (neutrals and ions) have been taken into account. The free convection term has been included in the momentum equation, and the inhomogeneous gas density distribution is also taken into account. More details can be found in the review paper of Kushner [38].

As shown in our previous paper [38], the substrate temperature plays a key role in the gas temperature distribution at lower pressures (50 mTorr). The calculated 2D profiles of the gas temperature at a substrate temperature of (a) 0 °C and (b) 550 °C are illustrated in figure 16. Note that the reactor walls are kept fixed at a temperature of 324 K (i.e., 51 °C). This value is defined based on typical values used in the semiconductor industry. It is clear that the plasma for the conditions under study is not efficiently heated without substrate heating, because the gas temperature is only about 34 K higher in the bulk plasma compared to the walls (see figure 16(a)). However, when the substrate is heated to 823 K (i.e. 550 °C), the heat transfer towards the bulk plasma is clearly displayed in figure 16(b). The gas temperature gradually changes from 823 K at the substrate to about 600 K in the bulk plasma, and reaches 324 K at the walls.

Figure 16 Calculated 2D gas temperature profiles for a CH4/ H2 gas mixture at a pressure of 50 mTorr with a gas ratio of 20:80. The other operating conditions are the same as in figure 2. The substrate is heated to (a) 0 °C and (b) 550 °C.

The distribution of gas temperature influences the plasma chemistry in two aspects: First, the reaction rate constants for neutral reactions are often temperature-dependent (see tables in [40]). When the substrate is heated to 823 K or more, a large temperature difference (several hundred K) can be found in the plasma bulk, which will lead to 1-2 orders of magnitude difference in the rate constants. Second, the gradient of gas temperature will push the species to the low-temperature region in order to keep a constant pressure (cf. ideal gas law). Although the first effect will enhance the rate constants for neutral reactions, the lower density of neutrals in the higher temperature region due to the second effect will result in only a slight change in the plasma chemistry.

Figure 17 Calculated 2D number density profiles of CH4 at the same conditions as in figure 16.

The calculated 2D number density profiles of CH 4 for the substrate temperatures of 0 °C (a) and 550 °C (b) are shown in figure 17. As expected from above, a relatively uniform distribution of the CH 4 density is observed when the substrate is not heated. On the other hand, when the substrate is heated to 823K, the CH 4 density shows a distribution opposite to the corresponding gas temperature, i.e., the CH 4 density exhibits relatively low values in the high temperature region. This indicates that the gradient of gas temperature indeed plays a key role in the species distribution when the substrate is heated, at least for low gas pressure.

Conclusions

An ICP reactor operating under conditions typically used for CNT/CNF growth was investigated by means of hybrid plasma simulations. The influence of processing parameters including gas mixture ratios for four different gas mixtures (i.e., CH 4 /H 2 , CH 4 /NH 3 , C 2 H 2 /H 2 and C 2 H 2 /NH 3 ), ICP power, gas pressure, bias power, and substrate temperature on the plasma chemistry is investigated. The fluxes of the various plasma species bombarding the substrate, as well as the decomposition rates (DR) of the feedstock gas molecules, are calculated and analyzed for a large range of process parameters. Furthermore, the ratio of etching species (H) to the carbon source both for CNT/CNF growth (C 2 H 2 + C 2 H 4 ) and for amorphous carbon film deposition (CH 3 ) is investigated in the same parameter range, because this can give more insight in the conditions for "clean" CNT growth.

In general, it was observed that the fluxes of C and C 2 to the substrate were the lowest of all radicals, which confirms that the carbon source for CNT/CNF growth mainly arises from the decomposition of hydrocarbon molecules on the surface of the catalyst [41].

With respect to the gas mixture ratios, in the CH 4 /H 2 mixture, a low CH 4 fraction (below 20%) resulted in a high ratio of etching species (H) to growth precursors for CNTs/CNFs (C 2 H 2 + C 2 H 4 ) as well as for an amorphous phase (CH 3 ). This is expected to result in "clean" conditions for CNT/CNF growth, as the amorphous phase, which might be present in the growing tube, will be etched away by the H-flux and moreover, the carbon supply for CNT/CNF growth is also well controlled. Moreover, the DR of CH 4 in the plasma was found to be the highest for a low CH 4 fraction, both in the CH 4 /H 2 and CH 4 /NH 3 gas mixture, which also points out towards favorable conditions for CNT/CNF growth, as it is generally accepted that CH 4 cannot easily decompose at the catalyst surface, in contract to higher hydrocarbons [41]. Similar results were also obtained for the C 2 H 2 -containing gas mixtures. The DR of C 2 H 2 turns out to drop significantly upon increasing C 2 H 2 fraction, suggesting a lower CNT/CNF growth rate, because C 2 H 2 is considered as the main growth precursor. Moreover, the DR of NH 3 also drops significantly with increasing C 2 H 2 fraction, thereby reducing the supply of etching H species to the growing CNTs. Finally, at higher C 2 H 2 fraction, there is an excess of heavy hydrocarbon ions, which typically give rise to an amorphous phase. Hence, these calculation results lead us to conclude that an amorphous carbon film will be formed at higher C 2 H 2 fraction, which cannot easily be etched away because of the low amount of etching H atoms, and this will suppress the growth of CNTs/CNFs. Therfore, in general it can be concluded that a lower fraction of carbon-supplying gases (CH 4 and C 2 H 2 ) compared to etching gases (H 2 and NH 3 ) will lead to more "clean" CNT/CNF growth conditions, which is in agreement with literature observations [7,8,11,16,18,47]. A higher ICP power will increase the dissociation and ionization of molecules, which results in lower fluxes of the molecules (CH 4 , C 2 H 2 , C 2 H 4 , C 2 H 6 , C 3 H 8 , and C 4 H 10 ), and an increase of the lighter radicals (H, CH, C, and C 2 ) and ions. The reduction of CH 3 and increase of H radicals at higher ICP power indicates that a relatively "clean" condition for the formation of CNTs/CNFs could be achieved with higher ICP power. With respect to the gas pressure, the low ratio of H flux to fluxes of C 2 H 2 + C 2 H 4 and the high ratio of H flux to CH 3 flux at pressures above 100 mTorr, in combination with the reduced DR of CH 4 indicates that SWCNTs could be synthesized at moderate pressure of around 1 Torr, where the carbon supply for CNTs/CNFs could be well controlled in the CH 4 /H 2 plasma. This is indeed reported in literature [START_REF] Lin | [END_REF].

The DC bias voltage and sheath electric field are calculated for different values of the bias power, and our results are consistent with experimental observations, which indicate that aligned CNTs/CNFs could be grown at the conditions under study. The increase of DC bias voltage with rising bias power indicates that more energetic ions will bombard the substrate, which might result in a higher surface temperature, and consequently in a higher CNT/CNF growth rate. In addition, the high-energy ions will promote the ion-enhanced etching of amorphous carbon film by atomic hydrogen to improve the surface diffusion of carbon on the catalytic nanoparticles. Indeed, Lin et al. [START_REF] Lin | [END_REF] reported that the growth rate of CNFs increased significantly with the bias power. Finally, we investigate the effect of the substrate temperature on the plasma behavior, as CNTs/CNFs are typically grown at elevated substrate temperature [5,11,17]. It is found that the substrate temperature influences the distribution of gas temperature, and further affects the profiles of neutral species in the plasma bulk. Indeed, the large gradient of gas temperature drives the species to the low temperature region, which leads to a lower density of species in the region above the substrate where a high gas temperature exists. At higher substrate temperature, the ratio of etching species (H) to the carbon source for an amorphous carbon film (CH 3 ) drops, leading to less favorable conditions for clean CNT growth. On the other hand, the surface reaction rates, as well as the DR of CH 4 , increase with substrate temperature, giving rise to species which can more easily react at the catalyst surface. These two opposite effects will result in an optimum temperature window for CNT/CNF growth, which is indeed reported in literature [7,11,12,16,[START_REF] Wei | Study of Growth of Vertically-Aligned Carbon Nanofibers by Plasma Enhanced Chemical Vapor Deposition-Growth Mechanism and Field Emission[END_REF] (i.e., in the range of 550~900°C). In summary, we conclude that a lower fraction of hydrocarbon gases (CH 4 or C 2 H 2 , i.e., below 20%) and hence a higher fraction of etchant gases (H 2 or NH 3 ) in the gas mixture result in more "clean" conditions for controlled CNT/CNF growth. The same applies to a higher ICP power, a moderate gas pressure above 100 mTorr (at least for SWCNTs), a high bias power (for aligned CNTs), and an intermediate substrate temperature.

Figure 1 :

 1 Figure 1: Two-dimensional TCP reactor geometry used in the model. The reactor is cylindrically symmetric, so only one half plane of the reactor is shown.

Figure 4

 4 Figure 4 Calculated radially-averaged fluxes of (a) extra neutrals and (b) extra ions bombarding the substrate as a function of CH4 fraction for a CH4/ NH3 gas mixture. The other operating conditions are the same as in figure 2.

3 Figure 5

 35 Figure 5 Decomposition rates (DR) of the background gas molecules, calculated for (a) CH4/H2 and (b) CH4/NH3 gas mixtures. The other operating conditions are the same as in figure 2. The negative values mean that more background gas species are formed instead of decomposed.

1 Figure 6

 16 Figure 6 Calculated radially-averaged fluxes of (a, b) neutrals and(c, d) ions bombarding the substrate as a function of C2H2 gas fraction for a C2H2/ H2 gas mixture. The other operating conditions are the same as in figure2.

Figure 7

 7 Figure 7 Calculated radially-averaged fluxes of (a) extra neutrals and (b) extra ions bombarding the substrate as a function of C2H2 gas fraction for a C2H2/ NH3 gas mixture. The other operating conditions are the same as in figure 2.

Figure 8

 8 Figure 8 Decomposition rates (DR) of the background gas molecules, calculated for (a) C2H2/H2 and (b) C2H2/NH3 gas mixtures. The other operating conditions are the same as in figure 2. The negative values mean that more background gas species are formed instead of decomposed.

Figure 11

 11 Figure 11 Decomposition rates (DR) of the background gas molecules, calculated for the CH4/H2 gas mixture as a function of the ICP power. The other operating conditions are the same as in figure9.

Figure 13 Figure 14

 1314 Figure13 Ratio of etchant species (H) to the carbon source for CNTs (C2H2 + C2H4) and to the carbon source for an amorphous film (CH3) as a function of gas pressure at the same operating conditions as in figure12.

Figure 15

 15 Figure 15 Variation of DC bias (left axis) and sheath electric field (right axis) on the substrate vs. bias power, for a CH4/ H2 gas mixture at a pressure of 50 mTorr with a gas ratio of 20:80. The other operating conditions are the same as in figure2.

Figure 19

 19 Figure 19 Decomposition rates (DR) of the background gas molecules as a function of substrate temperature for the same conditions as in figure 2.

  (b) that most ion fluxes show a rapid decrease as the CH 4 fraction increases ) rise with increasing CH 4 concentration. It is worth noting that the total ion flux decreases only slightly as a function of the CH 4 fraction in the gas mixture. Moreover, because the fluxes of the heavy ions, i.e. C 2 H x + (x=2~6), rise upon increase of the CH 4 fraction, this may result in enhancement of physical sputtering and hence cause damage of the CNTs/CNFs.

	except for C 2 H x + (x=2, 3, 4, 5, 6). The C 2 H 2 + and C 2 H 3 + fluxes show a local maximum at 10% CH 4 gas fraction, while C 2 H x 20 40 60 80 100 10 9 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 10 18 10 19 10 20 10 21 1: H 2: H 2 3: C 4: CH 5: CH 2 6: CH 3 7: CH 4 8: C 2 9: C 2 H 10: C 2 H 2 11: C 2 H 3 12: C 2 H 4 13: C 2 H 5 14: C 2 H 6 15: C 3 H 8 + (x=4, 5, 60 10 8 16: C 4 H 10

  Figure3Ratio of etchant (H) to the most probable carbon source for CNTs (C2H2 + C2H4) (left axis) and to the most probable carbon source for an amorphous film (CH3) (right axis) as a function of CH4 gas fraction at the same operating conditions as in figure2.Therefore, the ratio of H fluxes (representing etchants) to the fluxes of C 2 H 2 + C 2 H 4 (representing the carbon supply for CNTs/CNFs) as well as the ratio of H fluxes to CH 3 fluxes (as a source for amorphous carbon) are plotted in figure3, as a function of CH 4 gas fraction. Both ratios drop rapidly at a small fraction of CH 4 , until about 20% of CH 4 , and then they further decrease slightly at high CH 4

						700
		60		[H]/([C 2 H 2 ]+[C 2 H 4 ]) [H]/[CH 3 ]	600
						500
	4 ]) 2 H	40				400
	[H]/([C 2 H 2 ]+[C	20				200 300	[H]/[CH 3 ]
						100
		0
						0
		20	40	60	80	100
			CH 4 gas fraction (%)

  It is clear that CH 4 has a higher DR at small fraction of CH 4 in both gas mixtures, but it exhibits a different behavior upon increase of the CH 4 gas fraction for the two different dilution gases. When a small amount of H 2 is mixed into the CH 4 (corresponding to a high CH 4 gas fraction), the DR of CH 4 decreases slightly from 0.46 at 100% CH 4 to 0.43 at 50% CH 4 . For a lower fraction of CH 4 , and hence a higher fraction of H 2 , the DR of CH 4 is dramatically improved up to about 0.7 at 5% CH 4 . On the other hand, in the CH 4 /NH 3 plasma, a linear increase is found for the DR of CH 4 with decreasing CH 4 gas fraction, from 0.46 at 100% CH 4 to about 0.8 at 5% CH 4 . In general, a high DR of CH 4 in the plasma at low CH 4 fraction in the gas mixture points again towards favorable conditions for CNT/CNF growth, as it is stated in literature[41] that CH 4 cannot decompose easily on the catalyst surface, in contrast to higher hydrocarbons. The H 2 feedstock gas hardly decomposes in the CH 4 /H 2 discharge, and even much more H 2 molecules are formed under CH 4 -rich conditions rather than decomposed. In contrast to the H 2 gas, NH 3 shows a very high and fairly constant DR of around 0.9, for all gas mixture ratios. This high DR of NH 3 has also been reported in the literature[10]. c. Acetylene-hydrogen plasma (C 2 H 2 /H 2 ) In the C 2 H 2 /H 2 plasma, C 2n H 2 (n=2, 3), C 6 H 4 and C 2n H 6 (n=4, 5, 6) become important molecules besides the background gases C 2 H 2 and H 2 , as can be observed from figure6 (a). H 3 (n=1, 2, 3) radicals are mainly formed by H insertion into C 2n H 2 (n=1, 2, 3), and the significant decrease of the H radicals with increasing C 2 H 2 fraction should be responsible for this. From figure6(c), it is clear that the total ion flux shows a steady downward trend with increase of C 2 H 2 gas fraction. Indeed, a large number of heavy ions such as C 2n H 6 + (n=4, 5, 6) are formed in the C 2 H 2 plasma, which become predominant with increase of the C 2 H 2 fraction. The lower mobility of these heavy ions compared to light ions results in the decrease of total ion flux bombarding the substrate.

	Similar to the CH 4 /H 2 discharge, the lighter ions such as H + , H 2 + , C 2 H 2 + and C 2 H 3 + are predominant under H 2 -rich conditions, while the heavier ions (i.e., C 10 H 6 + and C 12 H 6 + ) turn to be important under C 2 H 2 -rich conditions. It is worth noting that a large flux of C 4 H 3 + (see figure 6(d)) was observed for all conditions.
	Therefore this ion is suggested to play an important role in the growth of CNTs/CNFs, for the conditions
	under study.
		20 10							1: H 2
		10 19							2: C 2 H 2
	.s -1 )	10 18	2						3: C 4 H 2 4: C 6 H 2
	flux to the substrate (cm -2	10 12 10 13 10 14 10 15 10 16 10 17	5	3	12	10 9	11 8	7 6 4	5: C 6 H 4 6: C 8 H 2 7: C 8 H 4 8: C 8 H 6 9: C 10 H 2 10: C 10 H 6 11: C 12 H 2 12: C 12 H 6
		10 11
		0	20	40	60		80	100
			C 2 H 2 gas fraction (%)
									The fluxes of C 2n H 2 (n=2, 3)
	follow the same increasing trend as C 2 H 2 upon increasing C 2 H 2 gas fraction, while the C 6 H 4 and C 2n H 6
	(n=4, 5, 6) fluxes are clearly less dependent on the C 2 H 2 gas fraction. This can be explained because the
	C 2n H 2 molecules are mainly formed by C 2 H insertion into C 2n-2 H 2 (n=2, 3), which results in similar trends
	of the C 2n H 2 (n=1, 2, 3) fluxes. However, the C 6 H 4 and C 2n H 6 (n=4, 5, 6) species are formed by
	neutralization of the corresponding ions on the wall, and they stay in the reactor much longer due to their
	heavy mass.

The primary radicals (see figure

6 (b)

) are H and C 2n H 3 (n=1, 2, 3). The H flux drops linearly upon increase of the C 2 H 2 fraction (and hence decrease of the H 2 fraction), while the fluxes of C 2n H 3 (n=1, 2, 3) species rise gradually with the C 2 H 2 fraction and reach a maximum at around 40% C 2 H 2 . When the C 2 H 2 fraction further increases, the fluxes of C 2n H 3 (n=1, 2, 3) species begin to drop. This is because the C 2n

  (a) for the C 2 H 2 /H 2 plasma and in figure8(b) for the C 2 H 2 /NH 3 plasma. It is clear that C 2 H 2 has a quite high DR (more than 0.75) when the gas fraction of C 2 H 2 in the mixture is less than 30%. Such high DR of C 2 H 2 leads to the reduction of C 2 H 2 in the bulk plasma, and hence lowers the C 2 H 2 flux arriving at the substrate. This might result in a relatively low growth rate of CNTs/CNFs, which was indeed observed in[7,21] , because the C 2 H 2 species are believed to be the main precursors for CNT/CNF formation in a PECVD system[8,47]. When the gas fraction of C 2 H 2 is in the range of 30% to 70%, a rapid drop is observed for the DR of C 2 H 2 (from 0.75 to around 0.2). In this region, the carbon supply for CNT/CNF growth rapidly becomes greater for two reasons: (i) the percentage of C 2 H 2 in the mixture increases and (ii) the DR of C 2 H 2 decreases. When the gas fraction of C 2 H 2 is further increased, the C 2 H 2 gas molecules are hardly decomposed in the plasma.

  4 , C 2 H 2 , C 2 H 4 , C 2 H 6 , C 3 H 8 , and C 4 H 10), and an increase in the fluxes of lighter radicals (H, CH, C, and C 2 ) and ions. Consequently the drop of C 2 H 2 and CH 3 will result in a reduction of carbon supply for the growth of CNTs/CNFs, on the one hand, and amorphous carbon film, on the other hand. In addition, the increase of H radicals will enhance the removal of amorphous carbon film.

	10 19 10 20	2				1: H 2: H 2
	10 18					3: C
	10 17 10 16 10 15					4: CH 5: CH 2 6: CH 3 7: CH 4
	10 14					8: C 2
	10 13					9: C 2 H
	10 12					10: C 2 H 2
	10 11					11: C 2 H 3
	10 10					12: C 2 H 4
	10 9					13: C 2 H 5
	10 6 7 8 10 10					14: C 2 H 6 15: C 3 H 8 16: C 4 H 10
	0	200	400	600	800	1000

  CH 3 ) are plotted in figure18, as a function of substrate temperature. It is clear that the ratio of H flux to CH 3 flux decreases from 200 for a substrate temperature of 0 o C, to 100 at 550°C, and further to 60 at 1000°C, while the ratio of H flux to C 2 H 2 and C 2 H 4 flux remains almost unchanged. This indicates that an amorphous carbon film could be removed more efficiently at a lower substrate temperature. On the other hand, a higher substrate temperature will result in a higher temperature on the catalytic surface, which will enhance the carbon diffusion into the particles and increase the surface reaction rate constants, thereby increasing the growth rate of CNTs/CNFs[50]. Moreover, the DR of the feedstock molecules, CH 4 and H 2 , increase with substrate temperature, as is shown in figure19. Without substrate heating, the H 2 is not decomposed (i.e. a negative value of -0.18 is calculated for the DR, which indicates that there are more H 2 molecules formed than decomposed), but the DR increases to 0.2 (i.e. 20%) for a substrate temperate of 1000 °C. The DR of CH 4 increases almost 2 times (from 0.3 to 0.56) when the substrate is heated to 1000 °C, thereby forming other hydrocarbon species, which can react more easily at the catalyst surface, and contribute to CNT/CNF growth. Hence, due to these opposite effects, most probably there will be an intermediate temperature range, which is most suitable for CNT/CNF growth. It is indeed reported in literature[7,11,12,16,[START_REF] Wei | Study of Growth of Vertically-Aligned Carbon Nanofibers by Plasma Enhanced Chemical Vapor Deposition-Growth Mechanism and Field Emission[END_REF]] that a temperature range of 550~900 o C, is most suitable.

		11					220
						[H]/([C 2 H 2 ]+[C 2 H 4 ])
						[H]/[CH 3 ]	200
		10
							180
	2 H 4 ])	9					160
	[H]/([C 2 H 2 ]+[C	7 8					100 120 140	[H]/[CH 3 ]
		6					80
							60
		5
		0	200	400	600	800	1000
				Substrate temperature (	o C)
	Figure 18 Ratio of etching species (H) to the carbon source for CNTs (C2H2 + C2H4) and to the carbon source for an amorphous film (CH3) as a
	function of substrate temperature at the same operating conditions as in figure 2.
	The ratio of etching species (H) to carbon sources for CNTs (C 2 H 2 + C 2 H 4 ) and for an amorphous carbon
	film (

Acknowledgements

We would like to thank the Fund for Scientific Research (FWO Flanders) and the Prime Minister's Office through IUAP-VI for financial support as well as the CalcUA computing facilities of the University of Antwerp for calculation support. We are also very grateful to M. Kushner and group members for providing the HPEM and useful advice.


P F Ambrico

M Ambrico

A Colaianni

L Schiavulli

G Dilecce

S De Benedictis

Thermoluminescence study of the trapped charge at alumina surface electrode in different dielectric barrier discharges regimes

Keywords: 52.25.-b {Plasma properties} 52.25.Mq {Dielectric properties} 51.50.+v {Electrical properties} 78.60.Kn {Thermoluminescence} 72.20.Jv {Charge carriers: generation, recombination, lifetime, and trapping}

In the present study charge trapping effect in alumina dielectric surfaces has been deeply investigated by means of a dedicated dielectric barrier discharge apparatus under different discharge regime and gas mixtures. These work further validates our previous findings in the case of air discharges under filamentary regime. The long lasting charge trapping has been evidenced by ex-situ thermoluminescence characterizations of alumina dielectric barrier plates exposed to plasma. The density of trapped surface charges was found to be higher in the glow discharge with respect to pseudoglow and filamentary regimes and for all regimes a minimum trap activation temperature was of 390 K and trap energy less than or around 1 eV. This implies that in the case of glow discharges a higher reservoir of electrons is present. Also, the effect was found to persist for several days after running the discharge.

Introduction

The surface charge trapping at dielectric surface due to exposure to atmospheric pressure dielectric barrier discharge (DBD) plasma can influence the discharge regime [1]; in fact surface charges act as a reservoir that can contribute to stabilize a glow discharge regime for instance in air discharges [2]. Golubovskii et al. suggested that many seed electrons necessary for a uniform/homogeneous discharge could be produced by electrons trapped on the dielectric surface [3]. Recently, long lifetime of charge trapping on alumina used as dielectric in DBD plasma has been evidenced by Thermally stimulated current [1] and Thermoluminescence technique [4]. We found that the adsorbed electrons in the case of alumina were trapped in shallow traps during plasma running and have mainly an energy of about 1eV [4], i.e. at a much lower energy than the intrinsic alumina electrons and much easier to be removed from the dielectric. These trapped electron could also explain the fact that irradiating the dielectric surface with low fluence laser beam could result in the triggering of a discharge for a voltage lower than the breakdown value [5].

From what stated above, it follows that different discharge regimes are expected to act differently on the surface charge trapping since the plasma electron energy distribution and current can be different. It is also furthermore known that DBD can run under filamentary or diffuse mode depending on discharge geometry and gas mixture. For instance, the nitrogen discharge can be run in different regime depending on the geometry and other discharge parameters [6,7]. Moreover, the addiction of small quantities of oxygen to a nitrogen discharge transform the regime from glow to filamentary [8]. Conversely, running an helium discharge this will lead to a quite distinct glow regime [9].

The aim of this work is to study the surface charge trapping effect under different discharge regime and gas mixture at atmospheric pressure running in a dedicated experimental set up. The effect of surface charge trapping on the dielectric barrier plates after plasma exposure will be evidenced by ex-situ Thermo Luminescence glow curve (TL GC) measurements as already preliminarly described in ref. 4. The correlation between the discharge regimes and and the observed glow curves parameters will be discussed.

Experimental

A DBD discharge apparatus has been build up in order to easily control the surface area exposed to the plasma; respect to previous experimental configuration [4], each single specimen of alumina (mean diameter 0.5 mm), constitute one of two dielectric barrier plates, covering the metallic electrodes, exposed to plasma.

A drawing of the discharge apparatus is shown in figure 1. The parallel plates discharge is composed of two brass electrode 3 mm in diameter, two 0.7 mm thick alumina plates (Coorstek fine grain, 96% purity) that completely cover the electrodes and two spacers designed to vary the discharge gap from a minimum of 2 mm (for N 2 main gas mixtures) and 5 mm for He main gas mixtures. The minimum distance between electrodes is limited by the geometry of the electrode support. The electrodes are completely isolated by highly insulating plastics except the surface in contact with the aluminum dielectrics. The discharge vessel is made of a stainless steel and PVC flanges for the high voltage (HV) connections and is equipped with vacuum fittings. The discharge regimes characterizing the working conditions of DBDs in the present study are shown in figure 2. In the case of Helium discharges, the DBD is homogeneous/diffuse along the plane of the electrode and in the discharge gap. The glow character is associated to one major current peak for half cycle. The discharge in nitrogen and nitrogen helium is homogeneous and assume the pseudoglow [10] discharge aspect, with usually a first current pulse which has a faster rise time and shorter duration, and a second pulse in both polarities which has not only an appreciably longer rise time but also a rather long decay time constant. Both current peak have a pulse duration of few microseconds. In the case of air and oxygen the discharge is in a filamentary state that is consisting of a large number of narrow filaments stochastically distributed over the electrode area. The discharge current has the form of multiple peaks (micro-discharges) of some tens of nanosecond duration.

From the current measurements the electron current transferred charge can be estimated by the integration of the current peak, using Q=∫i(t)dt for a current peak recorded in single-shot after subtraction of the displacement current. Of course the charge measured using this method is generally slightly underestimated [11] in the case of filamentary regime, in which faster signal are involved and the oscilloscope sampling can be affected by higher error. Since the current for one cycle is monitored continuously an average transferred charge per cycle can be easily estimated, and the total current transferred charge can be estimated by multiplying it for the total number of cycles during the measurements period.

During all the experiments several alumina disk plates (Ø = 6 mm and 0.7 mm thick) taken from the same 7x7 cm 2 slabs were used as dielectric barrier of ground electrode so to be easily removed after discharge run and analysed ex-situ by TL apparatus.

The thermoluminescence glow curves were collected on alumina samples gas plasma by using an automated Before each plasma exposure the alumina disks were thermally cleaned at 800°C for two hours, in order to deplete spurious trapped charges due to exposure to environmental radiation.

After plasma exposure the alumina disks have been promptly dismounted in dark conditions stored in a black box, to avoid or reduce any possible thermo luminescence glow curve intensity reduction due to bleaching effect, in dry air and mounted in the TL apparatus. The overall time from the switch off of the plasma to the start of the Thermoluminescence measurements was about 20 minutes. The Plasma induced luminescence [13] counts at the beginning of the measurements in the UV region covered by the TL filters were negligible.

The Thermoluminescence protocol after plasma exposure was the following: a) Thermoluminescence readout (that takes about 90 seconds); b) Thermoluminescence background. In all the sample after different plasma exposure the collected background was comparable to the reference indicating that no luminescence was coming from the sample after the thermoluminescence signal readout. We can exclude thermally activated reaction from the surface as reported in [13] .

c) Control Thermoluminescence readout following the beta radiation exposure protocol. For all the samples the beta irradiated thermoluminescence were always very close to the control one collected at the beginning.

This is an indication that the surface was not modified by the plasma or for beta radiation damage or sensitization.

Plasma exposure times have been varied ranging from 5 to 90 minutes in the case of air discharge and from 5 to 30 minutes in the case of He and He N 2 discharges. In the case of He two different high voltage values (3 kV pp and 5 kV pp ) were used that is leading to different discharge current. As a matter of comparison, thermoluminescence glow curves were also collected on a set of alumina samples after exposure and varying the irradiation time from 60s to 2100s i.e. for a total dose ranging from 7 Gy to 250 Gy.

The thermoluminescence glow curves have been analyzed by using the free downloadable GLOW FIT program [14] capable of simultaneously processing up to ten TL glow peaks following the first order kinetics model [START_REF] Mckeever | Thermoluminescence of solids[END_REF].

Results and discussion

The thermoluminescence technique

The charge trapping effect due to plasma exposure was approached by using the thermoluminescence properties of the dielectric plates used as barrier in DBD discharge. It could be useful to remind that in a pure insulator (but this hold also for semiconductors) there are two relevant energy bands: (i) an almost completely filled valence band and (ii) an almost empty conduction band separated by a forbidden gap (called band-gap energy E g ). Transitions of electrons between the valence band and the conduction band can occur if the valence band electron acquires an energy ≥ E g . Imperfections in the crystal, associated with impurities and/or lattice defects may create new localized energy levels in the forbidden band gap. Under certain conditions, some of these defects are capable to trap an electron. One of this conditions is ionizing radiation exposure producing free electrons that can be trapped on one of more than of these sites. Some of these traps can be thermally depleted and recombine on recombination centers emitting a photon. This is the basic phenomenon on which the thermoluminescence technique works. The trap determined after a TL measurements is characterized by the energy E t (which is referred to as the trap depth) that an electron must acquire from lattice vibrations to escape to the conduction band where it can move freely in the crystal and by the characteristic temperature T m at which the thermal vibrations of the crystal lattice are sufficient to cause the release of trapped electrons. The rate at which the electrons, or holes, escape from the traps is roughly governed by the vibrational frequency (or attempt-toescape factor or frequency) s of the charge within the trap and the trap depth E. The overall escape rate is proportional to S•exp(-E t /kT).

The thermally stimulated light emission from an insulator or a semiconductor following the previous absorption of energy from ionizing radiation results in the typical Thermoluminescence glow curve from which the information on the electron traps present in the band gap can be extracted. By looking at Figure 3, under the hypothesis that the total electron retrapping probability (N-n)A n is much lower that the recombination probability mA m (i.e. slow retrapping condition), the thermoluminescence intensity for single peak is given by the well known first order kinetic equation [START_REF] Chen | Theory of Thermoluminescence and Related Phenomena[END_REF] in the case of a linear temperature gradient:

𝐼 𝑇 = 𝑛 0 𝑆 exp - 𝐸 𝑡 𝑘𝑇 exp - 𝑆 𝛿 𝑒𝑥𝑝 - 𝐸 𝑡 𝑘𝑇 ′ 𝑇 𝑇 0 𝑑𝑇 ′ (1)
Where  is the heating rate, T 0 is the initial temperature, n 0 the initial number of filled traps, E t is the trap energy, S is the above expressed frequency factor (s -1 ) indicating also the number per second an electron interacts with the lattice. The exponential integral in equation ( 1) could be only analytically solved [START_REF] Horowitz | [END_REF] and gives a representation of the single peak glow curve as a non linear function of trap energy E t , peak temperature at maximum T M and peak maximum intensity I M . The integral in ( 1) is then the representation of a glow peak with a maximum intensity I M at a characteristic temperature T M following the equation:

𝛿 𝐸 𝑡 𝑘𝑇 𝑀 2 = 𝑆 𝑒𝑥𝑝 - 𝐸 𝑡 𝑘𝑇 𝑀 (2)
It then follows that the integral light intensity depends on the number of trapped charges that are in turn depending on the irradiation dose and independent on the heating cycle. The characteristic temperature T M does not depend on the number of trapped charges and relates with the trap energy E t .

Moreover, the trap energy depth E t , the peak maximum temperature T M and the width of the peak  (defined as the ratio A/I M i.e. between the glow peak area and the peak intensity at its maximum), are related among them by the following relation [18]:

𝐸 𝑡 ≅ 𝑘𝑇 𝑀 2 𝜔 (3)
From eq.(3) it should be expected that glow peak at higher temperature correspond to deeper traps. However, when complex glow curve resulting from peak overlapping are analyzed this is not a followed rule since also the width of glow peak contributes in defining the correspondence between the energy and glow peak maximum temperature [18] The analysis of such complex curves can be nowadays afforded by a friendly free downloadable software namely GlowFit program [14] specially designed to simulate thermoluminescence glow curve resulting from up ten single or superimposed glow peaks following the first order kinetics. The GlowFit software allows to determine the trap energy depth E t , the peak maximum temperature T M , the peak maximum intensity I M and the frequency factor S as output best fit parameters and calculates the peak area A. Moreover, the goodness of the fit is expressed through the figure of merit (FOM) value that is a further program output and is defined as :

𝐹𝑂𝑀(%) = 100 • ∆𝑦 𝑖 𝐴 𝑇 𝑛 𝑖=1 (4)
where n is the number of data points, y i is the difference between the experimental and fitted points and A T is the integral of the fitted glow curve in the region of interest [19].

Effect of different discharge regimes

In figure 3 the collected thermoluminescence glow curves (TL GCs) for a 30 minutes plasma exposure time and different gas mixture discharges and GC referred to 90 seconds  exposure are reported. In analogy to the terminology used for the  radiation, we will refer to "plasma radiation" as the sum of all agents (electrons, photons, ions) that, impinging on the dielectric,are capable to excite an electron into a surface trap level and term "plasma radiation dose" the corresponding estimated dose.

The TL GC intensity of the different observed spectra shown in figure 4 relates well with the measured current in the different plasma regime conditions. In fact the higher electron current transferred charge is obtained in the helium plasma glow regime, then the pseudo-glow regime of helium-nitrogen and nitrogen plasma and last the filamentary regime of air and oxygen plasma (see table 1). It is evident that exposing the alumina samples for the same time to different plasma produces thermoluminescence glow curves with different intensities. Furthermore, the plasma induced thermoluminescence glow curves display features similar to those observed after  irradiation which is constituted of high energetic electron current. Possible effects of the alumina exposure to UV radiation although present in the plasma as irradiation source have been excluded since, as previously observed, glow curve observed after UV (mercury lamp) exposure display a different shape due to the UV light induce bleaching effect [4]. Respect to previously published results for the case of synthetic air [4], referring to glow curve collected after some days from plasma exposure, the short delay between the N 2 -O 2 plasma exposure and thermoluminescence measurements results in a much more intense glow curve.

The radiation dose after plasma exposure was estimated by using the known  radiation source dose rate as a reference. First of all the linear dependence of the thermoluminescence glow curve area on the total radiation dose has been verified (see figure 5) Therefore, it has been possible to estimate the total plasma exposure dose from the ratio of the plasma thermoluminescence glow curve area and the  thermoluminescence glow curve area for a given radiation dose (i.e. 10.7 Gy). To minimize the experimental error on the plasma radiation dose estimate the reference signal obtained after exposure to the  radiation source were collected on each sample after collecting the plasma thermoluminescence glow curve. The experimental error can be due to small differences on the geometrical area of the alumina slabs or to different GC intensities produced by  irradiation due to sensitization effects. The reference signal enable us also to verify that no radiation damage or sensitization effect was produced on the dielectric surface.

The total plasma radiation dose for the different discharges are reported in Table 1. As can be observed, He plasma is highly effective in filling several traps in the overall thermoluminescence temperature range while the O 2 plasma is the least effective one. It must be however pointed out that despite the not so much different current from the case of N 2 -O 2 discharge the number of counts observed in O 2 plasma produced glow curve is smaller. The counts reduction observed in O 2 discharge can be ascribed to the presence of an higher level of ozone producing de-trapping effect associated to the ozone-surface interaction. It has been in fact demonstrated that ozone annealing efficiently eliminates the charge trapped in the dielectric used as capacitor material [20].

270

The peak deconvolution procedure [14] helps to better elucidate on the plasma radiation thermoluminescence 271 glow curve features and involved trap energies. In figure 6 The best fit parameters obtained after peak deconvolution, referring to each peak, have been listed in Table 1 and represents the thermoluminescence glow peak maximum temperature (T m ), trap activation energies (E t ), frequency factor S, glow peak area ( A) and figure of merit values (FOM) [21]. The frequency factor s and has been found higher for the lowest temperature peaks. The FOM accounts for the goodness of thermoluminescence glow curve modeling and respect to previously published results [4], the fitting procedure has been improved by reducing the figure of merit (FOM) values less than 2% (see Table 1). The deconvolution of glow curve produced after plasma exposures evidence five contributing peaks. The results reported in Table 1 can be more easily understood if we consider figure 7.

It can be observed that traps filled by the plasma are similar in the case of air and oxygen discharge, but with a trapping efficiency higher for the air like plasma (see Table 1). We speculate that in N 2 -O 2 plasma the lower ozone production leads to a lower ozone-mediated detrapping effect.

The glow curve intensities produced in the case of glow (He) and pseudo glow (N 2 , He-N 2 ) regime show very strong similarities. In particular the higher temperature peaks are the same with slight differences in the peak temperatures (< 15K) and energies (< 10 meV). These attributions are furthermore justified when considering the similar order of magnitude of the frequency factor S values.

We can conclude that the different discharges characterized by different regimes (i.e. different plasma current and electron energy) are more or less effective in filling the electron traps in the dielectric materials.

We can also speculate that the trap filled by different plasmas are keeping memory of the active species (metastable, or electronegative gases, etc.): in fact different trap at dielectric surface are filled giving a different signature on the thermoluminescence glow curve.

Effect of the exposure time

The thermoluminescence glow curves were collected for different total exposure time of the alumina samples to He and N 2 -O 2 plasmas, in order to observe the effect of two extreme plasma regimes (glow and filamentary respectively) on charge trapping. In figure 8 the obtained glow curves are reported together with the estimated dose for the different exposure time. In the legend the estimated total dose are reported together with the total exposure time. (colour online)

At the lowest doses, the thermoluminescence glow curve intensity is higher in the lower temperature region than in the high temperature region. Increasing the exposure time the thermoluminescence glow curve intensities for the two temperature region seem to converge to an almost common value. This effect is due to the presence of several trapping states that can act one as active and other as competitor traps. Generally, the trapping probability of the competitor trap is higher than that of the active one so that the glow peak area tends to saturate due to the fast filling of competitor trap levels; after competitor level saturation more electrons are trapped to the active states that shows a fast linear trap filling [START_REF] Mckeever | Thermoluminescence of solids[END_REF]. These effects may account for the behavior observed at the lowest doses in He and air discharge.

In the inset of figure 8 are represented the total thermoluminescence glow curve area values as a function of irradiation time, that in the case of beta irradiation can be easily converted in the total radiation dose. A saturation effect is clearly observed in He while in N 2 -O 2 it is less marked. It has to be stressed that saturation effect has not been observed after  irradiation both for doses similar or much higher than plasma ones. 1. (colour online)

The dynamic behavior of thermoluminescence glow curve has been exploited by examining the evolution of each glow peak when changing the plasma doses. It has to be underlined that since plasma dose depends on the discharge regime, the examined dose range is different although exposure time is the same. Figure 9 shows the glow peak areas as a function of the corresponding irradiation dose under glow (He figure 9 The overall saturation effect observed in the case of plasma induced charge trapping can be explained if we consider that the plasma electron energy is typically of the order of a few eV, i.e., five orders of magnitude lower than the beta source, leading to an electron penetration depth of around tens of nanometer [22].

Therefore the plasma electrons are effective mostly on the first monolayers of alumina surface where they are readily stopped rather than on the overall bulk, which is instead fully crossed by beta radiation. This means that the real volume of the sample that is irradiate by plasma is smaller. If we assume that the traps are randomly distributed in the sample this means that the number of traps that can be filled by the plasma radiation is considerably lower, and as a consequence the saturation dose is also lower [23]. This is furthermore confirmed by comparing the glow curve area vs dose collected after  and plasma irradiation in the same dose range (up to 50 Gy) that was found linear for the former while saturates for the latter.

The strong correlation between the estimated plasma radiation dose and the plasma current is evidenced in figure 10. Several experiment were run for different gas mixtures and regime in He, He/N 2 , N 2 , N 2 /O 2 , the current was constantly monitored and the thermoluminescence measurements performed soon after each run, together with the corresponding calibration measurements by irradiation with  radiation. For values of the total dose less or equal to 11 Gy the plasma radiation dose is linearly correlated to the total current transferred charge estimated by the integration of the current peak, while start to show a saturation effect for higher dose rate. In particular saturation is easily reached in the case of Helium, and He N 2 gas mixture. If we look carefully at figure 10 we can observe that if the estimated total plasma current transferred charge is the same, then estimated plasma radiation dose is also the same. This can be a further indication that the electrons hitting the surface are the main responsible for the charge trapping. Moreover the observed charge trapping generated by plasma exposure is a long lasting effect. A set of dedicated experiment was run in the case of He discharges in order to clearly show this effect. Figure 11 is an example of the time evolution of the thermoluminescence curve collected on the same alumina sample just after the plasma exposure and by left the sample under dark for 70 hours after plasma exposure. The plasma irradiated sample was kept under dark in order to avoid the superposition of environmental light bleaching to fading effect. In the last case, the glow curve area is about a factor of two lower with respect to those of the as exposed sample evidencing the presence of the fading effect [START_REF] Mckeever | Thermoluminescence of solids[END_REF]. Here, the high temperature glow curve region relates to the initial one since the trap temperature and energy distribution were not modified. Conversely, changes in the temperature and energies of trapped charge distribution (see Table 2) affect the low temperature glow curve region. The fading effect accounts for the high frequency factor S of the lowest temperature peaks indicating that these traps are more easily released in time and can relax toward a more energetically stable trap distribution.

Conclusions

Evidence of DBD plasma induced trap filling effect on alumina by using thermoluminescence techniques was clearly observed. The thermoluminescence signal originates from long living traps previously filled by plasma electron current, that are subsequently depleted by heating. The plasma generated thermoluminescence signal was found to be maximum for the Helium glow discharge plasma and in general higher for the homogenous discharge case. Evidence of a strong correlation between the thermoluminescence signal, i.e. the filled electron trap, and the total discharge current charge was demonstrated. Due to the low energy of the plasma electron the penetration depth of the electrons could only be few nanometers, leading to a saturation of the thermoluminescence signal with increasing exposure time. The generated charge traps was observed to last for several days, with a redistribution of the charge on deeper energy level. The redistribution of the trapped charge after several hours from plasma exposure tends to fill higher temperature trap with trap average energy slightly above 1 eV.

Figure 1 .

 1 Figure 1. Schematic of the experimental apparatus (colour online).

Figure 2 .

 2 Figure 2. Typical voltage and current waveforms for: (A) He, (B) He-50%N 2 , (C) N 2 , (D) N 2 -20%O 2 , (E) O 2 plasmas.

Figure 3 .

 3 Figure 3. Scheme of principle of charge trapping/detrapping and recombination mechanisms in an insulating material leading to a luminescence (or thermoluminescence) effect. Here the simplest case on one trap and one recombination center energy distribution are displayed. N is total trap state concentration, n the concentration of trapped electrons; m is concentration of available hole states (for recombination); E t is the trap energy; A n is the retrapping probability and A m is the recombination probability (colour online).

Figure 4 .

 4 Figure 4. Thermoluminescence glow curves after alumina exposed to different gas mixture discharge plasma. The GC data refers to 30 minutes plasma exposure. Glow curve after 90 s of  exposure is also shown for comparison. (colour online)

Figure 5 .

 5 Figure 5. Thermoluminescence glow curves for different  radiation exposure time (i.e. total dose). The alumina sample response is linear with the dose. (colour online)

1 Figure 6 .

 16 Figure 6. Glow curve fitting curve (red straight line) and deconvoluted peaks resulting as the output of the application of the GlowFit software on the experimental thermoluminescence curve (circles) for He (a) and N 2 O 2 (synthetic air, (b)). The TL GC refers to 30 minutes plasma exposure. In the bottom part the residual values in the examined temperature range have been represented. The residual represents the difference at each temperature between the experimental and fitted points in the GC. The FOM values have been also reported. (colour online)

Figure 7 .

 7 Figure 7. Correlation between the discharge regimes and the deconvoluted peak parameters (T M and E t ) of Table 1: filamentary regimes (A) and glow and pseudo glow regimes (B). (colour online)

Figure 8 .

 8 Figure 8. Thermoluminescence glow curves for different time exposure in the case of (a) Helium and air (b) discharge.

2 Figure 9 .

 29 Figure 9. Thermo luminescence deconvoluted glow curve peak areas versus plasma dose for the case of He (a) and Air like plasma (b) discharge. N.i. represent the peak number as reported inTable 1. (colour online)

  (a))and filamentary (N 2 -O 2 (figure 9(b)) discharge regime. In the glow regime, the lower temperature and the highest temperature peak areas saturates(competitor traps), while intermediate temperature peak display a general linear behavior (active trap). In the filamentary regime, the highest temperature peak display an almost linear behavior (active trap) while the remaining peaks saturate with the dose (competitor trap).

Figure 10 .

 10 Figure 10. Estimated total doses for different plasmas as a function of the total discharge current estimated charge. The dose is linearly proportional to the charge up to dose of 15 Gy and deviates from linearity for higher doses, as observed when plotting the dose as a function of time exposure. (colour online)

Figure 11 .

 11 Figure 11. Thermoluminescence glow curve taken soon after the exposure to plasma and after 70 hours. (colour online)

  The applied voltage is pulse modulated with duty cycle T on =T off =5ms. Different discharge regimes have been produced under different plasma mixture. Specifically, a filamentary regime will be typical of N 2 -20%O 2 (air like mixture) and O 2 discharge, a diffuse range will characterize that of He while an intermediate regime will be that of N 2 and He-50% N 2 discharges. The discharge parameter, current and voltage, have been continuously monitored and registered during each run. Typical oscillograms of the applied voltage and discharge current for DBD for a total pressure of 760 torr, flow rate of 1 liter/minute and different gas mixture area reported in figure2.

						8
	30
						6
	20
						4
	10
	I(mA)	0				0 2	V(kV)
						-2
	-10
						-4
	-20
						-6
	-30	(E)			O 2	-8
			2.42	2.44	2.46	2.48	2.50
					Time (ms)

Before operation the discharge volume is evacuated to few tens of mTorr by a 30 m 3 /h rotary pump. The gas flow is operated by MKS flow meters/controllers, and pumping through an adjustable needle valve is used to maintaining the 760 Torr pressure under a total gas flow of 1000 sccm. Pure N 2 , O 2 and He (impurities less than 6 ppm) are used as gases supply. The HV supply is composed of a low voltage sinusoidal generator (Wavetek mod. 164), a power amplifier (Industrial Test Equipment Powerton 1000A), and a high voltage transformer.

Table 1 .

 1 Best fit parameters extracted using the GlowFit program, i.e. Peak Temperature T m (K); Trap Energy E t (eV);

	265
	266	Peak Area, A (a.u.); Frequency factor, s (s -1 ); Figure of Merit (FOM). The peak width and Dose (Gy) are calculated
	267	as described in the text. The fitted glow curves refers to 30 minutes plasma exposure for gas mixture plasmas leading to
	268	different discharge regime. In the table are reported the corresponding plasma macroscopic parameters i.e.: Energy T on
		(mJ); plasma current charge per cycle Q cycle (C).

  the deconvolution for the thermoluminescence 272 He and air discharge are reported as examples together with the residual and the figure of merit (FOM) for each fit.

	PLASMA PeakN°. glow curve obtained after T m (K)	E t (eV)	Peak Area (a.u.)	S (s -1 )		(Gy) Dose	(mJ) E Ton	(C) Q cycle
		1	390	0.755	2310	1.60 10 9	27
	O 2	2	458	0.888	20803	1.46 10 9	32
	FOM	3	474	0.608	27687	4.61 10 5	48	1.15	8.9	1.4 10 -9
	2.37%	4	520	0.562	9353	3.71 10 4	61
		5	575	0.500	4064	2.12 10 3	83
		1	388	0.756	6550	3.79 10 9	27
	N 2 -O 2 ,	2	462	0.890	53984	2.42 10 9	32
	FOM	3	473	0.620	118712	1.32 10 6	47	6.93	6	2 10 -9
	1.5%	4	530	0.562	36862	5.12 10 4	64
		5	571	0.500	188080	4.62 10 3	82
		1	388	0.852	11418	7.84 10 10	38
	N 2	2	418	0.99	12574	5.72 10 11	24
	FOM	3	475	0.759	290354	4.36 10 7	40	23.32	12	9 10 -9
	1.76%	4	552	0.703	344381	6.78 10 5	57
		5	580	0.500	701399	3.79 10 3	84
		1	390	0.868	12425	5.40 10 10	23
	He-N 2	2	422	1.090	15618	3.63 10 12	22
	FOM	3	475	0.770	296911	2.87 10 7	39	26.17	5.9	1.1 10 -8
	1.68%	4	559	0.622	432134	4.71 10 4	64
		5	587	0.500	769263	1.66 10 3	86
		1	390	0.810	77232	1.77 10 10	25
	He	2	425	0.991	216310	3.50 10 11	25
	FOM	3	470	0.758	1080551	5.47 10 7	38	69.37	7.55	2.8 10 -8
	1.18%	4	542	0.638	1235783	2.20 10 5	59
		5	576	0.500	1430699	4.15 10 3	83

Table 2 .

 2 Peak temperature and energies for glow curves taken just after exposure to plasma, 20, 40 and 70 hours.

		0 hrs	20 hrs	40 hrs	70 hrs
			Peak Temperatures (K)
	Pk 1	390
	Pk 2	425	429	431	431
	Pk 3	470	469	470	467
			494	494	487
	Pk 4	542	547	547	546
	Pk 5	576	574	576	574
			Peak Energies (eV)
	Pk 1	0.810
	Pk 2	0.990	1.18	1.31	1.38
	Pk 3	0.760	1.03	1.04	1.14
			1.72	1.82	1.35
	Pk 4	0.640	0.77	0.78	0.76
	Pk 5	0.500	0.50	0.52	0.52

  AknowledgmentsAuthors wish to acknowledge Prof. A. Minafra for fruitful scientific discussion and Mr. G. Casamassima and Mr D. Loiacono for technical support; G.S. and A.C. acknowledge Fondazione Cassa di Risparmio di Puglia Progetto GEOCRONO. This work was possibile thanks to the Laboratorio di Ricerca per la Diagnostica dei Beni Culturali dell'Universita' degli Studi di Bari.