D Köhl

M Luysberg

M Wuttig
email: wuttig@physik.rwth-aachen.de

Structural improvement of zinc oxide films produced by ion beam assisted reactive sputtering

Keywords: 68, 55, ag, 68, 55, jm

Structural improvement of zinc oxide films produced by ion beam assisted reactive sputtering

Introduction

Zinc oxide is widely used in many industrial applications. Typical fields cover e.g. surface acoustic wave devices [1], varistors [2], transparent electrodes [3] and thin film transistors [4]. Especially aluminium-doped thin films have increasingly attained focus in recent years as an n-type transparent conducting oxide (TCO) that could potentially replace Indium Tin Oxide (ITO) [START_REF] Ellmer | Springer Series in Materials Science[END_REF]. Due to the high abundance of both zinc and aluminium, ZnO:Al is a low-cost material. Therefore it is the TCO of choice e.g. in the fabrication of thin film solar cells, where it is used as a transparent front electrode [START_REF] Müller | [END_REF]. Another important market segment where Zinc Oxide is utilized is the fabrication of Ag based low-emissivity coatings. In this application thin Zinc Oxide buffer layers enable the growth of silver films with improved structural qualities due to the very small epitaxial mismatch between Ag and ZnO. Optimum performance of these coatings requires the control of both, texture and surface topography of the ZnO films [7]. Sputtering processes are preferentially applied for the deposition of Zinc Oxide thin films due to the excellent scalability of the process [8] required for coating large area substrates. Sputter-deposited Zinc Oxide thin films exhibit a hexagonal wurtzite structure and predominantly grow with the c-axis oriented perpendicular to the substrate surface. Optimum orientational order would be achieved under perfect thermodynamic equilibrium [9]. However, during thin film growth, the evolution of crystal structure is determined by many different aspects. Besides other deposition parameters, the temperature of the substrate and the growth rate determine the extent of deviation from thermodynamic equilibrium. Therefore, during sputter deposition of Zinc Oxide or aluminium doped Zinc Oxide, the substrates are usually heated to temperatures around 200 -300°C to yield optimum structural order [9,10,11]. This results in increased process costs and also limits the choice of substrates, thereby e.g. hindering the utilization of flexible substrates. These temperatures enable lower nucleation rates as well as defect annihilation, the latter needed to cure the damage caused by the high energetic oxygen ions originating from the cathode [12]. The bombardment of the growing film by these energetic ions is an unavoidable feature of the discharge in reactive sputtering of Zinc Oxide [13]. From an industrial point of view, it would be desirable to realize growth conditions that allow for high quality films without intentional substrate heating since it adds to product cost, increased energy consumption and system complexity. In a recent publication [14] we have already demonstrated that tailored ion bombardment from an auxiliary ion gun leads to a striking improvement of film quality and therefore complies with the requirements for large scale fabrication of high quality films on unheated substrates. It is the key objective of the present study to develop a comprehensive understanding of the mechanisms by which the ion bombardment controls structure formation of sputtered Zinc Oxide thin films. The clear identification of these mechanisms finally allows for the development of a growth model which does not only explain the experimental observations but also provides a clear understanding how films with the best possible structure can be produced at low deposition temperature.

Experimental Procedure

The geometry of the deposition system is shown in figure 1. An ion source (Tectra Gen II) with an additional differential pumping stage [cf 15 for details on the source] has been installed in a sputter deposition system such that simultaneous growth and bombardment of the films by an auxiliary ion gun is possible. Inevitably, in a reactive sputtering process, the sputtering target constitutes a second source of ions. Negatively charged oxygen ions, for example, are created at the racetrack and are accelerated towards the growing film. These ions represent a contribution to the total ion bombardment of the films which is very difficult to control. The bombardment by the oxygen ions may even result in severe structural damage [16]. However, these ions propagate on well-defined trajectories [12]. Therefore, it is possible to use a mechanical shielding device (cf figure 1) to eliminate this detrimental bombardment. With this prerequisite, the auxiliary gun enables a precise control of energetic ion bombardment. In this work, we will refer to this modified sputtering process as Ion Beam Assisted Deposition (IBAD), which is sometimes abbreviated to the term Ion Assisted Deposition (IAD). Typical IBAD processes [17][18][19][20][21] utilize very low pressure deposition techniques such as evaporation or ion beam sputtering. However, in recent years also sputtering discharges have been combined with ion assistance from an auxiliary gun [22]. As this deposition technique is widely used in many industrial large scale applications, a thorough understanding of the impact of ion bombardment during film growth is of scientific and technological relevance. In the IBAD process, the metallic Zn target (diameter: 76 mm, purity: 99.99%) is sputtered at a constant discharge current of 250 mA (~400 V) in a reactive Ar/O 2 atmosphere in oxide mode. A low pressure of 0.2 Pa is utilized to minimize scattering of the auxiliary ions on their trajectories towards the growing film. The bombarding species (Xe) is fed directly into the plasma cup of the ion source, improving the efficiency of the ionization and the purity of the ion beam. Typical Xe + ion energies are around 180 eV, while the ion to atom arrival ratio at the substrate is approximately 2%. This ratio has been defined as the ratio between the Xe + ion flux density at the substrate position and the flux density of ZnO molecules contributing to the film growth. The ion current has been measured utilizing a flat probe, neglecting the small portion of secondary electrons generated by the collision of ions with the probe. In good approximation, all ions are singly ionized and therefore we can express the ion flux density N Ion as

, 2 F I Ion e N Ion × × =
where I Ion is the measured ion current and e is the elementary charge. F is the area of the flat probe and the factor of 2 is a geometrical correction taking into account the 45°tilt angle of the impinging ion beam with respect to the substrate. The flux density of ZnO molecules N ZnO can be derived from the deposition rate.

, ZnO ZnO M N R N A ZnO × × = ρ
where R is the deposition rate, N A is Avogadro's constant, ρ ZnO is the mass density and M ZnO is the molar mass of ZnO respectively. The relative arrival ratio is then defined by ZnO Ion N N . As a substrate, a silicon (100) wafer with a thin native amorphous oxide layer was used. However, the structural improvements of the ZnO films discussed in the following also appear if glass substrates are utilized. The substrates have not been intentionally heated. Its temperature has not been measured in the present study. However, Joule heating of the substrate by the ion beam is negligible since the maximum energy transfer to the 2 × 2 × 0.65 cm³ Si substrate (specific heat capacity: 703 J/(kg × K)) is approximately 1 mJ/s and typical deposition times range from 100 to 1000 seconds. To study the impact of Xe + ion bombardment, films have been deposited with and without additional ion bombardment, respectively. Bombardment was always employed at the beginning of each deposition (except for the reference films), but was terminated after different lengths of time. The duration of the ion bombardment was varied to determine the effect of ion bombardment in different growth stages. In the following, the notation "IBAD A 1/4" identifies a bombarded film from series A, where bombardment was applied only during the first quarter of growth. The notation "REF A" describes the reference sample that has been grown under identical conditions but without additional bombardment. Table 1 gives an overview of samples and corresponding measurements discussed in this work.

The structural properties are investigated by X-ray diffraction (XRD), utilizing a Philips X'Pert Pro diffractometer with CuKα radiation, and by transmission electron microscopy (TEM). TEM specimens were prepared by standard techniques, involving mechanical grinding, dimpling and Ar ion milling. Plan view and cross-sectional specimen have been prepared, which allow the investigation of the microstructure parallel and perpendicular to the growth direction, respectively. TEM investigations were performed with a Tecnai F20 operated at 200 kV. For investigations of the surface topography, a DI Dimension 3100 Nanoscope atomic force microscope has been utilized. In-situ measurements of the mechanical growth stresses have been performed by a wafer curvature method. This setup has been described in detail elsewhere [23]. Some samples have also been investigated by X-ray reflectometry (XRR) to determine film thickness and mass density.

Experimental Results

X-Ray Diffraction:

Figure 2 shows diffraction data for ZnO films from series A. On the left hand side, θ-2θ-scans in Bragg-Brentano geometry are shown for five samples differing in the duration of the ion bombardment at the beginning of film deposition. It is apparent that all films grown under initial bombardment have a strongly improved crystalline quality, as the intensity of the (0002) Bragg peak is significantly increased. Rocking Curve scans displayed on the right hand side clearly show that this is due to an improved orientational order of the crystallite c-axis along the substrate normal. The widths of these peaks directly render the quality of the out-of-plane texture of the films. For the bombarded films, the corresponding FWHM is comparable with films deposited on glass at elevated substrate temperatures [cf e.g. 24]. Another striking fact displayed in figure 2 is that apparently bombardment only during the initial growth stage is already sufficient to produce high quality films. Starting from sample IBAD A 1/4, a further prolongation of the bombardment only leads to an angular shift of the (0002) peak (θ-2θ), resulting in a pronounced double peak structure in the intermediate stages (2/4 & 3/4 of total film grown under bombardment). This shift in the position of the XRD peak is indicative for differences in the film stress.

Mechanical Growth Stresses:

To further elucidate the origin of the shift of the XRD peaks and to relate it to the bombardment during film growth, the mechanical stress of the films has been investigated by means of an in-situ wafer curvature measurement technique [23]. Figure 3 shows the film stress and the instantaneous stress which have both been calculated from the film force and the deposition rate, which was determined after deposition by XRR. The film stress is defined as

, ] [ Thickness Film ] [ length unit per Force Film m m Pa × = σ [1] while the instantaneous stress i is defined by , ] [ Thickness) d(Film ] [ length) unit per Force d(Film m m Pa i × = σ [2]
This means that σ represents an average at each stage of film growth whereas σ i may be interpreted e.g. as the differential change of stress induced by each new deposited layer. Thus, sudden changes in the stress generating mechanisms should occur as a step in the latter quantity. Figure 3 shows a reference ZnO sample (no bombardment) in comparison with an IBAD sample that has been bombarded only during the initial half of the growth. From the upper graph it is evident that, while the ion bombardment interacts with the growing film, additional compressive forces act on the film structure as compared to the reference film. When the bombardment is terminated, a very distinct change in the stress generating mechanisms clearly manifests itself in the instantaneous stress (lower graph). The IBAD sample shows an abrupt change from compressive to tensile forces acting on the structure. It is noteworthy that the strength of the tensile contribution seems to significantly exceed the corresponding forces in the reference sample.

Surface Topography:

The evolution of structural differences as a result of the ion bombardment is also evident from the surface topography. To describe the data, in this section we will use the term "grain" to refer to the surface features observed by atomic force microscopy. We are aware of the fact that these features in the AFM images do not necessarily represent crystal grains. However, in later sections experimental evidence will be presented which suggests that the observed surface features might indeed represent crystalline grains. Since the results shown in figure 2 indicate that the ion bombardment has a major influence already in the early growth stage, extremely thin films have been produced for this investigation. Figure 4 shows the topography of an only 2.2 nm thin reference sample and a 2.5 nm thin IBAD sample. The film thicknesses have been deduced from XRR data, which allows determining the average film thickness with angstrom precision. The images shown in figure 4 have been post-processed with a convolution filter to enhance the contrast of the surface corrugation (cf [14] for the original images). However, all statistical evaluations that will be shown have been applied to the original topography data to avoid an impact of the postprocessing on the analysis. From figure 4 it is evident that there is a striking difference in surface structure, i.e. the IBAD sample shows a more homogenous grain size distribution. This is supported by the RMS roughness that has been calculated to be 0.88 nm and 0.44 nm for the reference and the IBAD sample respectively. Differences in topography are clearly visible from image 5, where a line profile is shown for both films. It is apparent that the surface of the reference sample is governed by a large variation of grain heights and widths while the IBAD sample shows grains with rather equal dimensions in contrast. This interpretation is supported by the surface height distributions shown in figure 6. The graphs have been normalized to ensure that the area under the graph is unity. The centre of mass of the distributions has been adjusted to agree with the thickness determined by XRR. These distributions can be interpreted in the following way: The FWHM is a measure for the roughness R of the surface and corresponds to the average deviation from the mean height (FWHM = 2R). The shape directly reflects the nature of the topography. The large right hand side tail for the reference sample is due to some grains which are significantly larger and hence higher than the average (cf figure 5). To investigate how the film topography changes with thickness, thicker films were studied as well. For this purpose, the approximately 120 nm thick films sputtered for the mechanical stress analysis have been selected for AFM measurements as well. Analogous to figure 4, post-processed images are shown in figure 7. The structural differences that have already been present for the thin films are even more pronounced for the thick films. There is a marked difference in the lateral structure size and distribution. The line profile shown in figure 8 again displays a large variation in grain heights for the reference sample in striking contrast to the IBAD film. Large differences in lateral sizes are also clearly visible only for the reference, but not for the IBAD sample. The surface height distribution presented in figure 9 clearly highlights the topographical homogeneity that is found for the IBAD sample, whereas the reference film exhibits a rather broad distribution as observed already for the thin reference sample. For the thick films, the width of the distributions corresponds to an RMS roughness of 3.9 nm for the reference and only 1.37 nm for the IBAD sample. As the structure size for the thick films has increased, it was also possible to successfully apply a watershed algorithm on the topography data in order to detect and analyze the grains. Hence, figure 10 shows a statistical analysis of the grains in terms of their equivalent lateral disc diameter. The absolute number of grains with different diameters has been plotted. The smooth lines are a guide to the eyes, while the original curves show some noise. It is evident that the IBAD sample on average exhibits much smaller grain diameters (approx. 15 nm) than the reference (approx. 24 nm) and that there is also a smaller distribution of different grain sizes for the IBAD film compared with the reference. From a comparison of the surface structure of sample series B and C it is evident that for the reference film a major change in the structure scale occurs upon increasing film thickness. On the other hand, the respective change for the IBAD film is far less pronounced. Apparently, ion bombardment establishes a growth behaviour where the lateral scale of the surface structure exhibits almost no change upon film growth.

Microstructure:

To further unravel the changes in film growth and the influence of the ion bombardment, TEM measurements have been performed on samples REF A and IBAD A 1/4. Figure 11 displays dark field images of these two samples grown without (figs. a, b) and with Xe + bombardment during growth (figs. c, d). In both cases a columnar growth is observed, where columns extend throughout the whole layer. In figure 11a one crystalline column with a conical shape is seen, which grows from a seed of a width of about 10 nm. At the top of the layer the column reaches a width of about 20 nm. In the lower part of the column a Moiré fringe contrast appears, which is caused by the overlap of two slightly misaligned crystalline grains. In the upper part irregular lines appear which are typical for planar faults on the (0002) planes such as stacking faults. In addition to the column, a crystalline grain shows weak contrast at the left hand side of the figure. Obviously, it does not extend in columnar fashion. The corresponding diffraction pattern (figure 11b) reveals that the (0002) reflections of individual ZnO grains (marked by arrows) extend along an arc of about ±20°with respect to the growth direction, which is indicative of a textured growth. (Reflections arising from the Si substrate are marked by circles). For the bombarded sample a similar microstructure is observed, i.e. a columnar growth. In contrast to the non-bombarded sample, for most cases investigated, the diameters of the nuclei are observed to be constant throughout the whole layer with a width of about 15 nm, which confirms the findings from atomic force microscopy (figure 10). This is demonstrated in figure 11c, where two columns with identical in-plane orientations are shown which have a total width of 25-30 nm. Again some few contrast lines appear parallel to the substrate, which are indicative of planar faults. In addition, a fringe contrast with a spacing of 5.4±0.2 Å is observed, which agrees with the distance of the (0001) planes. The electron diffraction pattern (figure 11d) reveals that the texture is well defined, i.e. the (0002) reflections show only a small deviation of ±5°with respect to the growth direction.

In plan-view, the diffraction patterns corresponding to the bright field images reveal a striking difference (see figs. 12 a, c). The reference sample is characterized by crystallites of almost random distribution around the texture axis, i.e. (0001). This can be deduced from the ring pattern, which reveals closed rings of individual reflections that are perpendicular to the (0001) axis. Only few (0002) reflections are detected, which correspond to crystallites not obeying the textured growth. In contrast, the diffraction pattern of the IBAD sample is dominated by an arc-like intensity distribution along the rings. This implies an almost identical crystallographic orientation of a majority of crystalline grains seen in figure 12c. However, this orientation relationship between neighboring grains does not extend throughout the whole sample, since the arc within the diffraction pattern is found to "rotate", if a different area of the sample is selected. I.a.w. adjacent crystallites show almost the same crystallographic orientation. On larger scales, i.e. > 500 nm, the orientation of the grains is found to vary.

Discussion

Summarizing the experimental results, ZnO films grown with Xe + ion beam assisted sputtering exhibit considerably improved structural properties compared to conventionally sputtered films under otherwise similar conditions. This advancement is disclosed in smaller surface corrugations, homogeneous feature sizes on the surface, in particular for thicker films, as well as in an almost identical crystallographic orientation of adjacent crystallites, and a well defined, textured growth, where the c-axis is aligned in growth direction. It should be emphasized that an ion bombardment only during the initial stage of film growth results in the formation of a drastically improved structure and that there is no further improvement for longer durations of ion bombardment. This implies that IBAD induces important structural changes in the nucleation regime. The structural evolution of the following growth stages is solely governed by the improved structure of the nucleation layer.

In order to understand, in which way IBAD affects the nucleation, the stress within the ZnO films is inspected closer. Figure 2 reveals that there is a noticeable shift of the (0002) peak towards lower angles as the duration of the bombardment increases. This is caused by an increased distance of the (0002) planes, which is a typical effect of compressive stress in sputtered ZnO thin films. The pronounced double peak for intermediate ion bombardment durations is indicative for the co-existence of two phases with different lattice spacing. We can immediately understand this feature from the stress behaviour shown in figure 3. There is a significant change in the evolution of instantaneous stress at the time when the auxiliary ion bombardment is stopped. While the ion bombardment is active, the film shows an increased compressive stress as compared to the reference. This is attributed to the implantation of atoms into e.g. interstitial places, resulting in an increased average inter-atomic spacing. Figure 13 displays the ion bombardment induced lattice expansion schematically. In consequence, the increased lattice constant leads to the peak shift in the XRD diffraction pattern. Upon the termination of ion bombardment there is no further implantation and hence the equilibrium interatomic distance is lower. However, now the subsequent layers grow on a textured film with larger inter-atomic spacing (see figure 13). This results in a tensile biaxial film force as detected in the stress measurement. Without implanted interstitials the planar distance in direction of the c-axis is smaller. Hence, the XRD (0002) Bragg peak occurs close to the literature value of about 34.4° [START_REF]Powder Diffraction Files[END_REF]. We can now interpret the double peak feature as contributions from the bottom and top part of the film, where bombardment was active and inactive, respectively. Since a pronounced structural modification takes already place in the early growth stage, a corresponding change in morphology can be expected for very thin films. This is confirmed by the AFM images of nominally 2.2 and 2.5 nm thick reference and IBAD samples, respectively (figure 4). Graphs 5-6 provide further confirmation of a considerable change in surface topography upon Xe + ion bombardment in this very early stage of growth. Hence, the structural changes have their origin in the nucleation and coalescence stage of film growth.

In the later stages, grain growth proceeds in columnar fashion. The TEM images (figure 11) clearly show that the reference film exhibits a conical columnar grain growth. This is linked with a competitive, proliferating growth of neighbouring grains, where grains overgrow each other. For IBAD samples the grains appear to grow in a rather parallel columnar fashion. Hence, the competitive behaviour is less pronounced and the columns are therefore assumed to grow with similar speed. These findings and interpretations are supported by the AFM data. While large changes of lateral structure sizes are observed with increasing thickness for the reference sample, the thick IBAD sample shows topographical features in line with the expected parallel columnar growth in non-proliferating fashion.

The most plausible process responsible for the structural changes seen is a forward sputtering mechanism: atomic peening [START_REF] Heurle | [END_REF]27] (sometimes also referred to as ion peening). This mechanism is characterized by the implantation of near surface atoms into the film by low energy ion bombardment. A number of findings for the IBAD films are consistent with this scenario. First, there is the compressive growth stress that accompanies the ion bombardment, which is evidence for an implantation mechanism. Additional support is the observed densification of the films. From XRR measurements of 20 nm thick films and subsequent fitting of the data the mass density of standard ZnO was determined to 5.25±0.05 g/cm³, whereas the density of IBAD samples was 5.45±0.05 g/cm³ (cf bulk density: 5.61 g/cm³). Second, from experiments with different bombarding species we found that the structure modification strongly depends on the ion species. If oxygen ions are utilized there is no change except for the expected detrimental effects at higher ion energies and fluxes. Argon ions cause a noticeable structural improvement at moderate energies. However, the effect is small compared to a Xenon based IBAD process. This is consistent with the fact that the atomic peening mechanism is governed by the effective momentum (rather than energy) transfer to the film [28,29,30]. Due to its small mass, a reflecting oxygen ion transfers only a small fraction of its momentum to the growing film. There is a better match between the masses of Argon and Zinc Oxide, which explains the small positive effects that have been found. Xenon however is assumed to transfer a large fraction of momentum to the growing film in a multi-collision cascade due to its large mass. This allows for a significantly increased momentum transfer (compared to Argon ions) at moderate fluxes and small energies. It is also important to mention that the dynamic nature of the IBAD sputtering process seems to play an important role in structure modification by ions. Experiments have also been performed where film growth and ion bombardment have been performed sequentially. Very thin layers (nominally < 1 nm) have been deposited and subsequently bombarded for different times. The procedure has been repeated 8 times before a thick layer has been deposited to yield a total film thickness of approximately 60 nm. None of the resulting films shows any structural modification due to an improved nucleation layer, which is in strong contrast to the films grown under simultaneous ion bombardment. For standard sputtered ZnO samples it is often reported [31,32] that in the early growth stage the films are rather non-textured, i.e. they consist of small grains with very different crystallographic orientations. It is also reported that in crystal growth processes the (0002) face exhibits a much faster growth speed than the other faces [33]. In [32] it was argued that this might also apply to the growth of sputtered films. Therein, a corresponding growth model was suggested and it was also argued that the negative oxygen ions have a significant albeit detrimental influence on film growth. The orientational disorder at the early growth stage in combination with different growth speeds of the crystallographic orientations would explain why there is competitive growth that finally results in a (0002) texture for the standard samples. The connection between the atomic peening mechanism and texture control presumably originates from the fact that the (0002) planes are the most densely packed planes. Densification of the structure by atomic peening therefore supports a preferred orientation with the (0002) planes parallel to the substrate. Hence, ion bombardment influences the film texture already in the nucleation stage. The fact that the ion bombardment leads to a well defined orientational order already in the early growth stage is supported by an XRD scan of a very thin film, which shows a pronounced (0002) peak (figure 14). The grain height has been estimated with the Scherrer equation:

, cosθ λ × × = B K D GS [3]
where D GS is the vertical grain size, λ is the wavelength of the radiation used, B is the FWHM of the Bragg peak in radians and θ is the diffraction angle. The constant K depends on the method used to determine B and typically varies between 0.89 and 1. It has been set to 0.9 here. The fact that there is a detectable Bragg peak intensity at all and that the grain height approximately matches the thickness of this very thin film proves that there is a highly ordered crystalline structure already present at this early stage. The exclusive formation of highly oriented grains already in the nucleation phase eliminates a competitive growth mode from the very beginning. This also explains why no further ion bombardment is necessary after the initial growth stage.

From the presented data and the foregoing discussion a detailed model of the growth of ZnO thin films is now proposed, which demonstrates which role the Xe + ion bombardment plays in the IBAD process (figure 15). A distinction between IBAD samples and the standard reference films is already evident after the initial nucleation regime (1). For the reference sample there is a rather random distribution of crystallite orientations (1a). Consequently, surface roughness and lateral structure size distribution are first indications for the onset of competitive growth. Some grains already exhibit larger surfaces and start to overgrow others due to different growth speeds along the various orientations. This behaviour further develops as the film grows thicker (2a). At some stage (3a) the first grains are fully overgrown mainly by crystallites growing in (0001) direction as a result of the proliferating growth. This leads to a broad distribution in the alignment of the (0002) crystal planes which is responsible for the poor crystalline quality that is observed in the XRD measurement. For the IBAD sample atomic peening leads to a preferred orientation already during the nucleation regime (1b). Hence, there is a noncompetitive growth already at this early growth stage which continues in subsequent stages (2b & 3b). Even when the ion bombardment is already interrupted when approximately 3 nm of the film have been grown (not shown here), thick films with exceptionally high crystal quality are obtained. This demonstrates that stages (2) and (3) in terms of crystal quality are solely governed by the ultra-thin nucleation layer produced in stage (1). Hence, it is especially the nucleation regime that is susceptible to ion bombardment. This observation is important for applications where a perfection of film structure is required.

Due to the technological importance of texture formation in thin films, a number of studies have focussed on this topic. We will hence relate the present findings with previous studies of texture formation in ZnO films employing different deposition techniques. Particularly noteworthy is a work from Claeyssens and co-workers [34] where ZnO films have been deposited using an ArF-PLD process. Substrate heating for different durations revealed that for the fabrication of highly textured films it is sufficient to apply the heating only during the early stage of growth. This finding is in line with our experiments which also demonstrate the importance of the nucleation stage. Both studies provide compelling evidence that the texture of the films is solely determined by the conditions that govern the nucleation regime. Apparently this statement even holds for different thin film fabrication techniques.

There are also studies that link mechanical stresses to texture evolution. Materials that exhibit a large anisotropy in their elastic properties tend to grow in a preferred orientation under the influence of mechanical stresses [35]. However, the anisotropy in the Zinc Oxide compliance tensor [36] is by far less pronounced than for the films reported on in [35]. Therefore the growth stresses generated by the Xe + ion bombardment are presumably not the main reason for texture formation in thin films of Zinc Oxide. We also exclude any processes based on preferential ion sputtering or damage of specific grain orientations due to channelling [37,38] since the Xe + ion energies utilized are much smaller than typical energies required for this effect. Also, the inclination of the ion beam of approximately 45°w ould not result in the (0002) texture as the corresponding channelling direction is in the substrate plane (90°).

Conclusion

Xe + ion bombardment during the growth of reactively sputtered Zinc Oxide films was shown to lead to a distinct improvement in the films' crystalline quality. The structural changes already occur in the nucleation stage, which governs the texture evolution of the whole film. This finding appears to be a fundamental property of Zinc Oxide thin films. The impact of ion bombardment can be explained in terms of an atomic peening mechanism. Hence a deposition process has been developed that yields high quality Zinc Oxide films on unheated substrates.

List of figures:

Figure 1. Geometry of the IBAD process: A zinc target is sputtered in a reactive Ar/O 2 atmosphere to yield stoichiometric Zinc Oxide films. a) An auxiliary ion gun is installed to simultaneously enable a well controlled ion bombardment at an inclination angle of approx. 45°. b) A mechanical shield is utilized to avoid the undesirable bombardment of the growing film with oxygen ions originating from the oxidized target surface. While these ions are blocked there is still a partially diffusive ZnO particle flux to the substrate. The two graphs at the top show an un-bombarded reference sample, which is characterized by a weak intensity of the wurtzite (0002) peak and a broad distribution of crystallite orientations as evident from the rocking curve. Despite identical film thicknesses, all films grown with initial auxiliary ion bombardment show strongly increased peak intensities. This fact is most pronounced for films grown under short (1/4) or long (4/4) duration of the bombardment. The structural enhancement is also evident from the corresponding rocking curves that give evidence for a strongly improved orientational order. The dashed lines represent the 2θ literature value of 34.4°for the θ-2θ scans. For the Rocking Curves it represents the position of θ. The IBAD sample reveals some degree of inplane texture, evident from the intensity distribution along an arc in the ring pattern (d). However, there is no long range order, as the arc segment "rotates" when a different area of the sample is scanned. (1). The section lining indicates the orientation of the (0002) planes in each crystallite. There is no preferred orientation of grains during nucleation of the standard sample (1a). Different growth speeds (indicated by the vertical arrows) of the different crystal facets result in a competitive growth where the (0002) oriented grains overgrow neighbouring grains with different orientations (2a). This leads to conical grains and poor order of crystallite orientation (3a). In case of the bombarded sample, a highly (0002) oriented film is established by an atomic peening mechanism already in the nucleation regime (1b). Hence, competitive growth is avoided (2b) and the resulting structure consists of parallel columnar grains in combination with a high degree of orientational order (3b).

Sample

Thickness

Figure 2 .

 2 Figure 2. Left: XRD scans in θ-2θ geometry. Right: Corresponding Rocking Curve measurements.The two graphs at the top show an un-bombarded reference sample, which is characterized by a weak intensity of the wurtzite (0002) peak and a broad distribution of crystallite orientations as evident from the rocking curve. Despite identical film thicknesses, all films grown with initial auxiliary ion bombardment show strongly increased peak intensities. This fact is most pronounced for films grown under short (1/4) or long (4/4) duration of the bombardment. The structural enhancement is also evident from the corresponding rocking curves that give evidence for a strongly improved orientational order. The dashed lines represent the 2θ literature value of 34.4°for the θ-2θ scans. For the Rocking Curves it represents the position of θ.

Figure 3 .

 3 Figure 3. Upper graph: In-situ measurement of the mechanical stress for a reference sample (no Xe +ion bombardment) and an IBAD sample that has been bombarded during the first half of the growth time. It is evident that the ion bombardment causes an additional amount of compressive stress. Lower graph: The instantaneous stress represents the differential change in film stress and is therefore sensitive to abrupt changes in the stress generating mechanisms. The interaction of the ion beam with the growing film is apparent in this graph, where a sudden change in the stress generating mechanisms manifests itself in a jump from compressive to tensile forces when the auxiliary ion bombardment is terminated.

Figure 4 .

 4 Figure 4. Surface structure of a 2.2 nm thick standard ZnO sample and a 2.5 nm thick IBAD sample. Images have been post-processed (for this figure only) to highlight the surface corrugation.

Figure 5 .

 5 Figure 5. Cross-sectional height profile of the surfaces shown in figure 4. The IBAD sample shows a smaller distribution of grain heights than the reference.

Figure 6 .

 6 Figure 6. Height distribution of the thin films shown in figure 4. The centre of the distributions (vertical lines) is adjusted to represent the average film thickness determined by XRR.

Figure 7 .

 7 Figure 7. Surface structure of a 127 nm thick IBAD sample and a 119 nm thick standard ZnO sample (reference). The IBAD sample shows a smoother surface and a narrower distribution of grains sizes. The images have been post-processed (for this figure only) to highlight structural features.

Figure 8 .

 8 Figure 8. Cross-sectional height profile of the surfaces shown in figure 7. In contrast to the IBAD sample, the reference shows a larger lateral structure size and a stronger variation in the heights of individual grains.

Figure 9 .

 9 Figure 9. Height distribution of the surfaces shown in figure 7. As for the thin films (figure 6), the centre line of the distributions corresponds to the XRR thickness. The distribution of the IBAD sample is very narrow compared to the standard ZnO sample.

Figure 10 .

 10 Figure 10. The surfaces of the films discussed in figures 7-9 have been analyzed with a watershed algorithm to detect grains and measure their size. The graph shows the distribution of the equivalent

Figure 11 .

 11 Figure 11. TEM images of a standard ZnO sample (a, b) and an IBAD sample (c, d) respectively. The images on the left (a, c) show dark field images where single columnar grains are visible. The corresponding diffraction patterns are shown on the right (b, d). Circles mark reflections from the Si substrate. Some of the Si reflections almost coincide with a (0002) ZnO reflection and are therefore marked with a single arrow at the top of the images. The arrows in the lower half of figures (b, d) point to the (0002) reflections of ZnO.

Figure 12 .

 12 Figure 12. Plan-view images of samples REF A and IBAD A 1/4. The bright field images (a, c) show almost identical grain sizes at the surface. The crystallites of sample REF A are randomly distributed around the texture axis, evident from the ring pattern (b).The IBAD sample reveals some degree of inplane texture, evident from the intensity distribution along an arc in the ring pattern (d). However, there is no long range order, as the arc segment "rotates" when a different area of the sample is scanned.

Figure 13 .

 13 Figure 13. Ion bombardment leads e.g. to interstitials (atoms marked with an "I") that expand the lattice by exerting forces in all directions in space. If bombardment is interrupted, epitaxial growth on the expanded layer leads to tensile biaxial forces because equilibrium conditions have changed. There also occurs a change in the distance between the (0002) planes.

Figure 14 .

 14 Figure 14. Bragg-Brentano XRD scan of a 4.6 nm thick IBAD ZnO sample. A pronounced (0002) Bragg peak with a FWHM of 1.87°is observed, which corresponds to a grain height of approximately 4.4 nm.

Figure 15 .

 15 Figure 15. Growth model for standard ZnO (without auxiliary ion bombardment) and IBAD ZnO (with auxiliary bombardment). Sketches (1) to (3) represent different growth stages of the films, starting with the nucleation regime (1). The section lining indicates the orientation of the (0002) planes in each crystallite. There is no preferred orientation of grains during nucleation of the standard sample (1a). Different growth speeds (indicated by the vertical arrows) of the different crystal facets result in a competitive growth where the (0002) oriented grains overgrow neighbouring grains with different orientations (2a). This leads to conical grains and poor order of crystallite orientation (3a). In case of

Figure 1 (Figure 2 (Figure 3 (Figure 4

 1234 Figure 1 (Figure_1.tif)

Table 1 .

 1 List of samples and corresponding measurements explicitly discussed in this work.

		(nm)	Ion bombardment	Measurement
	REF A	82	none	XRD, TEM
	IBAD A 1/4	81	stopped after 20 nm	TEM
	IBAD A 2/4	81	stopped after 40 nm	XRD
	IBAD A 3/4	79	stopped after 60 nm	XRD
	IBAD A 4/4	80	yes	XRD
	REF B	119	none	AFM
	IBAD B 1/2	127	stopped after 63 nm	AFM
	REF C	2.2	none	AFM
	IBAD C 1/1	2.5	yes	AFM
	IBAD D 1/1	4.6	yes	XRD

Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft (Wu 243/13) is gratefully acknowledged.


L Zommer

A Jablonski

Calculations of Auger intensity versus beam position for sample with perpendicular layers to its surface

Keywords: 72.10.-d, 72.90+y Electron-solid interactions, elastic and inelastic scattering, Monte Carlo algorithm, Computer simulation, Continuous slowing down approximation, Backscattering yield, Auger current

Recent advances in nanotechnology are a driving force for the improvement of lateral resolution in advanced analytical techniques such as SEM or SAM. Special samples with multilayers which are perpendicular to their surface are presently proposed for testing the lateral resolution, as discussed in recent works of Senoner et al (Senoner M, Wirth Th, Unger W, Osterle W, Kaiander I, Sellin R L and Bimberg D 2004 Surface Interface Anal. 36 1423). The relevant experiment needs a theoretical description based on a recent progress in the theory. Monte Carlo simulations of electron trajectories make possible an accurate description of the considered system. We selected exemplary samples, with layers perpendicular to the surface. The layer materials are elemental solids with high, medium and low atomic numbers, i.e. Au|Cu|Au and Au|Si|Au. For these systems calculations of the Auger current versus beam position were performed. We found that, for system with layers consisting of elements of considerably different atomic numbers, the relation can have unexpected extreme. This observation can happen to be important in analysis of SAM pictures.

Introduction

Analytical applications of Auger electron spectroscopy (AES) require knowledge of a theoretical model that describes the Auger electron intensity emitted from a sample of a given structure. Well known application of AES is the determination of the surface composition from measured intensities of Auger electron signals. Another application of this technique is the measurement of the overlayer thickness. Under ion bombardment, we can measure the in-depth profiles of component element for non-uniform samples. However, a possibility of focusing the primary beam and scanning the surface opened an important application of determining the lateral elemental distribution on a surface (mapping). Scanning Auger microscopy (SAM) is particularly useful for analysis of non-uniform samples consisting of different chemical species.

An obvious parameter determining the resolution of SAM images is the diameter of the focused electron beam at the surface. In modern spectrometers, this diameter is below 10 nm which facilitates imaging of nanostructures at surfaces. The image may be affected by 3D structures at the surface which results in shadowing effect of electron recapture by surface protrusions. However, already in 1970s, it has been realized that the lateral resolution is also affected by the physical phenomena [1,2]. The backscattered electrons may ionize surface atoms far from the point of a beam impact which is decreasing the image resolution. This effect is visualized theoretically by determination of the radial distribution of the points of electron exit (the point spread functions) (Cf.

Ref. [START_REF]Practical Surface Analysis[END_REF]). This issue has been recently addressed by Powell [START_REF] Powell | [END_REF] and Jablonski and Powell [5]. New parameters were proposed to describe the radial distribution.

Lateral resolution of SAM may be determined experimentally, however this approach requires special reference samples. One of the samples that can be used for this purpose is the thin overlayer with a sharp edge [5]. We can determine then the "edge resolution" for a given spectrometer.

Unfortunately, the measured signal, apart from the backscattering effects, is affected by the 3D structure of the surface region. The influence of the surface structure on the measured AES signal has been analyzed in detail by Tuppen and Davies [6].

A new type of the reference samples for testing the lateral resolution of surface techniques has been proposed by Senoner et al. [7,[START_REF] Senoner | Nanoscale Calibration Standards: Dimensional and Related Measurements in the Micro-and Nanometer Range[END_REF][START_REF] Senoner | [END_REF] and Vila-Comamala et al. [10]. The sample is a multilayer system, with layers of known thickness. The surface submitted to analysis is perpendicular to the planar interfaces. In that case, one is avoiding the effect of the 3D structures since the surface can be plain. The authors proposed the layers of AlGaAs and InGaAs grown on the GaAs substrate as a reference [7,[START_REF] Senoner | Nanoscale Calibration Standards: Dimensional and Related Measurements in the Micro-and Nanometer Range[END_REF][START_REF] Senoner | [END_REF]. Such sample can be used as a reference for different techniques, e.g. SIMS, and XPS. The authors also suggest usefulness of reference samples for AES [7].

In a recent publication, the Monte Carlo strategy was proposed for simulation of electron trajectories in a surface region of idealized samples with perfectly flat surface and perpendicular layers to their surface having infinitesimally thin interfaces [13]. Presently, we extend this model for calculating the Auger electron signal intensity during the primary beam scan perpendicular to the interfaces. We try to interpret the found unexpected extremes for investigated systems with layers filled by elements of considerably different atomic numbers, i.e. Au|Cu|Au and Au|Si|Au.

Theory

The Monte Carlo model

A solid is considered as a system composed of a number perpendicular layers to its surface of different materials, see example of such a structure in figure 1. The layers are homogeneous and amorphous throughout, in which the scattering centers are distributed randomly. The electron moving in the solid undergoes two independent processes: elastic and inelastic collisions. The latter events are described by the continuous slowing down approximation (CSDA). Within this approximation, an electron energy is a function of a distance traveled in a solid. According to the CSDA approximation the energy losses are described by the stopping power function (SP), S(E), which is defined as the energy loss with respect to the path length, s:

ds dE E S - = ) ( (1)
If electron of energy E 1 passes the distance s along its trajectory, then its energy decreases to E 2 . New energy, E 2 , can be calculated from the equation:

- = 2 1 ) ( E E E S dE s (2)
Details can be found in refs [11] or [12].

The elastic scattering is considered as a series of straight segments. The end of each segment represents a random scattering event where new direction and new path length of the electron is set.

Generation of a new scattering angle is described for example in ref. [11] and the way of generating the path length in layered sample in ref. [12]. The electron trajectory is followed from its entry point into the sample until it leaves the surface or its energy reaches the cutoff energy, i.e. the ionization energy, E i , corresponding to selected Auger transition.

Auger current calculations

The formula for the Auger current [14], J A , emitted into the unit solid angle of α direction and coming from the analysed atoms in a uniform solid of density N (number of atoms in a unit volume) can be written as:

α λ θ θ σ π α cos sec sec ) ( 4 ) ( 0 0 0 Q P r E N I C J A p A = (3)
The symbols have the usual meaning: C contains spectrometer transmission and detector efficiency, I 0 is the primary beam current, σ(E p ) is the ionization cross section of the level corresponding to the selected Auger transition for the incident energy E p , r is the backscattering factor (BF), P A is the probability that the Auger transition follows the ionization, 0 is the incident angle of the primary beam, Q is a correction parameters accounting for the elastic scattering effects, is the inelastic mean free path (IMFP) and is the emission angle of the Auger electron with respect to the surface normal.

The formula properly modified can be used to describe Auger current for layered sample with layers parallel to its surface [12]. However, the aim of this paper is an attempt to determine the Auger current emitted from the sample with perpendicular layers to its surface versus incident electron beam position. The question arises if the formula (3) can be used for such sample. For example, if an incident electron beam of energy E p changes its distance, x, to the Si layer (see figure 1), the BF, r, may vary. Thus, to obtain J A , assuming that eq. ( 3) applies to such sample, we should know the BF as a function of the electron beam position x. Besides, we can not exclude that the parameter Q, responsible for electron elastic scattering, also depends on x.

These difficulties encouraged us to look for the alternative in the problem solution. We propose the Monte Carlo (MC) simulation which makes possible to determine the Auger current versus the electron beam position which omits problem of the BF calculation. Although a theoretical description of the electron transport phenomena in a solid is now well-known, an algorithm applicable to samples with perpendicular layers to its surface has not been developed yet, with exception of a report devoted to a paradox of backscattering yield (BY) dependence on electron beam position for the same kind of samples [13].

We would like to express Auger current in such a way that can be adopted for other, more complicated, sample geometry. Since the ionizations efficiency and probability of Auger electron escape from sample depend on depth, z, we divide the sample into very thin layers ∆z, parallel to the surface (we assume ∆z=1Å). The number of ionizations in i-th ∆z layer is proportional to sum of the products:

= = n j k k k j i k j i i j s E 1 1 , , , , , ) ( σ (4)
where s i,j,k is k-th segment from k j,i segments of the j-th trajectory in i-th thin ∆z layer within perpendicular layer of interest. Example in figure 2 shows an j-th trajectory which crosses an i-th ∆z layer and has four segments in it within Si layer (k j,i =4) for a given transition. σ(E i,j,k ) is a cross section for ionization of an atom by electron having energy E i,j,k at the moment when it moves along segment s i,j,k . n is a total number of generated trajectories. In our calculations we used the ionization cross section of Casnati et al [15].

The Auger electron signal is proportional to the following expression:

= = = ∆ = T i n j k k k j i k j i A z i s E n x J i j 1 1 1 , , , , ) , ( ) ) ( ( 1 ) , ( , α ϕ σ α (5)
where ϕ(i∆z,α) is the emission depth distribution function (DDF) for depth i∆z, and α is the emission angle with respect to the surface normal. The DDF is a parameter typically used in the formalism of AES, and is defined [START_REF]ISO 18115, Surface Chemical Analysis -Vocabulary -Amendment 2[END_REF][START_REF]Standard Terminology Relating to Surface Analysis, Annual Book of ASTM Standards 2006[END_REF] as the probability that Auger electron leaving the surface in a specified direction originated from a specified depth measured normally from the surface into the material. T is a number of ∆z layers within information depth. We omitted here for clarity some constants such as the density of the analysed atoms in a solid, or the probability that the Auger transition follows the ionization. It is rather obvious that the Auger current, J A (α, x), depends in general on beam position, x, since even the same trajectory as, for example, that one seen in figure 2, would cross the Si and Au layers differently if it was moved in x direction by some distance; in a result the number of trajectory segments in ∆z layer merged in Si and their individual lengths as well their summary length would change in general.

Function ϕ was determined by MC simulations [11]. According to frequency concept of probability, function ϕ (i∆z,α) should be a ratio of the number of Auger electrons leaving the sample into direction α and produced in the thin layer ∆z at the depth i∆z, ∆I(i∆z, α), to their total number created in the same layer ∆z, ∆I t (i∆ z):

) ( ) , ( ) , ( z i I z i I z i t ∆ ∆ ∆ ∆ = ∆ ϕ α α (6)
In our MC calculations Auger electrons are generated with a uniform distribution at a certain depth interval. They are assumed to be attenuated exponentially along the trajectory length in a solid. Thus, when an Auger electron represented by j-th trajectory generated at depth i∆z in thin layer ∆z escapes sample with angle α, its contribution to the Auger electron current, for multilayered sample having p material layers perpendicular to its surface, is

= = = - = ∆ ∆ i l m j p l k k l i j l k d z i I 1 1 1 , , , , exp ) , ( λ α

Results and discussion

In the MC calculations the total Auger electron emission current was determined; normal incidence of the beam on a sample has been assumed. The electron beam was assumed to have the diameter of 10 nm and the uniform cross-section. The calculated Auger signal intensity depends on number of factors, between them are, for example, probability of Auger transition, transmission function of the analyzer, detector efficiency etc. It is difficult to determine these factors thus the calculated Auger current intensities are presented in arbitrary units. Besides, we are not interested in absolute Auger signal values but in a shape of the signal versus beam position relation.

Figure 3 presents calculated relation of the Auger signal for Si 92 eV transition (99 eVionization energy) versus electron beam position, x, for the Au|Si(100nm)|Au system for electron primary energies, E p , of 1, 2.5, 5, 10 and 25 keV. We see that the signal is not constant for the Si layer in general, as one could expected. For 5 keV beam energy the minimum is clearly seen, while the maximum is observed for 2.5 keV.

It seems worthwhile to see the relation for various Si layer thicknesses of the Au|Si|Au system.

Figure 4 shows the results for the Si layer thicknesses of 30, 100, 200 and 500 nm for selected primary energy E p =5 keV. We see two minima for the Si layer of thickness 500 nm in contrast to the case of 100 nm.

Before we explain these results qualitatively let us see the relation for the system with element with atomic number larger than Si, between Au layers, for example for copper. Figure 5 presents the results for the Au|Cu(100nm)|Au system for primary energies of 2.5, 5, 10 and 25 keV for Cu 920 eV transition (933 eV -ionization energy). In contrast to the case of Au|Si|Au system, we see no minimum. Additionally in the relation for 5 keV energy we see the maximum. Figure 6 presents the same relation for various Cu layer thicknesses of 30, 100, 200 and 500 nm for the selected primary energy of 5 keV. We see that for thicker Cu layer the Auger current becomes constant, except beam positions at distances less than 50 nm from the Cu|Au interfaces where it decreases when the beam moves to the Au layer.

These results can be explained qualitatively. In ref. [13] we analyzed the dependence of the BY versus beam position for the Au|Si|Au and Au|Cu|Au systems. The BY is a the ratio of the total number of electrons emitted from the sample with energies greater than 50 eV to the total number of electrons incident at a given energy and angle of incidence [START_REF]ISO 18115 Surface Chemical Analysis-Vocabulary, International Organisation for Standardisation[END_REF]. We have found that, depending on the beam position, the BY can have values substantially lower or higher than those corresponding to elements composing the layered sample. This phenomenon is due to differences in the cross sections for electron elastic backscattering on atoms and SP of the elements filling the layers. One could suppose that for different beam positions on a given layer, for which the BYs differ, the corresponding Auger currents should also differ. The reason of such a conclusion is an expectation that the number of ionisations is large where BY is large, because large BY means large number of outgoing electrons which cause atom ionizations in surface region. One must remember however that one should account for only these backscattered electrons which have energy not less than the ionization energy, E i , for the Auger transition of interest. It means that, we should consider the BY not for cutoff energy of 50 eV, but for the energy equal to ionization energy, E i , for respective transition. Let us denote such a BY as a BYE to stress that it is the ratio of the total number of electrons emitted from the sample with energies greater than ionization energy, E i , corresponding to Auger transition of interest, to the total number of incident electrons, N t . Thus we can write the following

= p i E E s t dE E N N BYE ) ( 1 (9)
where N s (E) is the energy spectrum of the electrons scattered on a sample. As far as we know, no analytical expression exists which enable the BYE calculations depending on layer thicknesses of a sample, electron beam position, etc. Thus the MC approach seems to be only reliable theoretical tool.

Let us first consider the Auger signal case of the Si 92 eV transition (E i =99 eV) for the Au|Si(100nm)|Au system for primary energies of 5 keV and 1 keV (see figure 3). For the first energy we observe in figure 3 a clear minimum, but for the second one the signal is practically constant on the Si layer. The corresponding BYEs are presented in figure 7a, and, to facilitate analysis, the related signals are in figure 7b. We see in figure 7a that the BYE on the Si layer for 5 keV (open circles) is smaller than the BYE for uniform Si (denoted by dash line) and maximum deviation reaches 33% at the middle of the layer. We believe that it should have consequence in decrease of ionization number in surface region, thus, in decrease of the Auger electrons. In fact, beam position for which the BYE reaches minimum exactly corresponds with the signal minimum. A different situation is for the case of 1 keV primary energy, because the BYE on Si layer (figure 7a, full squares) almost does not deviate from the BYE for uniform Si (denoted by solid line), except small distances from the Si|Au interfaces, equal or less than diameter of the electron beam (10 nm). It implies that the signal (figure 7b, full squares) is practically constant except mentioned small distances from the interface where the beam starts to enter the Au layer.

It is of interest to understand why for the primary energy of 2.5 keV the AES signal for Si 92 eV transition reaches maximum (see figure 3), in contrast to the signal case with primary energy of 5 keV when it reaches minimum. It is helpful to consider figure 8. In figure 8a, we see the BYE (for the cut-off energy equal to E i =99 eV) versus beam position for the Au|Si(100nm)|Au sample for primary energies of 2.5 keV and, to facilitate comparison, for 5 keV. Figure 8b presents corresponding Auger signals. We see in figure 8a that for the primary energy of 2.5 keV the BYE (open squares) behaves differently from the primary energy case of 5 keV (open circles). When the beam moves to the middle of the Si layer the BYE, for 2.5 keV case, increases (except small region of the beam diameter dimension in vicinity of the Si|Au interfaces), then reaches maximum. In consequence the corresponding signal behaves similar (see figure 8b, open squares), and reaches maximum at the middle of the Si layer. One may say that the shape of the signal run on the Si layer reflects itself in the corresponding BYE.

It seems rather obvious that the Si 92 eV signal is also observed when the beam impinges at the Au layer, not too far from the Au|Si interface (see figure 3), since backscattered electrons in the Au layer may penetrate the Si one and cause its atoms ionizations. Thus, it is understandable that for higher primary electron energy slower decrease of the Si 92 eV signal on the Au layer takes place with the increase of the beam distance to the Au|Si interface. The higher primary energy means greater possibility of electron penetration from the Au layer into the Si one where it can bring about the Si 92 eV transitions. When analyzing such a AES image one may ask where there is position of the material interface. We propose tentatively the inflection point of the image as an approximate position of the interface. Similar analysis as above can be performed for the case of the Au|Cu|Au system. For example, the fact that the Cu 920 eV signal for the primary energy of 5 keV (figure 5, open circles) has maximum but the signal Si 92 eV for the Au|Si|Au system (figure 3, open circles) for the same primary energy has minimum can be readily explained with the help of figure 9a. However, some comments may need differences in runs of the signals Si 92 eV for the Au|Si(500nm)|Au system (figure 4, stars) and Cu 920 eV for the Au|Cu(500nm)|Au system (figure 6, stars) at the same primary energy of 5 keV, because the former has two minima, the latter has no minimum. The Cu 920 eV signal, in contrast to the Si 92 eV one, diminishes when the beam incident on middle layer approaches the interface. Figure 9b In almost all beam positions on the Cu layer the BYE is constant apart from the beam distances to the interface less than about 50 nm where it diminishes approaching the interface (except distance less than beam diameter); in result the Cu 920 eV signal (figure 6, stars) behaves similar to the BYE. Though we see increase of the BYE on the Cu layer (figure 9a, full squares) when the beam approaches interface, in its close vicinity, we do not see subsequent increase of the corresponding Cu 920 eV signal since the BYE increase starts when the beam distance to the interface reaches values less than the beam diameter (10 nm). Thus only diminishing fraction of the beam generates signal; in consequence the signal diminishes.

Conclusions

We performed the MC simulation of electron transport for selected exemplary systems with layers perpendicular to the surface. The layer materials were elemental solids with high, medium and low atomic numbers, i.e. Au|Cu|Au and Au|Si|Au. For these systems the calculations of the Auger current versus beam position were performed. We found that, for system with layers filled by elements of considerably different atomic numbers, the relation can have unexpected extremes. This observation can turn out to be important in analysis of SAM pictures.

Figure captions

  th segment of the j-th trajectory in l-th perpendicular layer, starting at depth i∆z (starting within the material layer of interest), and emerging from sample in α direction; the l-th perpendicular layer of material is crossed by the j-th trajectory k l times; λ l is the respective IMFP for a material filling the l-th perpendicular layer. m i is a number of trajectories of Auger electrons generated in layer ∆z at deph i∆z. Thus, it follows that

  figure 9b (filled squares). In almost all beam positions on the Cu layer the BYE is constant apart from

Fig. 1 .

 1 Fig. 1. Example of the electron trajectory in a layered sample with layers perpendicular to its surface.

Fig. 2 .

 2 Fig. 2. Example of a j-th trajectory crossing a very thin ∆z layer at depth i∆z. This trajectory has four

Fig. 3 .

 3 Fig. 3. Auger signal (Si 92 eV) versus electron beam position for the Au|Si|Au sample for various

Fig. 4 .

 4 Fig. 4. Auger signal (Si 92 eV) versus electron beam position for the Au|Si|Au sample for various Si

Fig. 5 .

 5 Fig. 5. Auger signal (Cu 920 eV) versus electron beam position for the Au|Cu|Au sample for various

Fig. 6 .

 6 Fig. 6. Auger signal (Cu 920 eV) versus electron beam position for the Au|Cu|Au sample for various

Fig. 7 .

 7 Fig. 7. The BYE (a) and corresponding Auger signal (Si 92 eV) (b) vs primary electron beam position

Fig. 8 .

 8 Fig. 8. The BYE (a) and corresponding Auger signal (Si 92 eV) (b) vs primary electron beam position

Fig. 9 .

 9 Fig. 9. BYE corresponding to Si 92 eV and Cu 920 eV transitions versus primary electron beam

Fig. 1 .

 1 Fig. 1. Example of the electron trajectory in a layered sample with with layers perpendicular to its

Fig. 2 .

 2 Fig. 2. Example of a j-th trajectory crossing a very thin ∆z layer at depth i∆z. This trajectory has four

Fig. 3 .

 3 Fig. 3. Auger signal (Si 92 eV) versus electron beam position for the Au|Si|Au sample for various

Fig. 4 .

 4 Fig. 4. Auger signal (Si 92 eV) versus electron beam position for the Au|Si|Au sample for various Si

Fig. 5 .

 5 Fig. 5. Auger signal (Cu 920 eV) versus electron beam position for the Au|Cu|Au sample for various

Fig. 6 .

 6 Fig. 6. Auger signal (Cu 920 eV) versus electron beam position for the Au|Cu|Au sample for various

Fig. 7 .

 7 Fig. 7. The BYE (a) and corresponding Auger signal (Si 92 eV) (b) vs primary electron beam position

Fig. 8 .

 8 Fig. 8. The BYE (a) and corresponding Auger signal (Si 92 eV) (b) vs primary electron beam position

Fig. 9 .

 9 Fig. 9. BYE corresponding to Si 92 eV and Cu 920 eV transitions versus primary electron beam


Vitezslav Stranak
email: stranv00@physik.uni-greifswald.de

Marion Quaas

Robert Bogdanowicz

Hartmut Steffen

Harm Wulff

Zdenek Hubicka

Milan Tichy

Rainer Hippler

Effect of nitrogen doping on TiO x N y thin film formation at reactive high-power pulsed magnetron sputtering

Keywords: TiOxNy, HIPIMS, time resolved optical emission spectroscopy, thin film diagnostic (XRD, XPS, spectroscopic ellipsometry) PACS: 52.25.Jm, 52.70 82.80.Pv

The paper is focused on a study of formation of TiO x N y thin films prepared by pulsed magnetron sputtering of metallic Ti target. Oxygen and nitrogen were delivered into the discharge in the form of reactive gases O 2 and N 2 . The films were deposited by high-power impulse magnetron sputtering working with discharge repetition frequency f = 250 Hz at low (p = 0.75 Pa) and high (p = 10 Pa) pressure. The substrates were on floating potential and thermally stabilized at room temperature during deposition process. Post-deposition thermal annealing was not employed. The chemical composition from XPS diagnostic reveals formation of TiO x N y structure at low flow rate of oxygen in the discharge gas mixture. This result is confirmed by XRD investigation of N elements incorporation into the Ti-O lattice. Decrease of band-gap to values Eg ∼ 1.6 eV in TiOxNy thin film is attributed to formed Ti-N bonds. The discharge properties were investigated by time-resolved optical emission spectroscopy. Time evolution of particular spectral lines (Ar + , Ti + , Ti) is presented together with peak discharge current.

Introduction

Titanium oxide is well known as a photocatalytic material since 1970s [1]. Photocatalytic activity together with other interesting features (high adhesion, hardness, refractive index, transparency, high dielectric constant, semiconducting properties) makes TiO 2 a promising coating material. However, photocatalytic efficiency of pure TiO 2 after irra-diation by solar spectrum is very low. Because of high energy band-gap of TiO 2 only the UV part of the solar spectra (< 5 % of solar energy) is able to initiate photocatalytic reactions. Hence, the photocatalytic reactions are strongly reduced in locations with limited UV radiation, e.g. in rooms, etc.

The photocatalytic activity of TiO 2 can be improved by doping. Two basic group of dopants can be used: (i) cations of transition metals such as Fe, Ni, Cr, Mn, V, Ag, Au, which can increase absorption of visible spectra but usually suffer from thermal instability [2][3][4][5][6], and (ii) non-metal anion such as N - [7][8][9][10], C - [11], S - [12], F - [13], which shift the band-gap towards lower spectral frequencies. Among the doping elements, N was found to be most effective because (i) nitrogen has comparable ionic radius to oxygen and (ii) the p states of N contribute to bandgap narrowing by mixing with O 2p states [9,14].

Various deposition techniques, e.g. pulsed laser deposition (PLD) [15][16][17], sol-gel methods [18][19][20], ion-assisted electron beam evaporation [21,22], magnetron sputtering [10,[23][24][25][26][27][28][29][30][31][32][33][34] have been employed to prepare TiO x N y thin films. Owing to its numerous advantages, magnetron sputtering deposition is a well established method for coating which has been already extended to the industry. Nevertheless, deposition of crystalline TiO x N y by dc magnetron sputtering method is difficult and the process must be usually followed by thermal annealing [10,18,23,25,28] or high discharge current during deposition is applied [25,26]. However, nowadays, there is a growing need to deposit photocatalytic films on plastic, i.e. heat sensitive, materials. Hence, post-deposition thermal annealing excludes conventional dc magnetron sputtering as a method for industrial coating of TiO x N y thin films.

Dc magnetron sputtering was successfully combined with reactive gas pulsing process to get crystalline TiO x N y without thermal annealing [29][30][31]. With the same purpose Herman et al. employed dc pulsed dual magnetron working with repetition frequency 100 kHz and duty cycle 50 % [34]. The method of pulsed magnetron sputtering at medium frequencies was developed in [35] and lastly reviewed in [36]. However, an other method of pulsed magnetron sputtering, so-called HIgh Power Impulse Magnetron Sputtering (HiPIMS) [37][38][39][40][41] is a promising coating technique. Because of high power pulse density (∼ kW/cm 2 ) HiPIMS is suitable for deposition of oxides in particular phases at low (room) temperature as was shown in [42][43][44]. In spite of this fact HiPIMS technique has not been yet tested for deposition of TiO x N y thin films.

The main goal of our investigation is focused on deposition and formation of TiO x N y films by HiP-IMS at room temperature. The basic properties of thin films (chemical composition, crystallography, optical properties) are discussed together with comprehensive plasma diagnostic by optical emission spectroscopy.

Experimental details

Thin film deposition

Thin TiO x N y films were prepared by pulsed planar magnetron sputtering operated in HiPIMS conditions. A detailed description of the experimental setup can be found in our previous papers, see [42,45].

The commercial planar magnetron by Gencoa (Gencoa, Liverpool, UK), operated in unbalanced mode, is employed as a sputtering source. The source was equipped by a Ti target 50 mm in diameter. The sputtering source is situated in the lower part of a spherical-shaped stainless-steel UHV chamber. The vacuum chamber is pumped out by turbomolecular pump down to ultimate pressure 10 -6 Pa. The working pressure is adjusted by a throttle valve installed between the chamber and the pump. The flow rates of working gases are controlled by MKS flow controllers.

The discharge was excited using a combination of dc power supply AE MDX500 (Advanced Energy, Fort Collins, CO) with range down to -620 V designated for continuous regime and a power switch based on charging of large capacitors during idle part of the pulses. The switch was activated by a signal from waveform generator Agilent 33120A (Agilent, Santa Clara, CA). The generator served for triggering of time-resolved measurements as well. A ballast resistor (R = 2.1 Ω) serving as dummy load without magnetron discharge was inserted in series with the magnetron cathode path. Instant discharge current was calculated from the difference between voltage waveforms, measured by oscilloscope Tektronix TDS1012 (Tektronix, Richardson, TX), directly on the cathode U c and on serial connection of resistor R and cathode U c+R using Ohm s law.

Parameters of TiO x N y film deposition process are summarized in Table 1. The flow rates for Ar and N 2 were kept constant while the flow rate of O 2 was varied to get different stoichiometry of thin film composition. Mean discharge current was kept constant (I m = 400 mA) for all experiments. The pulsemodulated discharge was operated with frequency f = 250 Hz and pulse width t a = 150 µs.

The substrate holder was on floating potential and cooled by circumfluent water during the deposition. The temperature, measured by a thermocouple situated at the substrate holder plate, was stabilized at ∼ 40 • C. However, the temperature of the substrate surface/growing film is expected higher as studied e.g. in [46]. The time of deposition was 90 minutes. Films were deposited on polished Si(100) wafers. The thickness of the film was roughly about ∼ 100 nm (estimated from XR and SE measurements), i.e. deposition rate 1 -1.5 nm/min. Resputtering effect of the deposited film is completely neglected because of apparent deposition rate. The adhesion of the films on the substrate was very good and no bubbles or grains were observed.

Time-resolved plasma diagnostic

Pulse-modulated discharge was investigated using optical emission spectroscopy. The measurements were performed by Shamrock SR500D spectrometer (focal length 500 mm) equipped with iCCD detector iStar DH740I both by Andor (Andor Technology, Belfast, Northern Ireland). The spectrometer was equipped with three gratings 300, 1200 and 2400 lines per milimeter. The wavelength resolution of the spectrograph (∼ 0.1 nm) is sufficient to allow accurate evaluation of measured data. The optical fibre, connected with the spectrometer, was built directly into the vacuum chamber. The fiber was placed at a distance of 65 mm from the target surface, i.e. in the position of substrate holder. The range of scanned spectra were λ = (200-850) nm. The pulse generator Agilent 33120A provided triggering signal for iCCD. The measured spectra were analyzed by Spectrum Analyzer 1.7 [47].

Thin film characterization

Grazing incidence x-ray diffraction (GIXD, asymmetric Bragg case) measurements were done to determine the phase composition of deposited films, the respective methods are described e.g. in [START_REF] Wulff | Characterisation of thin films[END_REF]. All measurements were performed using Θ-2Θ-Diffractometer Siemens D5000 (Bruker AXS GmbH, Karlsruhe, Germany) with Cu Kα radiation (40 V, 40 mA). The scanned 2Θ range was 20 to 50 • at constant incidence angle ω = 1.0 • . The Powder Diffraction File was used to assign the measured x-ray reflections and identify the crystallographic phases [START_REF]Powder Diffraction File[END_REF]. From XR measurements we can conclude that the films are homogeneous because XR data can be very well fitted with a model with assuming constant film density.

The chemical composition of the thin films was investigated by x-ray photoelectron spectroscopy (XPS). The analyses were performed on an AXIS Ultra x-ray photoelectron spectrometer (Kratos Analytical, Manchester, UK) with a monochromatic Al K α x-ray source at 150 W (15 kV, 10 mA). A survey scan from 0 to 1200 eV was mapped with a pass energy of 80 eV. For high resolution measurements of the Ti 2p peak a pass energy of 10 eV was used. The quantification was done from the measured area of the XPS peaks, considering atomic sensitivity factors (ASF) given by the producer. The program package CasaXPS 2.3.15 was used for characterization. The validity of the ASF was checked by measuring samples of given composition (SiO 2 and TiO 2 ). Gaussian + Lorentzian functions with relation 30:70 % were employed for fitting the measured data. Shirley background was used for fitting of Ti 2p XPS peaks.

Ellipsometric investigations were carried out using a phase modulated ellipsometer Jobin-Yvon UVISEL (HORIBA Jobin-Yvon Inc, Edison, NJ) in the 1.8 eV -4.8 eV photon energy range at an angle of 70 • , due to Brewster's angle of Si wafer substrate. Angles ∆ and Ψ were analyzed using twolayers model based on TiO x N y and Si substrate. The optic indices of Si were obtained from the database [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF]. The complex dielectric function of TiO x N y was composed of Tauc-Lorentz and Cody-Lorentz oscillators [25,26]. Finally, the model was fitted to the experimental data using Levenberg-Marquardt nonlinear least-squares algorithm. The fitting measure mean square error (MSE) was used for verification of ability of the applied model to fit the experimental data [START_REF] Tomkins | Spectroscopic ellipsometry and Reflectometry[END_REF]. Band-gap energy E g was obtained by extrapolating the linear portion to the photon energy in α vs. E(hν) graph, where α is the absorption coefficient.

Results and discussion

Time-resolved diagnostics of plasma discharge

The overview spectrum of Ar/N 2 +O 2 discharge, shown in Fig. 1, mostly consists of the atomic lines of Ar, Ar + , Ti, Ti + , O, molecular bands of NO γ (A 2 Σ + -→ X 2 Π) system, which was not observed in the dc-mode, and of the N 2 first and second positive systems

(B 3 Π g -→ A 3 Σ + u , C 3 Π u -→ B 3 Π g ).
We observed strong N 2 bands in the spectrum but only one weak emission series of N (λ N = 821.1-821.6 nm) was recognized (studied in [START_REF] Wang | [END_REF]). Intensity of N lines was roughly three times higher in HiPIMS than in dc mode operated with the same experimental parameters and discharge current. However, we can expect presence of N atoms in the discharge volume as it was already demonstrated in [53]. In the reported experiments the N density, measured by mass spectrometry, reached the order of magnitude 2-4 × 10 18 m -3 at pressure about 2 Pa. The reactor consists of inductively coupled plasma source fed by argon, nitrogen and sputtered Ti. Hence, we suppose that in our case weak N lines in UV-VIS range of the spectrum are probably overlapped by other inten- sive lines or disappear in the background of noise.

The spectra and intensities of particular spectral lines are affected by the amount of reactive component O 2 added into the discharge. As expected, the intensity of atomic oxygen line (λ O = 777 nm) depends nearly linearly on the amount of added O 2 , see Fig. 2. The intensity of the N 2 2 nd positive system (λ N2-SPS = 357 nm) is observed almost constant for higher O 2 flow rates (F O2 = 0.5 -10 sccm). It means that the rate of N 2 excitation in the discharge volume is not significantly effected by oxygen in the plasma. An increase of the NO γ system (λ NO γ = 227 nm) was observed with increasing of oxygen partial pressure. It was shown in works [START_REF] Ricard | Reactive plasma. Sociate Francaise du Vide[END_REF][START_REF] Gordiets | [END_REF][56] that NO is preferentially produced as a result of nitrogen and oxygen reaction.

Time evolution of discharge current is shown in Fig. 3. The discharge current was calculated, using Ohm s law formula, from the voltage drop measured by oscilloscope on the ballast resistor (the method is described in detail in our earlier papers [43,45]). Time evolution of I D shown in Fig. 3 is typical for low pressure (p = 0.75 Pa) and slightly oxidized gas mixture. Peak discharge current reached about I p ≈ 23 A which corresponds to peak power of about P p ∼ 14.3 kW.

Discharge current is influenced by partial O 2 pressure. This phenomena can be explained by emission of secondary electrons induced by ion bombardment of oxidized cathode/target; the ion induced secondary electron emission coefficient is higher for oxides than for pure metal [42,58]. In this way, at p = 10 Pa and highly oxidized gas mixtures, the peak discharge current reaches maximum values I D ≈ 55 A (i.e. P p ∼ 34 kW) at time t a ≈ 130 µs after discharge ignition (not presented in the figure). Time evolution of peak discharge current and normalized intensities of particular Ar + (λ Ar+ = 487 nm), Ti (λ Ti = 390 nm) and Ti + (λ Ti+ = 335 nm) lines is shown in Fig. 3, too. The Ar + starts to develop as the first followed by Ti or Ti + lines, respectively. Similar features were also observed in a two-component (Ti target, Ar atmosphere) HiPIMS system, where evolution of gas and metallic ions was measured by energy resolving quadrupole spectrometry [59]. Increase of pressure, p =10 Pa, or oxygen flow results in a slower evolution of emitted lines.

The ratio of the measured relative intensities I Ar+ /I Ti ∼ 0.6 is more or less constant in the first half of the pulse width. This effect probably corresponds to re-sputtering of TiN film from the target surface poisoned by nitrogen (Y TiN = 0.43 for Ar + , Y TiN = 0.37 for N + ion energies of 500 eV [60]). After removal of the nitride film from target surface, the ratio of intensities decreases if the amount of oxygen in the discharge is low: F O2 0.5 sccm. Such effect is caused by higher sputtering yield of pure metallic target surface (Y Ti = 0.63 for Ar + , Y Ti = 0.46 for N + for ion energies of 500 eV [60]).

The effect of target poisoning was studied by measurements of hysteresis loops [61][62][63] and XPS anal- ysis of the target surface after discharge operation. Since the N 2 with higher partial pressure was used for all experiments the target surface can be considered as TiN. When O 2 was added into discharge atmosphere we observed transition of target state mode from -nitride to -oxynitride indicated by an increase of cathode voltage and also verified by measurement of the target surface composition. We observed broader hysteresis loops for poisoning of pure Ti than TiN target surface by oxygen. The poisoning transition was observed for oxygen flow rate F O2 = 0.5 -1.1 sccm. For oxygen flow higher than 1.1 sccm target becomes fully poisoned and intensity of Ti line rapidly decreases, i.e. I Ar+ /I Ti > 1, due to lower sputtering yield of oxides (Y TiO x = 0.015 for Ar + ion energy of 300 eV [64]). After target poisoning the intensities of gas as well as metal atoms/ions became virtually constant (not shown in the figure).

The time development of the intensity of Ti + line (λ Ti+ = 335 nm) is shown in Fig. 3, too. The positive Ti + ions are created by ionization of sputtered Ti atoms in plasma volume. Owing to lower ionization potential (E Ti = 6.82 eV) Ti atoms are preferentially ionized in comparison to Ar (E Ar = 15.78 eV). The preferential ionization of titanium can explain the intensity decrease of Ar + line while intensities of Ti and Ti + remain constant.

Chemical composition -XPS measurements

The nitrogen content of the films was determined by XPS methods. Fig. 4 shows the element composition of samples deposited at constant pressure (p = 0.75 Pa) and nitrogen flow (F N2 = 20 sccm). The flow rate of oxygen was varied. Thin films consist of Ti, N and O elements. Owing to surface contamination also impurities (mainly carbon) are detected. The content of impurities reached roughly 25 % of the total film composition (not included in Fig. 4). The high impurity/carbon concentration is caused by surface contamination during the transfer of the samples to XPS device. However, we can exclude the presence of TiC structure in the film because C 1s peak does not contribute any TiC.

A decrease of nitrogen content is observed for increasing the O to N ratio for particular deposition of thin films at low pressure, see Fig. 4. At higher pressures there is nearly no change in element composition caused by changing the ratio of the reactive gases in the discharge. Obviously, there is a preferred incorporation of oxygen into the growing film. If a sufficient amount of oxygen is present in the discharge volume, nitrogen is virtually not incorporated. With increasing oxygen flow not only the intensity of the N 1s peak, but also the contributions of TiN to the nitrogen 1s spectrum decreases while O 1s increases.

This observation is confirmed by high resolution measurements of the Ti 2p peak. Fig. 5 shows the Ti 2p peak of the film deposited at p = 0.75 Pa with F O2 = 0.2 sccm oxygen flow. We have to assume three possible bindings to fit the measured profile. The 2p Ti peak was fitted using three contributions: 458.5 eV, 457.1 eV and 455.7 eV correspond to Ti(IV) 2p 3/2, Ti(III) 2p 3/2 and Ti(II) 2p 3/2, respectively. The other three functions in the Fig. 5 correspond to 2p 1/2 peak. Unfortunately, TiO and TiN cannot clearly be distinguished, because both bindings contribute to the Ti(II) peak. The formation of TiO 2 can be attributed to surface oxidation on the film top during transport of the sample from the vacuum chamber to the XPS device in air as was already mentioned. With increasing oxygen ratio the amount of Ti(III) and Ti(II) components is decreasing. For oxygen flow F O2 > 1 sccm (Fig. 5) the Ti 2p region shows only two peaks which belong to Ti(IV) 2p 3/2 and 1/2 peaks. Because of negligible content of N in the film, the peak at Ti(II)/Ti(III) position was not detected. Occasional observation of weak nitrogen traces is attributed to surface contamination. Hence we can conclude that only TiO 2 is formed for higher oxygen flow rates.

Crystallographic phase composition -XRD measurements

XRD measurements were performed to get information about the phase composition of the layers. As expected from the XPS measurements, TiO/TiN as well as TiO 2 phases are observed (Fig. 6) as a function of particular experimental conditions. Thin films deposited at high oxygen flow rate (F O2 ∼ 10 sccm) consist of TiO 2 , which is found to be x-ray amorphous for high deposition pressure (p ∼ 10 Pa) or forms rutile phases at low pressure (p ∼ 0.75 Pa), respectively. The deposition of x-ray amorphous films at 10 Pa is probably due to lower energy transfer to the growing layer caused by increased number of particle collisions in plasma [42,43,46].

Fcc TiX (where X = O or N) is found at low oxygen flow. However, it is difficult to distinguish between TiO and TiN phases by x-ray diffractometry. Both structures show a cubic face centred Ti sublattice with oxygen or nitrogen incorporated in octahedral sites. Octahedral sites are filled completely if the ratio X/Ti = 1. This ratio can vary between 0 -1 as a function of different deposition condition [65][66][67][68]. However, the lattice constant depends on the amount of octahedral sites filled by anions and, of course, also on the incorporated elements. Hence it is impossible to determine both type of elements and the amount of incorporated atoms only from the lattice constant measurement by XRD technique. Because both N and/or O are incorporated and we do not know the ratio of O/N Vegards law can not be used. Hence, for our films we assume incorporation of both oxygen and nitrogen into the Ti lattice. This assumption is confirmed by XPS measurements. Their composition is therefore referred as TiO x N y .

For the samples prepared at low pressure the peak positions of TiO x N y are shifted towards lower angles compared to layers deposited at higher pressure. This implies larger lattice constants, i.e. a higher amount of incorporated interstitial atoms. The attain lattice constants determined from peak position are 4.23 Å for p = 0.75 Pa and 4.15 Å for p = 10 Pa. Theoretical lattice constants values are a TiN = 4.242 Å and a TiO = 4.185 Å. However, all deposited crystalline phases show comparably small grain sizes. Thus we assume x-ray amorphous amounts of TiO/TiN or TiO 2 to be present within the films, too.

Energy band-gap -spectroscopic ellipsometry

Spectroscopic ellipsometry (SE) was employed to investigate the optical properties of deposited TiO x N y thin films, namely the energy band-gap E g and refractive index n. If the flow rate of oxygen is decreased, E g is decreased, too -see Fig. 7. Similar behaviour of energy band-gap was observed in [25] as well. The lowest values of E g ≈ 1.7-2.1 eV are related to TiO x N y structure with incorporated nitrogen into the Ti-O lattice as described above. The highest values of band-gap energy E g ≈ 3.2 eV were measured for highly oxidized gas mixtures with oxygen flow ≥ 1 sccm independent of the total pressure. This value corresponds with band gap of TiO 2 [69].

The band-gap is related to the refractive index by semi-empirical relation known as Moss rule [70,71]), n 4 •E g = const., where const. = 95 eV. Comparison of refractive index values estimated from SE measurements for λ =500 nm and by Moss rule employing E g is displayed in Fig. 7. Crystalline phase of TiO x N y shows higher values of refractive index n. A shift of maxima of n(λ) distribution towards lower photon energies compared to TiO 2 prepared at high oxygen flow rate (not presented in the figure) was also observed.

The explanation of such behaviour was proposed in [25]. It is based on former research of Futsuhara et al. [72] who found that the band-gap is related to the difference in ionicity of metal-O and metal-N bonds. The electronegativity of oxygen is larger than that of nitrogen, which indicates that the Ti-O bonds involve a larger charge transfer than Ti-N bonds. Assuming that both, Ti-O as well as Ti-N, bonds coexist in the films, the shift of the bandgap to lower energy can be attributed to a decrease of ionicity due to formation of Ti-N bonds at lower oxygen flow rate.

Conclusion

The formation of TiO x N y by HiPIMS without post-deposition thermal annealing is proved in this report. The formation of TiO x N y is conditional to low partial pressure of nitrogen in (Ar)-N 2 -O 2 reactive discharge atmosphere. If sufficient amount of oxygen is present in the discharge volume, x-ray amorphous TiO 2 (at higher pressure p = 10 Pa) or rutile phase of TiO 2 (at lower pressure p = 0.75 Pa) is formed. Local domains of TiN and/or TiO with fcc structure are formed at low flow of oxygen F O2 < 0.5 sccm. The Ti-N bonds that exist in TiO x N y structure are responsible for a decrease of the energy band-gap to the value E g ≈ 1.7-2.1 eV and an increase of the refractive index n. The refractive index estimated from SE measurements corresponds very well to the values determined from semi-empirical Moss rule.

Fig. 1 .

 1 Fig. 1. Overview of the spectrum measured in Ar discharge with O 2 and N 2 reactive admixtures. Experimental conditions: p = 0.75 Pa, F Ar = 20 sccm, F N2 = 10 sccm and F O2 = 0.4 sccm. The spectrum was recorded at t a = 50 µs after discharge ignition.

Fig. 2 .

 2 Fig. 2. Plot of intensities of atomic line O and molecular bands of systems N 2 2 nd positive and NOγ vs. amount of O 2 added in the discharge. Experimental conditions: p = 0.75 Pa, F Ar = 20 sccm, F N2 = 10 sccm. Intensities were estimated from spectra recorded at ta = 50 µs after discharge ignition.

Fig. 3 .

 3 Fig. 3. Time evolution of peak discharge current I D (black line, left axis) and intensities of atomic spectral lines of Ar + (λ Ar+ = 487 nm), Ti (λ Ti = 390 nm) and Ti + (λ Ti+ = 335 nm) during the pulse width (right axis). Experimental conditions: p = 0.75 Pa, F Ar = 20 sccm, F N2 = 10 sccm and F O2 = 0.4 sccm.

Fig. 4 .

 4 Fig. 4. Chemical composition of TiOxNy -Ti, O and N elements are shown. The chemical content is normalized to 100 % -the absent content of elements belongs to impurities (mainly introduced by C) roughly about 25 %. Experimental conditions: p = 0.75 Pa, F Ar = 20 sccm, F N2 = 10 sccm.

Fig. 5 .

 5 Fig. 5. Ti 2p peaks measured by high resolution XPS measurements of film deposited under pulsed magnetron sputtering conditions: f = 250 Hz, t a = 150 µs, p c = 0.75 Pa. Upper graph: The Ti 2p 3/2 peak of film deposited at low oxygen flow F O2 = 0.2 sccm. The measured data are fitted by three functions Ti(IV), Ti(III) and Ti(II); Lower graph: The Ti 2p 3/2 peak of film deposited at high oxygen flow F O2 = 10 sccm. The data were fitted only by one function corresponding to Ti(IV).

2 Fig. 6 .

 26 Fig.6. The XRD patterns of deposited thin films at different experimental conditions. As a TiO x N y were identified x-ray peaks of films prepared at low flow rate of O 2 . The TiO x N y peaks of XRD patterns for p = 0.75 Pa and 0.2 sccm (green line) are shifted towards lower angles because of lower oxygen/nitrogen contents in the film composition. At higher F O2 rutile or TiO 2 x-ray amorphous films are formed.

Fig. 7 .

 7 Fig. 7. Energy band-gap and refractive index as a function of the amount of O 2 in the discharge for different discharge pressure: p = 10 Pa (upper panel), p = 0.75 Pa (lower panel). The full circle symbols represents refractive index calculated from SE measurement at λ = 500 nm. The open circle symbols represents refractive index calculated from the Moss rule using values of the band-gap.

Table 1

 1 Overview of experimental conditions during deposition of TiOxNy thin film using pulse-modulated discharge.

	abbreviation	value	description
	p	0.75 and 10 Pa	pressure
	F Ar	20 sccm	flow rate of Ar
	F N2	10 sccm	flow rate of N 2
	F O2	0.2-10 sccm	flow rate of O 2
	f	250 Hz	discharge frequency
	ta	150 µs	pulse width
	Vm	370-620 V	cathode voltage
	Im	400 mA	mean discharge current
	I D	23-55 A	peak discharge current
	i D	0.5-1.2 A/cm 2	peak current density
	Pp	0.3-0.7 kW/cm 2	peak power density

Acknowledgements

This work was supported by Deutsche Forschungsgemeinschaft through SFB/TR 24. Further projects KAN301370701, M100100915 of ASCR and research plan 1M06002 of Ministry of Education, Youth and Sports of the Czech Republic are acknowledged.