Effect of Al and Ta Impurities on Si Adsorption on (001) and (111) Surfaces of B1-TiN

1. Introduction

The application of wear resistant coatings is one of the most effective ways to improve the performance of structural and functional materials in various applications. In recent decades, coatings based on hard metal nitrides have been increasingly used to increase the resistance of structures and tools to wear [1,2], corrosion [3,4,5] and oxidation [6,7]. This has found applications in the automotive and aerospace industries [8,9], in the manufacture of cutting tools [10], and even in biomaterials [11]. Unfortunately, the coatings used are not always able to meet the growing demands placed on them. For example, the use of dry high-speed machining with a cutting tool, which ensures cost reduction and increased productivity [12], has created new requirements for increased resistance to oxidation and wear at temperatures above 1100 K [13].

A promising solution to this problem is the use of multicomponent coatings and multilayer compositions based on them. Coatings based on transition metal nitrides are best suited for this purpose. By adding various alloying impurities to such coatings, it is possible to effectively control their properties. For example, the addition of Al to TiN coatings, as proposed by Münz [14], ensures the preservation of high values of hardness and wear resistance up to temperatures of 900-950°C, and also significantly increases their resistance to oxidation (from 500°C to 800°C) [15,16,17]. At the same time, their fracture toughness (crack resistance) decreases at temperatures above 800°C due to the spinodal decomposition [18] of the metastable supersaturated solid solution Ti_1−xAl_xN into cubic domains enriched with TiN and AlN. The metastable cubic domains c-AlN are then transformed into a stable hexagonal wurtzite phase w-AlN with a volume increase to ~24% [19,20]. This leads to a decrease in the hardness of Ti_1−xAl_xN [15] and the formation of microcracks that accelerate oxygen diffusion, thereby reducing the oxidation resistance of the coatings [21]. In addition, Ti_1−xAl_xN is completely oxidized at 1000°C [22]. All this has stimulated an intensive search for ways to improve the properties of the Ti-Al-N system over the last two decades.

Intensive studies on the influence of three-, four- and five-valent alloying elements of the IIIB-VIB groups (X = Y, Zr, Hf, V, Nb, Ta, etc.) [21,23,24,25,26,27,28,29,30,31,32,33,34,35] on the thermal and oxidation resistance of Ti_1−x−yAl_xX_yN coatings have shown that the most promising alloying element is the pentavalent element, Ta. Ta doping increases the thermal stability of Ti_1−x−yAl_xX_yN by increasing the formation temperature of the w-AlN wurtzite phase by ~200-300°C (up to ~1200°C) [26]. Similar results were reported by Koller et al. [27]. As shown by ab initio calculations [26], the main reason for this is the increase in cohesive energy of Ti_1−x−yAl_xX_yN with increasing concentration of Ta substituting Ti and Al due to the increased covalency (sp³d² hybrid orbitals) and metallicity (t_2g orbitals), as well as the higher activation energy of diffusion of Ta compared to Ti and Al. According to calculations [36], Ta doping of Ti_1−xAl_xN solid solutions significantly reduces the ionicity of Al-N bonds, preserves the covalency of Ti-N bonds, and generally increases the metallicity of the chemical bond with increasing Ta concentration. In this case, the increase in metallicity is not only due to Ta-Ta bonds, which make the main contribution, but also to Ta-N bonds of covalent-metallic type. In addition, Ta significantly increases the fracture toughness (crack resistance) and consequently the oxidation resistance of the solid solution [28,29,37,38]. It is well known that an increase in the metallicity of the bonds usually means an increase in the fracture toughness of the material. Thus, in general, Ta alloying significantly increases the wear resistance of coatings based on the Ti_1−xAl_xN system [39,40,41], makes Ti_1−x−yAl_xX_yN coatings more compact, with a finer columnar structure [42].

However, when making protective coatings of Ti_1−x−yAl_xX_yN, it should be noted that a significant increase in Ta concentration leads to a decrease in the average strength of not only Ta-N bonds, but also Al-N bonds [38], and thus to a decrease in the overall strength of coatings and alloys based on such solid solutions, as well as fracture toughness and oxidation resistance [42,43,44,45,46]. It has also been shown that at the microscopic level, Ti-Al-Ta-N coatings with high Ta content consist of large columnar grains with straight boundaries [46]. Under cyclic loading, this can lead to cracking and rapid oxygen diffusion within the coatings at elevated temperatures.

A logical solution to this problem, more suitable for mass production, would be the formation of nanocrystalline structure by dynamic self-assembly during the growth of coating films. This idea was first realized by Shizhi et al. [47] and developed in a series of works by Veprek et al. [48,49,50,51] for a model system consisting of immiscible compounds TiN and Si₃N₄ [52].

During film growth at elevated temperatures, the immiscibility of TiN and Si₃N₄ compounds leads to strong surface segregation and the formation of a nanostructure of small TiN grains encapsulated in multiple monolayers (ML) of amorphous Si₃N₄ (a-Si₃N₄) tissue phase. This occurs dynamically as segregation of Si_zN on the surface of the TiN grains prevents their growth by forming encapsulating layers of the amorphous a-Si₃N₄ tissue phase, which in turn causes TiN to segregate on the surface of the Si_zN layer, nucleating a new grain. Repeated many times, this process results in a significant refinement of the TiN grains (3-4 nm), accompanied by a significant increase in their hardness (>45 GPa) [53].

Despite the rather long history of the study of the model pseudobinary nanocomposite nc-TiN/a-Si₃N₄ system, there are still many unresolved issues of both purely scientific (academic) and applied importance, such as the structure and properties of its interface, which critically determine the strength and other performance characteristics. The importance of this problem is evidenced by the large number of scientific publications each year. In addition, attempts have been made to study more complex multicomponent nanocomposite systems based on the binary TiN compound, for example with an admixture of Al or Ta (Ti-Al(Ta)-Si-N systems), in order to improve its useful operational properties, as mentioned above. However, it is only recently that several experimental works [54,55,56] dedicated to the study of nanocomposite systems based on Ti-Al-Ta-Si-N solid solution have appeared.

The vast majority of the works mentioned above are devoted to the experimental study of the processes of formation and growth of protective coatings based on the binary TiN compound, as well as to the study of their properties depending on the elemental composition and atomic structure. Meanwhile, there is a large body of literature devoted to the study of the systems of interest to us on the basis of first-principles calculations in the framework of density functional theory. These works can be roughly divided into two major groups: studies of the coating growth processes and studies of the properties of the coating-substrate interface, and in particular the structure of the Si_zN tissue phase. It should be noted that there are at least two detailed reviews [57,58] of the results of first-principles studies, as well as studies performed in the framework of the immersed atom method and molecular dynamics.

Previously, the mechanism of grain formation and coating-substrate interfaces during the deposition of Ti-Si-N and Ta-Si-N nanocomposite films was studied in [59,60] using first-principles calculations. The energetic stability and configuration evolution of Ti-Si-N and Ta-Si-N islands on the (001) surface of TiN and TaN were investigated. It was found that their most stable configuration is that in which metal, nitrogen atoms combine to form islands, and silicon atoms remain at their boundaries. In this case, the strength of the Si-Ti and Si-Ta bonds in the considered islands is higher than the strength of the Si-N bond.

However, these works mainly studied the energetic properties of nanocomposite films, and only in [60] a little attention was paid to the study of valence density redistribution. In [61,62] we have already studied the peculiarities of the interaction of Si atoms with the simplest structural units of the Ti-Al-Ta-Si-N system, such as TiN, AlN and TaN compounds. It was found that silicon adsorption on the (001) surface of AlN, TiN and TaN compounds increases the relaxation and corrugation of the surface layers, which significantly weakens the bonds between the nearest surface nitrogen and metal atoms. On the (111) surface, Si interacts more readily with the nitrogen atoms of the AlN and TiN compounds and the Ta atom of the TaN compound (the binding energy of silicon to the surface near these atoms is maximal). In addition, silicon adsorption significantly reduces the areas of low valence electron density between the second and third layers of the TiN(111) surface, which can be considered a strengthening effect.

Based on the already established facts for systems related to Ti_1−x−yAl_xTa_yN, we have investigated the behavior of Si atoms on the surface of the Ti_1−x−yAl_xTa_yN system itself in an attempt to reveal the nature of the mechanical properties and structural phase stability of the Ti-Al-Ta-Si-N composite. In the present work, two variants of TiN compound surface orientation are considered: (001) and (111). This choice is not accidental. There are many experimental studies, which have shown that when TiN films are grown, in the vast majority of cases they have exactly these orientations (001 and (111)) (see e.g., [63]). The growth of films with a more complex chemical composition shows that these orientations are still preferred. In the preparation of Ti_1−x−yAl_xTa_yN coatings [46] it was found that films with a low Ta content (y ≤ 0.2) have a (111) texture in the growth direction, whereas with a high Ta content (y > 0.35) the orientation changes to (200). A study of Ti-Al-Ta-Si-N coatings [54] showed that at a Si concentration ≤ 0.08 at.% the preferred orientation of the crystallites was (111), but with increasing silicon content it changed to (100). Therefore, we can consider that the film orientation variants chosen for the study are quite reasonable because they are typical for the Ti-Al-Ta-Si-N surface system studied by us.

Using the analysis of the valence electron density redistribution of pure TiN as a result of the formation of the Ti_1−x−yAl_xTa_yN system on its surface with the subsequent adsorption of silicon, as well as an interatomic bond study apparatus based on the calculation of a Crystal Orbital Hamilton Population and a Crystal Orbital Bond Index, the nature of the bonds between adsorbed Si and N, Ti, Al, Ta atoms of the Ti_1−x−yAl_xTa_yN surface system has been studied. This may help to find the optimal composition of multicomponent coatings with improved physical and mechanical properties.

2. Calculation Methods and Details

All calculations were performed in the framework of density functional theory using the ABINIT 9.10.3 software package [64,65] with the projector augmented wave (PAW) method [66,67]. The exchange and correlation effects were accounted for using the generalized gradient approximation proposed by Perdue, Burke, and Ernzerhof [68]. The plane-wave basis set had a cutoff energy of 408 eV. Monkhorst-Pack grids centered on the Γ-point were used to sample the k-space with a density of 10×10×10 k-points for bulk calculations and 7×7×1 for film calculations. The process of self-consistency of the electron density was completed when the root-mean-square deviation of the output valence electron charge density from its input value became less than 10^-3 electron/ų, corresponding to a convergence of the total energy no worse than 10^-6 eV. The equilibrium lattice constant of bulk TiN was determined by the total energy minimization method. The obtained result of 4.237 Å is in the range of both experimental values of 4.210-4.244 Å [60,69,70,71,72] and values previously obtained from ab initio calculations (4.230-4.265 Å) using different exchange correlation functionals [73,74,75,76,77].

A five-layer film in the √2×√2 structure and a ten-layer film in the 2×2 structure were used to study the interaction of silicon with TiN(001) and TiN(111) surfaces with Al and Ta substitutional impurities, respectively. As shown in Figure 1, each atomic layer of the heterogeneous (001) surface supercell contains 4 titanium and 4 nitrogen atoms. The film modeling the homogeneous (111) surface consists of alternating layers of nitrogen and titanium, each with four atoms. As can be seen in Figures 1b and 1c, the (111) film is stoichiometric, i.e., its surfaces have been terminated by layers of N or Ti atoms. Al and Ta substitutional impurities were present in only two surface layers of the films considered. For convenience, in the following discussion of our results, the surface layers of TiN films in which Al and/or Ta atoms substitute for surface Ti atoms will be referred to as the Ti_1−x−yAl_xTa_yN surface system. The silicon atom was located on the same surface and could be found in four highly symmetrical positions (Figure 1). On the (001) surface, these are the bridge site (B), two top sites (T^N and T^Ti), and a quadruple coordinated (Q) site. On the (111) surface, the highly symmetric sites are the bridge site (B), the top site (T^N or T^Ti depending on the surface termination), and the HCP and FCC hole sites. The distance between the Si atoms in the supercells used was ~ 6 Å, and the interaction between them was negligible. This allows us to say that we are studying the interaction of a single Si atom with the surface atoms of the considered compounds. The vacuum width was three lattice parameters: 12.78 Å. The relaxation of the atomic positions on the surface was performed for the three surface atomic layers using the Broyden-Fletcher-Goldfarb-Shanno algorithm and was considered complete when the force on each atom was less than 10 meV/Å. The remaining layers of the films were fixed as in the bulk.

The valence electron distribution and Bader charge [78] were calculated to study the character of interatomic bonding on the surfaces of the TiN-based multicomponent surface system. A Crystal Orbital Hamilton Population (COHP) analysis [79] was used to study the influence of silicon on the interatomic chemical bonding on the (001) and (111) surfaces of the considered systems. This technique, adopted for plane-wave electronic structure calculations (projected COHP) [80,81] and implemented in the Local Orbital Basis Suite Towards Electronic-Structure Reconstruction (LOBSTER) code [82], allows local bonding analysis. In addition, Crystal Orbital Bond Index (COBI) calculations have been performed. The value of this tool lies in the fact that COBI allows us to study multicenter interactions within the local orbital structure and to detect covalent bonds and, together with the Bader charge transfer analysis, the ionic type of bonding. In the LOBSTER code, pCOHP and COBI are calculated on the basis of a linear combination of atomic orbitals (LCAO). Therefore, the eigenwavefunctions of the electronic states of the atoms of the Ti_1−x−yAl_xTa_yN surface systems and of the adsorbed silicon atom, calculated by the pseudopotential method, were re-decomposed by the orthonormalized LCAO basis used in the Löwdin population analysis.

3. Results and Discussion

3.1. Binding Energy

In order to identify the most energetically favorable adsorption sites of silicon on the considered surfaces, its binding energy was calculated using the formula

E_b = E(Si) + E(MeN) − E(Si-MeN),

(1)

where E(Si), E(MeN), and E(Si-MeN) are the total energies of the silicon atom, the pure MeN film, and the film with adsorbed silicon, respectively. The calculated binding energy is the minimum energy required to release a Si atom from the surface of the MeN system. If this energy is positive, it is a quantitative characterization of the Si-MeN bond strength. Figure 2 shows the results of the binding energy calculations for stable positions of silicon adsorption on TiN film surfaces with the Ti_1−x−yAl_xTa_yN surface system (x and y take values of 0.00 and 0.25) obtained by replacing part of the Ti atoms with Al and Ta atoms in the two upper layers of the film.

Comparison of our results with the data available in the literature showed that the binding energies of Si with a pure TiN(111) surface obtained by us are in qualitative agreement with the results of other calculations [72]. The quantitative discrepancy is due to the difference in the thickness of the considered films (10 layers in our calculations and 5 layers in [72]), as well as the degree of coverage of the surface by silicon atoms (0.25 in our case and 0.0625 in [72]).

As can be seen from Figure 2, the highest binding energies of silicon with the TiN surface, where the Ti_1−x−yAl_xTa_yN surface system is formed, are observed on the N-terminated (111) surface (from 7.45 to 5.92 eV), while the lowest ones are observed on the heterogeneous (001) surface (from 4.48 to 1.98 eV). On the metal-terminated (111) surface these binding energies vary from 6.16 to 4.96 eV. That is, the lowest binding energy of silicon with the Ti_1−x−yAl_xTa_yN surface system on the (111) surface (4.96 eV for Si adsorbed above the surface Al atom) is 0.48 eV higher than its highest binding energy on the (001) surface (4.48 eV for Si adsorbed above the surface N atom near Ta). This may be a good reason why Ti_1−x−yAl_xTa_yN films in the presence of Si, at least in the initial growth stage, exhibit the texture (111) observed in the experimental works [54,83].

The observed peculiarities of the silicon binding energy on the Ti_1−x−yAl_xTa_yN surface system are apparently related to the fact that the most energetically favorable site of its adsorption on the (001) surface is the T^N site (Figure 2a), where the adsorbate interacts with only one atom of the film, whereas for both terminations of the (111) surface, silicon is adsorbed in the FCC site (Figure 2b and 2c), interacting with at least three surface atoms. Note the very large scatter of silicon binding energies E_b at each adsorption position on the nitrogen termination of the (111) surface (~ 1.32 eV) and the opposite small scatter of E_b values on its metallic termination (~ 0.48 eV) and on the (001) surface (~ 0.55 eV). This is most likely due to the different relaxation character of the surface layers of the nitrogen-terminated (111) film on the one hand and the (001) and Ti-terminated (111) films on the other hand. Thus, at the nitrogen termination of the (111) surface, a significant decrease of the first interplanar distance and an increase of the second one are observed, resulting in the formation of an N-Me “bilayer” with short bonds on this surface. The presence of substitutional atoms Al and Ta in the subsurface Ti layer, which differ significantly in their properties, affects the N-Si interaction differently and leads to a large variation in the energy of this bond.

The substitution of the Ti atom by the Al (Ta) atom in the immediate vicinity of the adsorbed Si atom on the (001) and (111) surfaces leads to a decrease (increase) in the binding energy of Si with the surface in most of the cases considered. The exception is the adsorption of Si in the Q site on the (001) surface, as well as in the FCC and HCP sites on the N-terminated (111) surface: here the opposite situation is observed. These configurations differ from the first mentioned in that there are two or more N atoms among the nearest neighbors of the adsorbed Si. That is, Al strengthens the bonding of Si to the atoms of the considered surfaces when more than one Si-N bond is formed. Substitution of some Ti atoms by Al and/or Ta atoms in the lower layer of the film (001) increases the binding energy of Si to the surface N atom under which these substitution atoms are located by 21 and 40 meV, respectively (these values are not shown in Figure 2). The presence of Al or Ta in the subsurface layer of the N-terminated (111) surface makes the Si position above the N atom unstable when the substitution atom is under this nitrogen atom.

Thus, depending on the position of Al and Ta atoms in the surface layers of the considered films, the binding energy of Si with the Ti_1−x−yAl_xTa_yN surface system can be both higher and lower than its binding energy with the surface of the binary TiN compound. This means that the non-uniform distribution of alloying elements in the Ti_1−x−yAl_xTa_yN surface system at high temperature modes of film formation, which provides significant mobility of deposited atoms, will lead to the nucleation and growth of Si_zN phases in the form of islands rather than a continuous layer, contributing to the formation of a tissue nanostructure.

3.2. Valence Charge Density Distribution

In order to study the nature of chemical bonding between Si atoms and the Ti_1−x−yAl_xTa_yN surface system, valence electron density distributions were calculated and analyzed. In analyzing the results obtained, we proceeded from the following simple schematic representations: the metallic type of bonding in a crystal is characterized by a rather uniform distribution of valence electron density over the crystal volume. Purely ionic bonding gives approximately the same distribution of valence charge density in the interatomic region, but unlike metallic bonding, it is characterized by the presence of a strong (significant) charge transfer from one type of atom to another. The covalent type of bonding is manifested by an extremely heterogeneous distribution of valence electron density, characterized by the presence of a rather large electron density in the region between the nearest atoms, which is interpreted as chemical bonds. The presence in the crystal of atoms with very different electrochemical potentials leads to charge transfer between types of atoms and to the appearance of ionicity in the crystal. This deforms the symmetrical pattern of electron density distribution characteristic of covalent crystals.

Figure 3 shows the results of the calculations both for pure TiN film surfaces and for film surfaces with Ti_1−x−yAl_xTa_yN surface system. In all panels shown, silicon atoms are adsorbed at the most energetically favorable positions, i.e., above the nitrogen atom on the (001) surface and in the FCC site on both (111) surface terminations.

The left part of Figure 3a shows the valence electron density distribution of the (001) film of pure TiN. Near the (001) surface, dumbbell-shaped regions of high electron density (0.05 electron/ų and more, shown in yellow) spanning Ti and N atoms are clearly visible in this figure. The asymmetry of these regions and the presence of high electron density between Ti and N atoms indicate ionic-covalent bonding between them. Between the second and third layers from the surface, regions of low electron density (0.02 electrons/ų and less) bounded by gray isosurfaces are seen in the interstitial sites of the TiN compound. This may indicate the possibility of brittle fracture between these layers.

As we noted in [62], silicon, when adsorbed on the TiN(001) surface, forms ionic-covalent bonds with the nearest atoms of the TiN film. In our case, this is evidenced by the dumbbell-shaped region of high valence charge density between the silicon atom and the nearest surface nitrogen atom in the left panel of Figure 3b. The ionic nature of this bond is evidenced by the asymmetry of the charge density around this pair of atoms. The region of high charge density around the N atom is larger than that around the Si atom. Note the regions of low electron density between the surface and subsurface layers of the TiN compound, bounded by gray isosurfaces. On the pure TiN(001) surface (left panel of Figure 3a), these low density regions between the first and second atomic layers are absent. Silicon adsorption causes these regions to appear in the surface layers and increases the size of the high electron density region between the Ti and N atoms. This indicates a change in the covalent component of the Ti-N bonds in the surface layers of the TiN(001) film as a result of silicon adsorption. Thus, silicon adsorption can strengthen the TiN surface layers, but make them more brittle. As a result of replacing one Ti atom by Al atom in the calculated TiN(001) surface cell (creating the Ti_0.75Al_0.25N surface system), an increase in the size of the regions bounded by gray isosurfaces near the Al atom and a slight increase (~5%) in the region of high valence charge density encompassing the silicon atom and the nearest nitrogen atom (left panel of Figure 3c) are observed. This indicates the formation of Al-N ionic-covalent bonds in the surface layers and an increase in the degree of Si-N covalent bonding, which can generally be considered as a hardening of the TiN(001) surface. For the Ti_0.75Ta_0.25N surface system on TiN(001) (left panel of Figure 3d), we observe a decrease in the size of the gray areas in the near-surface region near the Ta atom without changing the size of the dumbbell-shaped valence charge region forming the Si-N bond. This suggests metallization of the bonds near the impurity Ta atom without noticeable effect on the Si-N bond. In the case of the Ti_0.50Al_0.25Ta_0.25N surface system (left panel of Figure 3e), the pattern of the valence charge density distribution is quite similar to that observed for the Ti_0.75Al_0.25N surface system, with the difference that the degree of covalency of the Si-N bond decreases as the dumbbell-shaped region of yellow color decreases by about 18%. In general, however, the situation can be characterized as a hardening of the surface layers of the TiN(001) film.

The character of the valence charge density distribution near the surface of the nitrogen-terminated TiN(111) film (middle panel of Figure 3a) is very different from that of the electron density distribution of the (001) film. Large regions of low electron density (below 0.02 electrons/ų) are observed in the third layer from the surface (the layer of nitrogen atoms) of the TiN(111) film. As noted in [61], this is the result of a very non-uniform relaxation of the surface layers of the nitrogen terminated TiN(111) film, the maximum of which falls just on the third layer from the surface. It is very likely that this is evidence for weakening of interatomic bonds and reduction of strength in the near-surface layer as a result of the occurrence of Friedel oscillations of the charge density [84] near the nitrogen-terminated surface. In addition, it can be seen that near the (111) surface there are dumbbell-shaped regions (yellow color) of high electron density covering Ti and N atoms. The asymmetry of these regions and the presence of high electron density between Ti and N atoms indicate the predominance of ionic-covalent bonding near the nitrogen-terminated TiN(111) surface. The adsorption of silicon in the FCC sites of the nitrogen-terminated TiN(111) surface (middle panel of Figure 3b) leads to a significant decrease in the size of the low electron density regions in the third layer from the surface (shown in gray). A similar pattern is observed in the case of Si adsorption on the nitrogen termination of a TiN(111) film with an impurity Al atom in the subsurface (middle panel of Figure 3c). However, in this case, Si adsorption is not as effective in reducing the size of the low electron density gray regions in the third layer from the surface as in the case of a pure TiN(111) film. Adsorption of silicon on the nitrogen termination of a TiN(111) film with an impurity Ta atom in the subsurface layer (right panel of Figure 3d) reduces the size of the low electron density region (shown in gray) in the third layer from the surface more than in the case of a pure film. In this case, the Ta atom of the subsurface layer forms a covalent bond with the three nearest surface nitrogen atoms. In the case when the subsurface layer of the nitrogen-terminated TiN(111) film contains two impurity atoms, Al and Ta (middle panel of Figure 3e), the adsorption of silicon changes the electron density distribution almost in the same way as in the case of its adsorption on the Ti_0.75Al_0.25N(111) surface system, except for a decrease in the regions of the low electron density near Ta. This indicates the local character of the interaction of the adsorbed silicon atom with the Ti_1−x−yAl_xTa_yN surface system.

The character of the valence charge density distribution near the Ti-terminated (111) surface is similar to the character of the charge density distribution near the heterogeneous (001) surface, and very different from the character of the electron density distribution near the N-terminated (111) surface. The adsorption of silicon at the FCC site on a pure Ti-terminated TiN(111) surface (right panel of Figure 3b) leads to a barely noticeable increase in the size of low electron density regions (gray color) between the second and third layers near the adsorbed silicon atom and, most likely, to an increase in the metallicity of bonds on the surface. It is not possible to claim the formation of covalent Si-Ti bonds based on the present figure. In general, however, we can say that the adsorption of silicon leads to an increase in the degree of covalency in the surface layers close to the adsorbate, i.e., to their strengthening. The adsorption of Si on the TiN(111) surface in the presence of Al substitution impurity (right panel of Figure 3c) leads to the strengthening of ionic-covalent bonding in the TiN surface layers, as evidenced by the charge density distribution - the appearance of new regions of low electron density shown in gray. Based on the figure, we can only say that the bond is formed with an admixture of ionicity between silicon and titanium atoms.

In the case of Si adsorption on the TiN(111) surface in the presence of Ta (right panel of Figure 3d), a covalent bond is formed between Si and Ta atoms. This is evidenced by the clearly visible contours of a dumbbell-shaped region of high valence charge density (yellow color) encompassing both atoms.

The right panel of Figure 3e shows that the adsorption of Si on the TiN(111) surface in the presence of Al and Ta leads to a stronger effect than in the presence of Al and Ta alone. The appearance of a large number of large regions of low electron density (shown in gray) indicates a significant enhancement of ionic-covalent bonding in the TiN surface layers compared to when either Al or Ta atoms were present on the TiN(111) surface. In addition, a covalent bond is also formed between Si and Ta atoms.

Our analysis of the valence charge density distribution allowed us to draw detailed but only qualitative conclusions about the type and strength of interatomic bonds. Note also that as the number of components of the Ti_1−x−yAl_xTa_yN surface system increases, it becomes more difficult to make unambiguous conclusions about the type of bonding, because the effects due to each individual pair of atom types, which are easily observed in a simple system (with a small number of atom types), are superimposed, mixed, and it is difficult (and sometimes impossible) to separate and interpret them unambiguously. Therefore, in addition to studying the valence electron density distribution of TiN films and its change as a result of the formation of the Ti_1−x−yAl_xTa_yN surface system with subsequent Si adsorption, calculations and analysis of the Bader charge transfer between the components of this system were performed. Figure 4 shows the Bader charge transfer between N and Ti atoms of the clean TiN surface, N, Ti, Ta and Al atoms of the Ti_1−x−yAl_xTa_yN surface system and the adsorbed silicon atom.

The Bader charge transfer is defined as the difference between the number of valence electrons of an atom in the crystal, which is equal to the integral of the valence charge density over the volume of the atomic polyhedron, and the number of valence electrons of a free atom. Calculation of the charge transfer according to this scheme showed that on the clean TiN(001) surface (Figure 4a), Ti loses ~1.5 electrons and N gains ~1.5 electrons, indicating a high degree of Ti-N ionic bonding. In the bulk of TiN, the Bader charge transfer from titanium to nitrogen is equal to 1.46. Note that the observed Friedel charge oscillations decay rapidly in the bulk of the crystal: in the third layer of the heterogeneous (001) and Ti-terminated (111) surfaces, and in the fifth layer of the N-terminated (111) surface.

In general, Figure 4 shows that the presence of substitutional impurities (Al and/or Ta) as well as adsorbed Si atoms on the TiN surface has little effect on the charge transfer between Ti and N. It is mainly influenced by the type of surface and its termination. On the N-terminated (111) surface (Figure 4b), the subsurface titanium atom gives up ~1.7 electrons and the N accepts ~1.1 electrons. On the Ti-terminated (111) surface (Figure 4c), the titanium atom loses approximately ~ 0.9 electrons and the subsurface nitrogen atom accepts ~ 1.6 electrons. The large spread of charge transfer to the N atoms, especially on the (001) and nitrogen-terminated (111) surfaces, is noteworthy. This is explained by the fact that on these surfaces the N atoms are in the surface layer and experience more intense perturbation than the subsurface N atoms on the (111) surface with metallic termination.

On all three considered surfaces, Al loses from 2.3 to 1.0 electrons, i.e., it forms predominantly ionic bonds. The exception is the configuration of the Ti_1−x−yAl_xTa_yN surface system, when Al is located near the Ta atom on the Ti-terminated TiN(111) surface. In this case, the Al atom is displaced by 0.9 Å from the surface layer to the vacuum due to relaxation, moving away from the subsurface nitrogen atoms. The Ta atom also loses valence electrons, but to a lesser extent than Al. Taking into account that tantalum exhibits a greater number of valence electrons than both titanium and aluminum, it was established that, among metal atoms, tantalum retains the greatest number of electrons in all configurations of the Ti_1−x−yAl_xTa_yN surface system under consideration. These “extra” electrons of Ta in the system, most likely, participate in the formation of metal-like bonds, which is clearly indicated by the valence charge distributions presented earlier.

The behavior of adsorbed silicon is more diverse. As shown in Figure 4, replacing part of the surface Ti atoms with impurity atoms (Al and Ta) does not change the sign of the charge transfer on silicon, only its magnitude. Silicon gives up electrons only when nitrogen atoms are in its vicinity: T^N and Q adsorption sites on the (111) surface and all adsorption sites on the N-terminated (001) surface. On the heterogeneous (001) surface, the charge transfer on silicon is small compared to the other atoms in the system, ranging from about −0.50 to 0.37 electrons. On homogeneous surfaces, the charge transfer is more significant: it ranges from −1.58 to −1.84 electrons on the nitrogen-terminated surface, while it does not exceed 1 electron on the metal-terminated surface. In the latter case, the greatest influence of the impurity on the magnitude of the charge transfer on silicon is observed for adsorption in the top site above the metal. If the effect of Al and Ta impurities on the charge transfer on silicon is evaluated in general, it can be concluded that in most cases it is limited to no more than 0.21 electrons. The maximum change of this charge transfer is 0.41 electrons and is observed when Si atom adsorbed in the T^Al site on the metal-terminated (111) surface.

3.3. Silicon-Surface System Bond Type Analysis

For a detailed analysis of the silicon-surface bonding strength, as well as to study the effect of silicon adsorption on the bonding between the surface Me and N atoms, the projected Crystal Orbital Hamilton Populations (pCOHP) and the crystal orbital bonding index (COBI) were calculated and integrated over the energy from the bottom of the valence band to the Fermi level. The results of these calculations for the stable silicon adsorption positions are shown in Figure 5, Figure 6 and Figure 7. The integral values of -IpCOHP and ICOBI [85] can be interpreted as a measure of bond covalency (corresponding to bond strength) and bond order (the number of electrons involved in the bond between two atoms), respectively. ICOBI is a dimensionless quantity, while IpCOHP has the dimensionality of energy. Large ICOBI values (> 1) indicate a strong covalent bond, values in the range of 0.8 to 1.0 indicate the presence of an ionic bond, the range of 0.4 to 0.8 corresponds to a predominantly ionic bond, and small values from 0 to 0.4 indicate a less strong metallic bond with an admixture of ionicity. A comparative analysis of the integral values of -IpCOHP andd ICOBI for a pair of atoms, as well as taking into account the Bader charge transfer on the studied surfaces, allows to identify the degree of covalency, ionicity and metallicity of interatomic bonds [85,86] on the basis of quantitative indices, thus clarifying and complementing the conclusions drawn when discussing the distribution of the valence electron density.

Figure 5a shows the calculated values of -IpCOHP and ICOBI for Si-Me and Si-N bonds and Figure 5b for Me-Me, Me-N and N-N bonds on the pure TiN(001) surface and on the surface with the Ti_1−x−yAl_xTa_yN surface system on which the silicon atom was adsorbed. Figure 5a shows that on the pure surface the Si atom adsorbed at the T^N site forms a rather strong (-IpCOHP = 5.5 eV) ionic-covalent bond with the nitrogen atom underneath. With neighboring Ti atoms it interacts much weaker (~ 2.2 eV). In the Ti top site (T^Ti), the silicon atom forms a strong covalent bond with it (-IpCOHP = 5.6 eV, ICOBI = 1.27), practically not interacting with nitrogen atoms (almost zero value of -IpCOHP). A similar pattern is observed for the adsorption of silicon on the Ta top site (T^Ta). When adsorbed over an Al atom, this covalent bond has an admixture of ionicity (ICOBI = 0.75). In the case where both impurity atoms (Al and Ta) are present on the surface, silicon continues to form a rather strong ionic-covalent bond with the underlying nitrogen atom and interacts weakly with neighboring metal atoms, and its adsorption over the metal becomes unstable.

In the quaternary coordination site Q, silicon forms ionic-covalent bonds with a large fraction of ionicity with the two nearest nitrogen and metal atoms, and practically does not interact with the second neighbors. The latter can be clearly seen in the right part of both Figure 5a, where the -IpCOHP and ICOBI values for the Si-Ti bond are very close to zero, since the Ti atom is not among the nearest neighbors of the adsorbed silicon.

It can be concluded that on the TiN(001) surface, the impurity atoms Al or Ta have almost no effect on the Si-Ti and Si-N bonds, but form a strong covalent bond with them. The Si-Me bonding has a very local character, as evidenced by the near zero values of -IpCOHP and ICOBI for silicon bonds with second neighbors.

The analysis of Figure 5a helped to reveal the influence of substitutional impurities (Al and Ta) on the interaction between silicon and atoms of the Ti_1−x−yAl_xTa_yN surface system. Figure 5b provides information on the effect of silicon adsorption and the atomic composition of the Ti_1−x−yAl_xTa_yN surface system on the interaction between its atoms. Lest the abundance of symbols confuse the reader, let us explain what information is hidden behind them. Red diamonds correspond to N-N bonds and triangles correspond to metal-metal bonds. All of these atoms are second-nearest neighbors. Figure 5b shows that these atoms interact very weakly (-IpCOHP < 1.5 eV, ICOBI < 0.25). This is predominantly a metallic type of bonding, with a small admixture of ionicity. The presence of aluminum slightly weakens it, while tantalum significantly strengthens it.

The squares correspond to N-Me nearest neighbor bonds. In general, it can be seen that the adsorption of silicon in the top site over nitrogen strengthens the N-Ti ionic-covalent bonds, while over metal and in the Q site weakens them. In the presence of Al, some of the stronger N-Ti bonds are replaced by weaker N-Al bonds. The effect of Ta is the opposite - it introduces stronger bonds with a large fraction of covalency instead of less strong ionic-covalent N-Ti bonds. The combined presence of Al and Ta makes the picture more complex because in this case, in addition to the strengthening of the bond by tantalum, there is also a weakening of the bond by aluminum. This effect is better seen in binding energy calculations. In general, it can be said that silicon adsorption reduces the binding forces between nitrogen and metal atoms near the surface. The same effect is exerted by Al atoms, whereas Ta strengthens the bonds.

Figure 6 shows the calculated values of -IpCOHP and ICOBI for interatomic bonds on the N-terminated pure TiN(111) surface and on the surface with the Ti_1−x−yAl_xTa_yN surface system on which the silicon atom was adsorbed. From Figure 6a it can be seen that Si adsorption on the N-terminated surface (111) leads to the formation of rather strong ionic-covalent bonds with nearby nitrogen atoms, as already observed on the heterogeneous surface (001). The interaction with the metal atoms of the subsurface layer is mainly metallic in nature with a small fraction of ionicity. The presence of substitutional impurities (Al, Ta) in the subsurface layer has almost no effect on the bonding of silicon with the subsurface Ti atom.

Figure 6b, as well as Figure 5b, shows the effect of silicon adsorption and the atomic composition of the Ti_1−x−yAl_xTa_yN surface system on the interaction between its atoms. It can be seen that the second nearest neighbors interact weakly (-IpCOHP < 1.2 eV, ICOBI < 0.2). This is almost a purely metallic type of bonding. There is almost no bonding between the nitrogen atoms. As for the N-Ti bond, the presence of aluminum strengthens it by increasing the charge transfer covalency, while tantalum weakens it.

Figure 7 shows the same -IpCOHPs and ICOBIs as previously shown in Figure 5 and Figure 6, but for the Ti-terminated surface (111). Si adsorption on the Al and Ta top site shows almost the same effect as on the (001) surface - very strong localized Si-Al and Si-Ta covalent bonds are formed, and silicon does not interact with the Ti second coordination sphere. In general, the pattern is very similar to that observed for silicon adsorption on heterogeneous surface metals with the difference that now the Si-Me interaction is stronger and more covalent in nature.

As previously in Figures 5b and 6b, an almost complete absence of N-N interaction is seen, but an increase in metal-type interaction between the surface metals is noted. The interaction between nitrogen and metals is about the same as on the heterogeneous surface, but much weaker than in the subsurface of the N-terminated surface.

4. Conclusions

In the present work, an ab initio study of the peculiarities of the interaction of Si atoms with TiN(001) and TiN(111) surfaces, whose top two layers contain substitutional impurities and represent the Ti_1−x−yAl_xTa_yN surface system, has been carried out within the framework of density functional theory. The nature of the bonds between adsorbed Si and the components of the Ti_1−x−yAl_xTa_yN surface system was investigated using an interatomic bonding study apparatus based on Crystal Orbital Hamilton (COHP) and Crystal Orbital Bond Index (COBI) calculations. This may help to find the optimal composition of multicomponent coatings with improved performance. The main conclusions are as follows.

The highest silicon binding energies with the Ti_1−x−yAl_xTa_yN surface system are observed on the N-terminated (111) surface and the lowest on the heterogeneous (001) surface. The highest silicon binding energy on the (001) surface is 0.48 eV lower than its lowest value on the metal-terminated Ti_1−x−yAl_xTa_yN (111) surface.

The presence of an Al(Ta) atom close to the adsorbed Si atom on the (001) and (111) Ti_1−x−yAl_xTa_yN surfaces leads to a decrease (increase) in the Si binding energy in most of the cases considered. The exceptions are the configurations where there is more than one N atom in the first coordination sphere of Si. That is, Al (Ta) strengthens (weakens) the bonding of Si with atoms of the considered surfaces when more than one Si-N bond is formed. Thus, depending on the position of Al and Ta substitution atoms in the surface layers of the considered films, the binding energy of Si with the Ti_1−x−yAl_xTa_yN surface system can be both higher and lower than the binding energy of its bonding with the surface of the binary TiN compound. As a result, a heterogeneous distribution of Al and Ta atoms in the Ti_1−x−yAl_xTa_yN surface system at high temperature film formation modes, which provides a significant mobility of deposited atoms, can lead to nucleation and growth of Si_zN phases in the form of islands rather than a continuous layer.

It is shown that in the Ti_1−x−yAl_xTa_yN system Ti-N bonds have ionic-covalent character. The second neighbor nitrogen-nitrogen interaction is practically absent, and in the case of metal-metal bonds it has a metallic character. The bonding of adsorbed silicon with Ti_1−x−yAl_xTa_yN surface atoms is ionic-covalent in nature. At the same time, the Si-Ta interaction has the highest degree of covalency and strength, while the Si-Al interaction is predominantly ionic in most cases considered and is weaker than the Si-Ti and Si-N bonds. The combined presence of Al and Ta near the silicon atom complicates the nature of the bonds, making them more ambiguous, because in this case, in addition to the strengthening of the bond by tantalum, there is also a weakening of the bond by aluminum. Impurity atoms of Al or Ta have very weak influence on the Si-Ti and Si-N bonds due to the local nature of the interaction between the atoms of the Ti_1−x−yAl_xTa_yN surface system and the adsorbed silicon.

Very low electron density regions are observed near the third layer of the nitrogen-terminated TiN(111) surface due to non-uniform relaxation of the surface layers. The presence of such regions near the surface layers favors brittle fracture and spalling. Silicon adsorption significantly reduces the size of these regions, thereby strengthening the surface layers. The substitution of titanium by aluminum in the subsurface layer increases the size of low electron density regions, and the presence of tantalum, on the contrary, significantly reduces the size of these regions due to the increased metallicity of the bonds near Ta. In case of simultaneous presence of impurity atoms Al and Ta in the subsurface layer, their influence on the regions of low electron density is a superposition of the influence of each substitution atom separately, which also indicates the local character of bonds in the Ti_1−x−yAl_xTa_yN surface system with adsorbed silicon atom.