The Role of Hydrogen Incorporation into Amorphous Carbon Films in the Change of the Secondary Electron Yield

1. Introduction

The emission of secondary electrons from surfaces plays a key role on the generation of electron multipacting in high power radio frequency devices and particle accelerators with positively charged beams. In particle accelerators, it can result in the formation of clouds of electrons, causing beam instabilities, deterioration of the vacuum, or heat loads to cryogenics parts of the system, limiting the overall efficiency of the accelerator (i.e. the beam luminosity) [1,2,3,4,5,6]. A possible cure to this problem is to reduce the electron emission by coating the internal surfaces of the vacuum chambers with a thin film of low Secondary Electron Yield (SEY) material. Amorphous carbon (a-C) coatings have been successfully used in the Super Proton Synchrotron at CERN (European Organisation for Nuclear Research) to mitigate the electron multipacting [7], and it is now in the baseline for the High Luminosity upgrade of the Large Hadron Collider, (CERN, Switzerland), and the Electron Ion Collider, (Brookhaven National Laboratory, USA) [8,9].

Secondary electron emission can be conveniently described as follows [10]. Primary electrons that penetrate a material mainly lose their energy by different types of electron excitations (via plasmon excitations or by a direct energy transfer to valence and core electrons). This results in the generation of secondary electrons inside the material, with energy above the vacuum level. On their way out, these internal secondary electrons can efficiently lose their energy only by excitation of valence electrons. Finally, once they reach the surface, only the internal secondary electrons which still have energy above the vacuum level have a chance to be emitted. The whole process is strongly affected by the electronic structure of the material, which determines the energy loss processes of both primary and internal secondary electrons. Particularly important is the latter, which can be reduced by opening the energy gap. This is the origin of the high SEY of dielectric materials [11].

The efficiency of a-C coatings for suppressing electron multipacting depends on structural properties: only coatings with pronounced electrical conductivity can have a low SEY. It has been well established that the presence of hydrogen impurities is particularly harmful in that respect [12,13]. The effects of hydrogen and nitrogen impurities on the secondary electron emission properties of a-C coatings were a subject of two recent studies [14,15]. It was clearly demonstrated that adding hydrogen or deuterium in the discharge gas increases the SEY of carbon films, while the presence of nitrogen has an opposite effect. By combining SEY measurements with Ion Beam Analysis (IBA), a correlation between the deuterium content and the maximum SEY (SEY_max) was established. SEY_max increases linearly, from 1 to 1.4, with the overall hydrogen and deuterium (H + D) relative content up to 47%. Further increase of the H + D amount up to 54% is accompanied by a steep SEY_max growth to 2.2. The samples were also investigated by Optical Absorption Spectroscopy (OAS), enabling estimation of the optical energy gap using the procedure established by Tauc (so-called Tauc gap). These results reveal a strong correlation between the SEY_max and the Tauc gap, apparently offering a straightforward explanation for the SEY_max increase. However, a-C films are often non-uniform, i.e., they may consist of various regions with different composition and electronic structure (e.g., graphitic, diamond-like and hydrocarbon domains, the latter being a result of highly common hydrogen contamination) [16]. Such materials have different local energy gaps, limiting the interpretation of Tauc plots [17].

Robertson summarized measurements of the Tauc gap performed on different types of a-C (pure and hydrogenated) in his seminal review paper [18]. He concluded that the Tauc gap of a film is not determined by the hydrogen content, but by the relative amount and properties of the sp² carbon phase. Local energy gaps of diamond-like and various hydrocarbon phases are too large to be related with a Tauc gap below ≈2 eV. The gap is therefore related to the configuration of π states on the sp² sites. In a planar cluster model, the band gap of a given cluster is inversely proportional to the square root of the number of the hexagonal rings in the cluster [19]. Different types of defects (e.g., formation of pentagons or heptagons) will also open the gap. From this perspective, deviation from the linear dependence at low photon energies in Tauc plots should not be attributed to the so-called tail states (i.e., Urbach tail) but to the small quantity of graphitic clusters with small local energy gaps.

The abrupt increase of SEY_max, when the H+D relative concentration changes from 47% to 54%, suggests that the hydrogen content may not be directly responsible for the change of the secondary electron emission (SEE) properties of a-C. This doubt is further supported by the high correlation between the SEY_max and the Tauc gap [14,15], knowing that the Tauc gap can be independent of the hydrogen concentration [18]. This aspect motivates our study: since the Tauc gap in a-C is known to be affected by the concentration and size of graphitic domains, could the latter also influence the SEE?

In our recent work we performed deposition of a-C coatings using magnetron sputtering in Ar discharges with several fractions of D₂, identified the mechanism behind the incorporation of deuterium in the films during the production phase and its impact on the SEY [15]. In this work we report detailed analysis of the same samples by means of different electron and vibrational spectroscopic techniques. X-ray and UV Photoelectron Spectroscopies (XPS and UPS, respectively) were used to determine the surface composition, to identify different phases in the a-C films, and obtain information on their electronic structure. Further insights are provided by Raman scattering, Fourier Transform Infrared Spectroscopy (FTIR) and High Resolution Electron Energy Loss Spectroscopy (HREELS). Raman scattering, enabling the detection of the presence of graphitic carbon, was particularly valuable in supporting the XPS results. FTIR and HREELS were used to identify the character of C-D bonds in the most contaminated samples. These results are then compared with the corresponding SEY, OAS and IBA measurements, enabling us to reveal the actual mechanism behind the SEY increase by the hydrogen contamination.

2. Materials and Methods

All details of the thin film deposition procedure are explained in [15]. Briefly, the films were deposited by magnetron sputtering from a 50 mm diameter graphite target. The total operating pressure was set to 2 Pa, consisting of Ar and small quantities of D₂, to study deuterium incorporation into the films. The substrates were mounted 93 mm away from the graphite target and the discharge power fixed at 30 W. Five sets of samples were deposited on Si single crystal and quartz substrates for different characterisations: the reference (without D₂ added to the discharge gas), 0.2D (0.2 vol% of added D₂), 0.5D (0.5 vol% of D₂), 1D (1.3 vol% of D₂) and 10D (10.9 vol% of D₂). D₂ was added to distinguish deliberately introduced contaminants from hydrogen contamination from the residual gas. The system was baked prior to each run for 24 h at 230 °C to minimize the natural contamination, keeping the residual gas pressure in the low 10^-6 Pa range or better (N₂ equivalent). A new graphite target was used for each run. The deposition rate was 10-15 nm/h, generally growing with the D₂ partial pressure, pD₂. The thin film thicknesses are in the range from 486–719 nm (measured by SEM). The samples were transferred to different laboratories in stainless steel vacuum chambers, pre-evacuated by a turbomolecular pump and filled with N₂ gas.

UPS and XPS measurement s of ‘as-received’ samples were performed on AXIS SUPRA setup (Kratos Analytical), containing both UPS and monochromatic XPS sources. XPS measurements were performed using the monochromatic Al Kα line (photon energy of 1486.7 eV), and the spectrometer pass energy of 80 eV (survey spectra) and 5 eV (high resolution spectra). UPS measurements were performed by means of the He I α line (photon energy of 21.22 eV) and the spectrometer pass energy of 5 eV. The binding energy scale for UPS and XPS measurements were both calibrated using a sputter-cleaned Ag sample, based on the position of the Ag 3d_5/2 line and of the top of the valence band. Fitting of graphitic contributions was based on the XPS measurements of freshly cleaved Highly Oriented Pyrolytic Graphite (HOPG). A correction of the raw UPS spectra was made by removing the contributions of the He I β line (energy shift of 1.87 eV, intensity of 1.2% with respect to the He I α line). All samples were conductive, apart from the sample 10D, which was measured with charge compensation using an electron flood gun.

Raman spectroscopy measurements were carried out at room temperature in a backscattering geometry on an alpha 300 R confocal Raman microscope (WITec) using a 532 nm Nd:YAG laser (2^nd harmonic) as well as a 633 nm He-Ne laser for excitation. The laser beam with a power of 0.7 mW was focused on the sample by a ×50 lens (Zeiss), providing a spot with a diameter of about 1 μm. The spectra were collected with a 600 groove/mm grating using 5 acquisitions with a 2 s acquisition time. The same setup was used to perform photoluminescence measurements with two excitation wavelengths, 532 nm and 633 nm. For each sample, the spectra were acquired on several spots to check their lateral uniformity.

FTIR measurements were performed in vacuum in the wave number range 500-5000 cm^-1, using a Vertex 80v system (Bruker) in conventional reflection and transmission mode, as well as in the attenuated total reflection (ATR) configuration using a Ge crystal.

HREELS measurements were performed in a UHV system (operating pressure in the 10^-7 Pa range) using a LK Technologies 2000R spectrometer. Further details on this experimental setup are provided in the Appendix A, together with the experimental results.

3. Results

3.1. Composition, Electron Emission and Optical Properties of the Coatings

In this section, we summarise the main results of the thin films obtained by different techniques and reported in [15]. Thin film composition analysis performed by IBA revealed the presence of C, D, H and O uniformly distributed along the film depth, as confirmed by Secondary Ion Mass Spectrometry measurements. Results of the quantitative composition, the mass densities of the films, estimated from the IBA measurements and the film thicknesses (obtained by Scanning Electron Microscopy), as well as the results of SEY and Tauc gap (E_T) measurements are summarised in Table 1. The amount of incorporated deuterium steadily increases with D₂ partial pressure in the discharge gas (p_D2), getting relatively close to the theoretical maximum of 65 at.%, corresponding to saturated hydrocarbons. The dependence of the maximum secondary electron yield (SEY_max) on p_D2 in the films has a distinctively different trend: an increase of the H/D amount from 10 to 46 at.% changes SEY_max from 0.99 to 1.38, while additional 7 at.% of H/D increases the SEY_max abruptly to 2.2. SEY_max and the Tauc gap are strongly correlated. It appears that small changes of the D/H content in samples 1D and 10D are accompanied by the very different electronic structures, which govern both the secondary electron emission and optical properties. The latter is also clear from the fact that the sample 1D was conductive in contrast to the sample 10D. Namely the latter motivated usage of different approaches for the SEY measurements of the two samples [15].

From the mass densities and the Tauc gaps of the films we can already make a first estimation of their structure using general guidelines summarized in [20] and by considering that deuterated carbon films are generally somewhat denser than the equivalent hydrogenated ones. It appears that the reference, 0.2D and 0.5D samples, with their Tauc gaps clearly lower than 1 eV, are most probably dominated by graphitic and partially deuterated graphite-like (a-C:D) regions. The sample 1D with E_T of 1.38 eV, high density, and large H+D content, might be closest to diamond-like a-C:D. Finally, the sample 10D, characterised by a low density and E_T > 2 eV, could be a typical example of polymer-like a-C:D.

3.2. XPS Measurements

Apart from carbon, the survey XPS spectra of all samples show the presence of oxygen at the surface, estimated to be about 8 at.% in all cases. The samples were not charging during the measurements apart from the sample 10D, which was measured utilising an electron flood gun for charge compensation. The O 1s line in the first four samples was situated at 532.6 eV. Assuming that the O 1s line position is the same in the sample 10D, the latter was used as a binding energy reference for that sample.

Hydrogenated/deuterated a-C is expected to be a mixture of graphitic (pure sp² hybridised) carbon, diamond-like carbon and different hydrocarbons in which carbon could be both in sp² and sp³ hybridisation. Resolving these distributions in the C 1s photoelectron line is a complex problem due to their quite small chemical peak shifts, as extensively discussed in the literature [21,22,23,24]. The graphitic contribution is located at 284.3-284.5 eV, while a pure sp³ C contribution is usually encountered at about 285.2 eV [22]. The latter feature overlaps with different hydrocarbon contributions, around 285.0 eV, while at higher binding energies, further contributions related to various carbon bonds with O can be expected [24,25]. All peaks should be symmetric apart the one from the pure graphitic contribution, which is highly asymmetric [23,24]. The peak model for the graphitic contribution could be established by measuring the C 1s photoelectron line of the freshly cleaved Highly Oriented Pyrolytic Graphite (HOPG). Unfortunately, the asymmetry of the graphitic contribution is becoming less pronounced with the reduction of the cluster size and with the increase of the amount of defects in this phase. All this makes bond identification from the C 1s line fitting a challenging task without a straightforward solution. However, the elemental O concentration can be used as an additional constraint, which the carbon-oxygen bond contributions in the C 1s line need to follow. This approach, applied for all samples, except for the 10D (see below), strengthens the reliability of the interpretation of the spectra taken from the a-C coatings.

High resolution spectra of the C 1s photoelectron line of a freshly cleaved HOPG and the five samples considered in this study, together with the corresponding fittings, are presented in Figure 1. In all cases the background was calculated using the Shirley algorithm. As in [14], we again observe that the C 1s line becomes more symmetric with the increase of the D content in the films. One possible explanation of this trend is that the relative amount of graphitic C is being reduced and/or that the clusters are getting smaller with the increase of the D content.

The C 1s spectrum of HOPG (Figure 1a) was fitted using three contributions. The main peak (graphite), at 284.45 eV has asymmetric profile with a nomenclature LA(1.2, 2.5, 5) in CasaXPS software [26] and full width at half maximum (FWHM) of 0.34 eV. It should be stressed that the same peak profile was used by M. Biesinger, failing to secure perfect agreement with the measured spectrum [24]. Since a similar problem appeared in our spectra, we introduced the second peak (graphite sat), with the same profile and a FWHM of 1.3 eV. This peak is shifted with respect to the first towards higher binding energies by 1.47 eV, while their intensity ratio is 0.106. Finally, there is a well-known wide symmetric peak at about 291.2 eV attributed to the π-π* satellite always present in spectra of pure graphite [23,24].

It might be tempting to interpret the peak graphite sat as evidence of defects, such as sp³ carbon or C-H bonds. However, one should have in mind that such contributions would be symmetric. The asymmetry of this contribution would then imply non-negligible presence of other contaminants (typically O). Knowing that XPS is distinctively more sensitive to such contaminants than to C [27], the corresponding photoelectron lines would be clearly observable. Since this is not the case, we assume that both contributions originate from perfect graphite. They are introduced to better describe the shape of the C 1s line of HOPG, without attributing any physical interpretation to this separation. In our fittings of the graphitic contribution, we fixed the relative positions of the first two peaks and kept their intensity ratio approximately constant (see below). The intensity of the third peak was considered to be a free parameter (the latter is affected by the electronic structure and size of the graphitic clusters). The profile of all symmetric peaks (attributed to less conductive phases in a-C films) was of pseudo-Voigt type GL(30). They are attributed to sp³ carbon and C-H(D) bonds with both sp² and sp³ carbon (284.8-285.2 eV), C-O (≈286.6 eV), C=O (287.8-288.2 eV) and O-C=O (≈289.0 eV) bonds [22,25]. All symmetric peaks within one spectrum have FWHM fixed to the same value.

The essential element of the fitting procedure was to maintain the carbon-oxygen bonds of C 1s in accordance with the O:C ratio obtained from the quantitative analysis, being 8±0.8% for all samples. In this approach we consider that the C:O stoichiometric ratio is 1:1 for the C-O and C=O contributions and 2:1 for the COO contribution. Consistency between the composition and the C 1s fitting could only be achieved by successively decreasing the asymmetry of the graphitic line as the H+D amount increases. The degree of asymmetry is characterised here by the ratio of the parameters α and β of the line shape LA(α,β,m), which determine the spread of the tail on the high and low binding energy side, respectively (α/β being below 1 for asymmetric line shapes). In addition, final asymmetry tuning of the graphitic contribution was performed by slight modification of the intensity ratio between the main peak and the graphite sat in the range 0.078 – 0.106. This peak fitting model did not provide consistent results only for the sample 10D, as can be seen in Table 2 where the XPS fitting results are summarised. For this sample, the oxygen content is overestimated, most probably due to the charging problems that affected the shape of the C 1s line.

Fitting results of the C 1s line taken from the 5 samples and the relative content of hydrogen and deuterium taken from Table 1 are summarized in Table 2. The following general trends with the increase of the H+D relative content appear:

• The relative contribution of the graphitic component decreases and even disappears in the sample 10D;
• The relative contribution attributed to the sp³ carbon and the hydrocarbons increases;
• The asymmetry of the graphitic component becomes less pronounced.

Therefore, increasing the amount of incorporated H/D in the films is accompanied by the higher content of hydrocarbons and reduction of the graphitic content. Besides, the graphitic regions are becoming smaller and/or with higher defect concentration.

At this point, total disappearance of the graphitic content in the sample 10D is not certain. We can only claim that there is no need to introduce the asymmetric graphitic component to obtain a good fit of the spectrum presented in Figure 1f. Since the sample 10D was charging, one could expect a deformation of the line shape. Moreover, the latter certainly took place since it was not possible to perform a good fit that would justify the correct content of the oxygen amount. While one cannot reliably exclude the presence of some graphitic regions in that sample, their relative amount most probably does not exceed ≈10%.

3.3. UPS Measurements

In Figure 2 we present UPS spectra close to the Fermi level (binding energy of 0 eV) taken from the reference 0.2D, 0.5D and 1D samples, as well as of the freshly cleaved HOPG. The spectra are normalised with respect to their intensities at 2 eV. The same structure cannot be reliably taken from the sample 10D due to the charging problems.

The very top of the valence band of HOPG (binding energy range 0-1 eV) can be attributed to π electrons from the K point of the Brillouin zone [28]. Since the diamond-like and hydrocarbon regions have energy gaps well above 2 eV [18], the presence of the signal in other samples is additional evidence of the graphitic regions in the a-C samples. The intensity of this structure gradually decreases with the H+D content, just as previously concluded from the XPS spectra. Closer inspection of the spectra reveals that the top of the valence band is shifting towards higher binding energy with the H+D content, verifying opening of the local energy gap attributed to the graphitic regions. The gap opening implies size reduction of the graphitic regions [19,29].

The difference between the top of the valence band and the Fermi level (the latter corresponds to the 0 eV binding energy) in the spectra presented in Figure 2 is in the range 0.0-0.2 eV. Assuming that the Fermi level is around mid-gap position, the energy gap of the graphitic regions can be roughly estimated to be ≈0.2 eV for the reference and 0.2D samples, and ≈0.4 eV for the samples 0.5D and 1D. In a first approximation, the UPS value for the reference sample corresponds to its Tauc gap (Table 1), while the mismatches between the UPS and Tauc values for the other samples (particularly for 1D) are much higher. The latter is due to the character of the Tauc gap, which corresponds to the electronic properties of dominant components in the film, whereas UPS detects the highest occupied states. Therefore, reasonable agreement between the Tauc gap measurements and the UPS results of the reference and 0.2D samples is additional evidence of their graphitic character. On the other hand, the mismatch in the case of the other two samples confirms a lower graphitic content as already revealed by XPS.

3.4. Raman Spectroscopy

Further insight into the structure of the thin films was obtained from Raman scattering spectroscopy. Results of the Raman spectroscopy performed on the samples deposited on silicon using the 532 nm laser beam are summarised in Figure 3. The representative spectra of each sample (apart from the sample 10D) are presented in Figure 3a. The steady increase of the Raman signal with the D₂ content in the discharge gas is most probably due to the drop of the optical absorption [15], which is also manifested in the increase of the Tauc gap (cf. Table 1), combined with the monotonic increase of the film thickness with the H+D content.

A feature in the range 1100-1700 cm^-1 corresponds to the overlapping G and D bands, being typical for various carbon phases [30] (including deuterated a-C films [31]). The G band is attributed to sp² carbon atoms (it is not restricted to sixfold carbon rings in graphite nor to pure carbon phases). The D band is a fingerprint of isolated sixfold carbon aromatic rings, being forbidden in a perfect graphite [19]. Co-existence of both bands therefore implies presence of graphitic regions separated by disordered phases.

Apart from the G and D bands, an intense wide structure at about 2800 cm^-1 can be also observed in Figure 3a. Its intensity relative to the G and D bands increases with the amount of deuterium incorporated in the samples. In the sample 10D, the intensity of this structure is about 10 times greater than in the other samples measured under the same conditions, thus hindering eventual identification of the graphitic carbon (more details on this matter are provided in the Supplementary Information S1). Raman spectra of carbon-based materials may have some bands in this range. For instance, graphene is characterised by the 2D mode at around 2700 cm^-1 and a second order D+D’ band at around 2900 cm^-1 [32]; Raman spectra taken from polymeric amorphous carbon have in this range a C-H stretching band [30,33]. To clarify the origin of this band, Raman measurements were also performed with a He-Ne laser (wavelength of about 632.8 nm) resulting in the lack of this structure (cf. Supplementary information S1). The absolute energy position of this feature is ≈1.97 eV, corresponding well to the position of the broad emission band (1.9-2.5 eV) observed in a photoluminescence of hydrogenated a-C [34]. Therefore, we conclude that this feature is not a Raman signal but evidence of photoluminescence i.e. it is related to the excitation of electronic states. The latter also explains why this feature increases with the amount of incorporated deuterium in the sample.

Fitting of the Raman spectra is demonstrated in Figure 3b on the example of the sample 1D, while other fitting details can be found in the Supplementary Information S1. The spectra were fitted using 4 Lorentzian peaks after removing a linear background. Although this approach did not provide a perfect fit out of the range of interest (the latter being 1100-3000 cm^-1), it allows extraction of the most valuable information characterising the a-C samples. Two of the Lorentzians are readily attributed to the G and D bands at about 1550 cm^-1 and 1360 cm^-1, respectively. The peak widths and the position of the D band do not change significantly among the studied samples. There is, however, a substantial difference between the relative peak intensities from different samples as well as a clearly pronounced shift of the G band. The wide hump related to the photoluminescence (PL), was fitted by two contributions, at about 2800 and 2150 cm^-1. The latter one could also be, at least partially, attributed to the CD_x stretching band [30] (PL2/C-D). The measurements performed with 632.8 nm support this interpretation (cf. Supplementary Information S1).

Most of the findings concerning different a-C systems extracted from Raman spectra are related with the G and D bands. These bands have a large width (≈200 cm^-1) in all samples, being a characteristic of disordered systems [35]. The ratio of the intensities of the D and G bands, I_D/I_G, and the position of the G band are plotted as a function of the relative H+D content (Figure 3c). The increase of the H+D content in the films reduces the ID/IG intensity ratio from 0.75 to 0.45 (a similar trend has been reported in [36] due to the increase of the hydrogen content), while the G band position σ_D is shifted from 1563 to 1540 cm^-1. While the observed trends are ambiguous when considered separately, a unique interpretation of this joint information is that the increase of the deuterium content corresponds to stage two of the well-known amorphisation trajectory of graphite as proposed by Ferrari and Robertson [19]: transformation of nano-graphite into amorphous carbon. In this amorphisation stage, the ratio I_D/I_G is directly proportional to the average number of carbon atoms in the graphitic clusters i.e. to the square root of their diameter.

The fitting approach shown in Figure 3b was not applicable to the sample 10D due to the intense curvilinear background, mostly caused by the intense photoluminescence signal, which makes the extraction of signal in the range of the D and G bands unreliable. Nevertheless, such an attempt has been made by removing the background of a polynomial form, which resulted in an asymmetric structure that could be mainly interpreted as the G band, while the D band is apparently lacking. Although of a limited reliability, this result implies that the graphitic phase in the sample 10D is extremely small or even absent (see above). Details concerning the analysis of the Raman spectra taken from the sample 10D can be found in the Supplementary information S1.

In addition, an attempt was made to identify the character of C-D bonds using other vibrational spectroscopies, namely FTIR and HREELS. These results are presented in the supplementary material S2 and the appendix A, respectively. In the case of FTIR, the signal attributed to C-D bonds was identified only in the case of the sample 10D, revealing that about 60% of deuterium atoms is bonded to sp² carbon. A similar conclusion was obtained from the measurement of the sample 1D by HREELS, confirming that the character of C-D bonds, being practically the same, is not responsible for the large difference between the electronic structures of the two samples.

4. Discussion

The XPS results and the mismatch between the Tauc plot measurements and UPS spectra evidence that the samples are generally non-uniform. Hence, the films should be considered as mixtures of different carbon phases (being a frequent situation [19]), each characterised with their own local energy gaps. The steady increase of the films’ density with the amount of incorporated deuterium up to the sample 1D can be understood as the increase of the sp³ phases (cf. Table 1). At the same time the sample with the lowest density is 10D, despite the similar relative composition with that of 1D, clearly indicating formation of a polymeric phase [20]. These estimations are fully supported by the results of the XPS, UPS and Raman analyses, revealing that increase of the deuterium content is accompanied by a decrease of the overall relative amount of the graphitic regions and their size reduction (i.e., transition from nanocrystalline graphitic phase into amorphous carbon). This is particularly evident when comparing the samples 1D and 10D, characterized with the similar relative content of deuterium (Table 1) and practically the same character of the C-D bonds. The abrupt increase of the SEY and the Tauc gap from sample 1D to 10D can be only explained by the dramatic diminishing of the graphitic component (Table 1).

A similar conclusion has been obtained by Robertson [18], demonstrating a nearly linear dependence of the Tauc gap with the sp² fraction c_sp2 for its relative contents below 80%, practically independent from the hydrogen relative amount. Since the data presented in [18] are compiled from the works of different authors and measured on various a-C and a-C:H samples, the points are rather scattered. Nevertheless, the line E_T = 3 – 2.5∙c_sp2 represents well the observed trend with the Tauc gap uncertainty bar of about ΔE_T = ±0.25 eV [37]. The dependence of the Tauc gap and the SEY_max vs. the graphitic content, obtained from the XPS measurements, is shown in Figure 4. It can be observed that both E_T and SEY_max also decrease with the relative amount of graphitic regions. Moreover, the trend of the Tauc plot fits well with that of Robertson, presented by a dashed blue line, for the graphitic contents below 70%. The systematic shift between the two trends, which is within the uncertainty ΔE_T, can be explained by different means of measuring the graphitic content in [37] (using electron energy loss spectroscopy and nuclear magnetic resonance). Besides, at c_sp2 > 70% we observe faster drop of E_T, as expected having the non-existent band gap of graphite. These agreements imply that the methodology used to extract the graphitic fraction from the XPS spectra is quite reliable and can be also used to correlate the SEY with the graphitic content.

The decrease of the SEY with the increase of the graphitic content (observed in Figure 4) is in accordance with the expectations: higher the fraction of the sp² phase, lower the SEY. A simple model, based on the same assumptions as those used to derive the well-known semi-empirical equation for SEY [38], was developed to support the observed experimental dependence. This equation, originally derived for uniform samples, was recently modified to encompass multilayer systems [39]. The latter approach was used as a starting point to model non-uniform a-C films as mixtures of two different phases: a graphitic one, and a polymeric one. Therefore, the polymeric phase is considered as a representative of all non-graphitic phases in the films.

In the frame of the semi-empirical theory, the number of internal secondary electrons generated in a depth range (z, z+dz) is equal to S(z)∙dz/ε(z), where S and ε represent the stopping power of the primary electrons and the effective energy required to create one internal secondary electron, respectively. The secondary electrons created at depth z will be then emitted with a probability equal to 0.5∙exp(-z/λ) [40], where λ is the mean escape depth of secondary electrons, taken from the literature [11]. Since S, λ and ε are material dependent, they will be changing from point to point of the sample interior.

The first step is to determine the parameters that characterize the electron emission properties of the graphitic and polymeric regions. For that purpose, the SEY dependencies on the primary electron energy of the reference sample and the sample 10D [15] were used as representatives of pure graphitic and pure polymeric material, respectively. Then, for a defined relative graphitic content, it is possible to estimate the range of primary electrons R. The samples were then modelled as a multilayer system with predefined graphitic content. However, the depth distribution of different phases within each sample is unknown. Another difficulty in establishing this distribution is in the lateral non-uniformity of the samples. To overcome this problem, a set of M depth distributions were generated (here designated as configurations), each containing the same amount of graphitic carbon, using a Monte Carlo approach. Finally, for each of the configuration, the SEY(E) was calculated by generating S(E,z)∙dz/ε(z) electrons at all depths z in the range [0, R], and calculating their escape probabilities affected by the multilayer structure in the range [0, z]. The whole procedure is detailed in the Appendix B.

The result of the SEY model, obtained using M = 1000 configurations and for the primary electron energies in the range 50-1000 eV is presented in Fig. 4. Having in mind the simplifications introduced in the frame of the model, and that the calculated SEY curves were obtained without any adjustments to the existing experimental data, the agreement with the measured values is very good. There is also a built-in systematic error in the model due to the consideration that the reference sample would be purely graphitic, while its actual graphitic content is only 90%. This approximation is responsible for an overestimation of the SEY for the highest graphitic contents. Although the effective energy ε is indeed smaller in the polymeric (40.8 eV) than in the graphitic (60.4 eV) regions, the major difference between the characteristics of the two regions is the mean escape depth λ, being more than two times smaller in graphite (4.9 nm) than in polymers (11 nm). That is probably the reason why the theoretical SEY_max(sp² content) dependence can be described by an exponential decay function.

In a sample with sufficiently high content of the graphitic phase, the regions with large energy gap (e.g., diamond-like or hydrocarbon regions) will not contribute to the Tauc gap: photons that may penetrate large energy gap regions will be most likely absorbed once they enter a sufficiently large graphitic region. The reduction of the amount and size of the graphitic phase increases the optical transparency of the films and, consequently, the Tauc gap. A similar effect takes place during the transport of secondary electrons through the samples. The escape depth of internal secondary electrons, which is directly related with their energy loss mechanisms, is strongly affected by the electronic structure of a material. The efficient energy loss is secured by sufficiently long trajectories of the secondary electrons through graphitic regions characterised by very narrow energy gap. As in the case of light transmission, the graphitic phase serves as energy absorber. The increase of the graphitic content directly reduces the escape depth of internal secondary electrons and, therefore, the secondary electron yield.

Although the presence of hydrogen and deuterium in the thin films is not directly responsible for the SEY increase, it plays a key role in reducing the graphitic amount. Indeed, the H/D incorporation will naturally reduce the relative contents of both graphitic and diamond-like phases in a-C:H(D). It was revealed in the previous work that the deuterium incorporation is a consequence of target poisoning, yielding in the sputtering of CD and CD₂ molecules in parallel with C atoms [15]. At the same time, pure carbon phases can only be deposited by magnetron sputtering of C atoms. The relative amount of pure carbon phases is directly related with the flux ratio of C and CD_x particles leaving the target and travelling towards the substrate. In the case of the sample 10D, this ratio was very low due to the strong target poisoning, resulting in a typical polymeric film.

5. Conclusions

Amorphous carbon coatings, deliberately modified by deuterium incorporation during the magnetron sputtering deposition, were thoroughly analysed using different electron and vibrational spectroscopies. This data was combined with previous composition and optical measurements [15], to reveal the role of H/D incorporation on the change of the secondary electron emission characteristics.

Both XPS and UPS (in combination with the Tauc gap) measurements demonstrate non-uniform character of the samples, being common for a-C materials [16]. The increase of the deuterium amount in the films is accompanied with the decrease of the fraction of the graphitic component and the cluster size. We conclude that a high content of graphitic phases in the films is responsible for a low secondary electron emission, just as it is for the low Tauc gap [18]. This phase has a local energy gap approaching to 0 eV, which reduces the escape depth of electrons travelling through it and, consequently, the secondary electron yield.

The formation of pure carbon phases (graphitic or diamond like) and hydrocarbon regions are competing processes. In our experiments, the latter is the result of target contamination by D atoms formed in the plasma, followed by the physical sputtering of CD_x molecules representing building blocks of hydrocarbon phases [15]. Therefore, the flux ratio of CD_x and C particles approaching the substrate is detrimental in this case for the relative graphitic content in the films.