Incorporation of tungsten or cobalt into TaN barrier layers controls morphology of deposited copper

Progress in semiconductor devices, which has enabled the information and communications technology explosion of the 21st century, has been driven by Moore’s Law and the accompanying aggressive scaling of transistors. However, it is now acknowledged that the currently used copper interconnects are becoming a bottleneck in sub-nm scaling. Semiconductor devices require a diffusion barrier and a seed layer in the volume available to the interconnect metal. This then limits the minimum size of the interconnect and copper suffers from a preference to form 3D islands which are non-conducting rather than conducting films. Therefore there is a pressing need to either replace copper, which has its own difficulties, or to reduce the volume taken up by the diffusion barrier and liner; ideally finding a single material displaying both properties is needed. We have previously shown that incorporation of Ru into the surface layer of TaN is a strong alternative to the usual TaN/Ta or TaN/Ru stacks. In this work we study other possible metals that can be incorporated into TaN, namely Co and W, which are less expensive and critical than Ru and can potentially outperform it. Our first principles density functional theory results from static relaxations and ab initio molecular dynamics show that there are several compositions of both Co- and W-doped TaN which should promote growth of 2D copper interconnects without compromising the barrier properties of TaN. With this selection of materials it should be possible to design new experimental processes that promote downscaled copper interconnects for the next generation of electronic devices. Additionally, our work presents an improved method towards prediction of thin film morphology on a given substrate, which can be of use for a variety of materials science applications.


Introduction
Moore's Law [1], which states that the number of transistors in a typical integrated circuit doubles approximately every two years, has been a driver for semiconductor device miniaturisation. This has required aggressive decreases in dimensions to pack more and more transistors into a single device and ensure that Moore's Law continues [2,3]. To keep these miniaturised devices connected, the size of the interconnect must correspondingly decrease. However, interconnect scaling is now reaching its limits with current materials and processing technology [4,5]. The rate of increase in the number of transistors on a chip is slowing compared to Moore's Law and makes interconnect scaling a serious bottleneck and highly limiting factor in device miniaturisation [6,7]. Even with a move away from Moore's Law, device interconnects will continue to provide stern challenges.
Several layers of interconnect lines are needed to connect all the transistors in a device. The closer the interconnect is to the transistors the smaller it must be, resulting in extremely high aspect ratio structures at the lowest device levels. Currently, interconnects are made with Cu metal. To create a functioning interconnect, a diffusion barrier and a seed layer or liner (also referred to as adhesion promoter) need to be deposited in the interconnect via. As the name suggests, the role of the diffusion barrier is to prevent the diffusion of Cu atoms into the surrounding dielectric, while the liner material promotes deposition of smooth, conductive Cu films. Current diffusion barriers, such as TaN, are unable to promote the deposition of conductive Cu without the addition of the liner material. Common liner materials include Ta and Ru. The barrier and liner materials take up the limited available volume in the interconnect via, to the point that even with modern deposition methods such as atomic layer deposition (ALD) they cannot be thinned further without compromising their efficiency and this means that insufficient volume remains in the via to deposit the amount of Cu needed for a functioning interconnect [8,9]. New developments in interconnects are clearly needed in order to drive further advances in electronic devices.
The following properties are crucial in developing efficient barrier/liner materials: • Wettability and adhesion of Cu • Reduced material thickness • Thermal stability • Low overall resistivity • Low grain boundary diffusion • Low electromigration.
From an experimental perspective, a large variety of analysis methods are available to determine barrier and liner performance. However, it is usually not feasible to focus on more than one specific aspect of the system, such as the failure mechanism of the diffusion barrier. Additionally, there is overwhelmingly more literature on the topic of diffusion barriers than there is for liner materials, and there are few studies that examine a barrier and a liner material together, or test a material for both barrier and liner properties. Some of the materials studied as combined barrier/liner materials include NiP alloy [10], Cr [11], RuMo alloy [12], CoWB [13], Ru [14], MoC doped Ru [15], Ru(P) [16], RuCo [17], Co [18,19], Co(W) [20][21][22][23], MnN [24] and Ti [25]. There is also some precedence for building upon existing knowledge by combining known diffusion barrier and liner materials. Chakraborty et al studied mixed-phase RuTaN [26,27]. Eisenbraun [28] used plasma enhanced ALD to create mixed phase barrier/liner materials by layering known barrier (TaN, WCN) and liner materials (Ru, Co), starting with the barrier and ending with a liner layer. These materials showed comparable barrier properties to TaN. Additionally, the ratios of metals in the material can be used to further tune the material to have low resistivity and good wettability while maintaining strong barrier properties. This type of work also includes our work on Ru-doped TaN which demonstrated that Cu wetting can be promoted on TaN surfaces by incorporating a known liner material and provides the foundation for the work presented in this paper [29][30][31]. While the work on combined barrier/liner materials is relatively limited, there is even less work on using theoretical methods to screen for potential barrier, liner or barrier/liner materials. Just as a wide variety of experimental methods is needed to study all aspects of a potential barrier and liner material, theory also requires a range of methods to attempt to study all of the above properties. This is usually not feasible and therefore it is reasonable to select the primary properties of interest and focus on modelling these. Adhesion is the property that is most easily studied using theoretical methods [32,[32][33][34]. Activation energy for atom diffusion can be determined using nudged elastic band calculations and can give insight into surface mobility of atoms as well as the diffusion barrier properties [35][36][37]. Ab initio molecular dynamics (aiMD) calculations can be used to gain some insight into thermal stability as well as wettability and growth processes [33,38]. Additionally, electronic properties such as density of states (DOSs), atomic charges and electron density can be studied, which give useful insight into conductivity and band gap of the material and can also reveal trends that drive the formation of favourable structures [34]. Models have also been developed to screen for materials based on their electronic properties. These are particularly useful when combined with experimental methods [39]. Additionally, machine learning can now be applied to modelling the overall performance of interconnects which can save valuable time and resources during the development process [40]. Overall, theoretical studies make up only a small fraction of the research on advancing interconnect manufacturing leaving plenty of room to gain further insight into growth mechanisms and material interactions relevant for application in interconnect technology.
In our previous work [29][30][31] we showed that by doping Ru atoms into the top layer of a TaN surface, a single material with both barrier and liner properties can be created. Such a material can be deposited using ALD. Use of a single barrier/liner material frees up volume for Cu in the interconnect and reduces the number of process steps. As part of these studies, we also developed a computationally efficient method for predicting the thin-film morphology of Cu on potential single barrier/liner materials. This is based mainly on the understanding of the forces that drive the growth mechanism of a material. (a) Mechanism for homoepitaxial growth and growth on weakly interacting substrates, as described in [45]. (b) Metal structures of increasing size to predict thin film morphology. Information gained from the different calculations is labelled in blue. aiMD = ab initio molecular dynamics, NEB = nudged elastic band calculation. In this work we do not require NEB calculations to predict film morphology.
Three growth modes, namely Volmer-Weber, Frank-van-der-Merwe and Stranski-Krastanov in molecular beam epitaxy, are typically discussed in the literature [41]. However, these are all governed by the fundamental interactions taking place between the substrate and the deposited metal. The metal-metal and metal-substrate interactions are in competition during growth and finding approaches that can control the relative strength of these interactions will be important for tuning the morphology of a deposited metal film. Materials tend to follow a classical homoepitaxial growth mechanism [42][43][44] when there is a strong interaction between the deposited material and the substrate [45]. An example of this would be aluminium grown on aluminium substrate [46]. For strongly interacting substrates, the interaction with the substrate is stronger than the interaction between atoms of the deposited material. A higher temperature is associated with 2D growth, making annealing a reasonable approach to create a conformal film. In contrast, the opposite becomes true for growth on a weakly interacting substrate. Here, the interactions between the atoms in the deposited material are stronger than the interaction with the substrate. Consequently, increased temperature tends to promote 3D growth. This leads to faceted structures and rough surfaces which are not desirable for interconnects [38,45,[47][48][49][50]. Additionally, while migration of atoms across the surface can occur, Gervilla et al [45] described that upward migration of atoms to form new layers is not possible on strongly interacting substrates. This is a crucial difference between the two mechanisms. By enhancing the adhesion between the adatoms and the substrate, a homoepitaxial growth mechanism, of for example copper on a nitride, can be promoted, which in turn promotes 2D growth of the thin film. Computing the activation energies for atoms to migrate between layers lets us determine which mechanism is dominant based on the magnitude of the activation energy. The different migration pathways for homoepitaxial growth and weakly interacting substrates are shown in figure 1(a).
To the best of our knowledge, studies of growth mechanisms for similar systems tend to be carried out using kinetic Monte Carlo or mean field approximation methods [45,47,48,50], with some studies choosing to use classical molecular dynamics [38,49]. However, as the growth mechanism is governed by the competition between the adatom-substrate and the adatom-adatom interaction, we can use these in combination with the strength of adhesion and selected aiMD simulations, which account for temperature effects, to predict the likely growth mechanism and avoid expensive activation energy calculations.
For this paper we built on our previous approach [31] to extract the maximum amount of information on the interaction between Cu and the substrate, while keeping the computational cost manageable. Figure 1(b) gives an overview of the different models used and the information so obtained. Our aim is to use this approach for TaN surfaces modified with different metal dopants with the aim of studying how the interaction between Cu and modified TaN is affected by different dopants to identify new barrier/liner materials for advanced interconnects. Additionally, this allows us to evaluate the limitations of our approach for predicting the thin film morphology. For the purposes of this study we have selected W and Co as the dopants. These are more sustainable alternatives to currently used liner materials like Ru. Co was of particular interest to us, as it is known as a suitable liner material for Cu [18,32,33,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] and its incorporation into TaN gives a likely candidate for a single, combined barrier + liner film. Co and W also allow us to further investigate the effects of the difference in ionic radius between Ta and the dopant, because Co has the smallest ionic radius of 0.55 Å (high-spin) or 0.61 Å (low-spin) and W, with an ionic radius of 0.66 Å, is very similar in size to Ta, with an ionic radius of 0.72 Å [66]. Co is magnetic, therefore we tested the effects of high-spin vs low-spin on geometry and binding energy; this is discussed in the supporting information, section S2. To the best of our knowledge, while neither W nor W x N y have been studied as a liner material, W x N y is a known barrier material [65,[67][68][69][70][71][72][73][74][75][76][77][78]. Finally, ALD process chemistries are known for Co [79][80][81], W [82,83] and their respective nitrides [70,[84][85][86], permitting their introduction into TaN through ALD.
Similarly to the approach described in our previous work [29][30][31], we have doped the top layer of a ε-TaN(1 1 0) slab with W and Co. To do this, 25%, 50% or 100% of the Ta atoms in the top layer were replaced with the dopant. The surfaces will be labelled as W dopant−concentration or Co dopant−concentration , giving for example W 25 for 25% W doping or Co 100 for 100% Co doping. There are two coordination environments for metal atoms in the TaN (1 1 0) surface. The S-site forms a six coordinate structure with N, while the F-site is three coordinate with N. In our previous work, we found that Ru doping is more favourable at the F-site than the S-site, and that the number of dopants at each site affects the stability of the surface. This is also the case for Co and W doping. For 50% doping, we chose two different doping distributions [30], namely the most and least favourable 50% dopant distributions. These will be distinguished as W 50−F /W 50−S and Co 50−F /Co 50−S , as they contain the maximum number of F-site and S-site dopants, respectively. The resulting doped TaN surfaces are shown in figure 2 for W doping and in figure 3 for Co doping. The selected sites for single Cu adsorption are also highlighted.
Four more potential combined barrier/liner materials, in addition to those Ru-doped surfaces identified in our previous work, were identified using the above approach. These are 25% and 50% Co-doped TaN and 25% and 100% W-doped TaN, although the latter could also be considered as a layer of WN passivation on TaN. This shows clearly that it is possible to tailor the properties of a material through doping in the surface, which in the case of a barrier material like TaN would reduce the overall volume occupied by the barrier/liner without compromising the barrier properties. The selection of potential combined barrier/liner materials identified through our studies is based on materials that are already used in current manufacturing and should therefore be simple to include into a process recipe. Some material properties, such as resistivity and reliability, still need to be tested and optimised experimentally. This study also allowed us to determine the limitations of the different Cu models used and the information they can provide about the thin film morphology. Combined with insights on the effect of dopant ionic radius on the thermal stability of the material, we present a more computationally efficient approach to predicting the thin film morphology compared to our work in [31], which is useful for understanding growth morphology at material interfaces.

Methods
The models presented in this study are based on our previous published work and detailed descriptions of the same can be found in [29][30][31]. A description of the surface model is also available in the supporting information, section S1.
All calculations were performed using density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) v5.4 [87]. The core electrons are treated with the projector augmented wave method [88,89], whereas the valence electrons are treated explicitly by expanding the wavefunctions in a plane-wave basis set with an energy cut-off of 400 eV. The valence electron configurations are as follows: Ta 6s 2 5d 3 ; N 2s 2 2p 3 ; Cu 3d 10 4s 1 ; W 6s 2 5d 4 ; Co 4s 2 3d 7 . The k-point mesh is restricted to the Γ-point as we use a larger 2×8 surface supercell. A detailed description of the surface model is available in the supporting information, section S1. All calculations use the spin-polarised generalised gradient approximation as implemented in the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [90]. This functional is a standard functional for the modelling of surfaces and has been successfully used in our previous studies on TaN [29][30][31]. As we are dealing with metallic systems, rather than semiconductors, and are not interested in investigating the electronic structure in detail, this functional provides a good compromise between accuracy and tractability. Additionally, we aim to compare our finding in this study to our previous studies, which also employed the same computational set up, including PBE functional. Choosing a different functional for this study would prevent a consistent comparison. We use Gaussian smearing with σ = 0.1 eV. The convergence criteria for the energy minimisation is 1×10 −4 eV and the force threshold for the ionic optimisation is 0.02 eV Å −1 . The atomic charges are computed using the Bader charge partitioning scheme [91,92]. All charges discussed in the text and the supporting information are relative to the number of valence electrons of the specific element. The aiMD calculations are performed within the NVT ensemble (constant number of particles, volume and temperature) using the models obtained from the geometry relaxation. Here, we use a kinetic energy cut-off of 250 eV, a temperature of 500 K, a time-step of 5 fs and a simulation length of 1000 steps which yields a simulation time of 5 ps. Atoms in the bottom two layers of the slab are frozen.
Atomic structures of the Co-and W-doped surfaces and of Cu n (n = 1, 2, 4, 29) clusters adsorbed on these surfaces were optimised at 0 K in static DFT relaxations. The aiMD calculations use the optimised geometry as the first image.
The binding energy was calculated using the following equation: where E total is the total energy of the relaxed system with adsorbed copper, E surf is the total energy of the relaxed, bare surface before Cu adsorption, E Cu−atom is the energy of a free Cu atom in vacuum, which is typically used in these calculations and n is the number of Cu atoms. The doping energy for each surface was calculated with the following equation: Here, E total is the total energy of the doped, relaxed surface, E clean is the total energy of the bare TaN (1 1 0) surface, n is the number of dopants in the system, and E dopant is the energy of the bulk dopant in vacuum per atom. Similarly, E Ta is the energy of bulk Ta in vacuum per atom.
To evaluate the competition between Cu-surface and Cu-Cu interactions which play a large role in controlling thin film morphology, we calculate the Cu-Cu interaction energy. For this we first calculate E Cu−substrate , which is the binding energy calculated with reference to a gas phase Cu n cluster instead of a single Cu atom: To calculate E surf * we take the modified TaN surface that is relaxed after Cu adsorption remove the Cu adatom and compute the single point energy. Similarly, E Cu_cluster is the single point energy of the Cu n in the structure it takes after adsorption on the surface. By isolating the Cu-substrate interaction we can now calculate the metal interaction energy: Due to the smaller ionic radius of Co (0.55 or 0.61 Å, depending on high or low spin) compared to Ta (0.72 Å) [66], extremely strong surface rearrangements were observed on the Co 50−S , Co 50−F and Co 100 surfaces. For this reason, the binding energy and the Cu-Cu interaction energy for these surfaces were computed by using E surf* , the single point energy of the rearranged surface after removing Cu instead of E surf , the total energy of the relaxed surface before metal adsorption, as a reference. This is the same energy used to compute E Cu-substrate , which has the consequence that the Cu-Cu interaction energies are based solely on the difference in the Cu reference energies. However, they are still a reasonable indicator of the contributions of Cu-substrate energy and Cu-Cu energy to the total binding energy.
Structure and input data associated with these calculations are available on our GitHub repository: https://github.com/MMD-group/VASP.

W-doped and Co-doped TaN surfaces
To determine the relative stability of the different surfaces we have computed a doping energy for each surface using equation (2). Doping energies for each W and Co surface are shown in table 1 and are   compared to doping energies for Ru doping from earlier work [30]. W doping is more favourable than Ru doping and the doping energies for the two 50% doped surfaces are both negative and quite large in magnitude indicating that doping with this W content is favourable and is more favourable than doping with Ru, Co or other W contents. While all of the Co-doped surfaces have negative doping energies the most stable surfaces are Co 25 and Co 50−F . Additionally, we find that similar to our previous work on Ru-doped TaN [30], the F-site is the most favourable doping site for both Co and W.

Cu n adsorption on Co-and W-doped TaN
The relaxed W-and Co-doped TaN surfaces and their unique adsorption sites are shown in figures 2 and 3. The most favourable adsorption site for each surface was chosen for the adsorption of Cu 2 and Cu 4 species. The binding energies for each single Cu atom adsorption are detailed in the supporting information, table S1 (W-doped TaN) and table S2 (Co-doped TaN).
All Co-doped surfaces rearrange to some degree upon Cu adsorption, creating gaps on the surface that trap the Cu atom, depending on the adsorption site. This is due to the difference in ionic radius between Co (0.55 or 0.61 Å, depending on spin) and Ta (0.72 Å) [66]. While for TaN and all W-and Ru-doped surfaces the 5 coordinate site (A) is most favourable, only Co 50−S shares this most favourable adsorption site. On Co 25 and Co 50−F site (B) is the most favourable, as shown in figures S11 and S13, as well as table S2 in the supporting information. Site B is a four coordinate site with two metal atoms (in this case one Ta atom and one Co atom) and two N atoms. This site is likely more favourable than site (A) as the difference in ionic radius creates a gap between the Co and Ta atom. On Co 25 Cu can partially occupy this gap, as shown in figure 4(A). Figure 4(B) shows that the Cu atom on Co 50−F is bound to an N atom in the gap and does not incorporate into the surface in the same way as the Cu atom on Co 25 . However, the proximity to the gap and a slightly longer Cu-N bond compared to other adsorption sites is the only difference that sets this geometry apart, leading us to assume that the surface gap must nevertheless be an important factor in promoting a more favourable binding energy. On Co 50−S , there are two Co atoms at site (B) prior to relaxation. In the relaxation, a surface rearrangement occurs which leaves a gap between four Co atoms for Cu to occupy ( figure 4(D)). The result is a strong binding energy of −3.82 eV atom −1 . However site A on this surface forms a larger gap that allows Cu to fully incorporate into the surface layer leading to a particularly large binding energy of −4.61 eV atom −1 , as shown in figure 4(C).
The Co 100 surface rearranges to the point where it becomes difficult to describe an adsorption site after relaxation using our labelling. This is similar to Ru 100 in [30]. This is most likely caused by the difference in Figure 5. 100% Ru, W and Co doped surfaces before and after Cu adsorption. The Ru geometry is taken from [30]. Atoms are coloured as follows: Ru = purple, W = green, Co = pink, Cu = blue, Ta = gold, N = silver. the ionic radius of Co and Ru compared to Ta [66]. Figure 5 compares the Ru, Co and W 100% doped surfaces before and after Cu adsorption. Here, the effect of the difference in ionic radius becomes clear. From largest to smallest the ionic radius of the relevant atoms are: Ta ≳ W > Ru > Co. No rearrangements are observed for W 100 due to the similar ionic radius of W and Ta. A clear rearrangement is observed for Ru 100 , while Co 100 shows the most significant rearrangement due to the large difference in ionic radius. Additionally, without the presence of Ta atoms this 'CoN-like' layer begins to distort significantly as illustrated in figure 6. Here, we observe extremely large gaps that expose the underlying TaN slab. Additionally, several Co and N atoms migrate away from TaN and adsorb atop the remaining Co and N atoms to form a second layer of CoN (see figure 6). These rearrangements are most likely caused by the lattice mismatch and different unit cells for CoN (cubic) and TaN (hexagonal). More details on this are included in section S6 of the supporting information.
For the study of small Cu n clusters, we have selected five typical Cu 2 and Cu 4 geometries. All geometries are initially adsorbed at the most favourable single atom adsorption site for each surface. There are two Cu 2 models, 'close' and 'apart' where two Cu atoms are adsorbed either at neighbouring sites or separated by two unoccupied sites. This is a very basic model to determine an initial preference towards association or separation. For Cu 4 , we chose three different models. These are (i) a line along equivalent adsorption sites, (ii) a flat rhombus configuration or (iii) a 3D tetrahedron. This lets us determine if the preferred geometry at this early stage of nucleation corresponds to a preference of 2D or 3D film growth and shows how Cu-Cu interactions compare to Cu-surface interactions (see equations (3) and (4)). Analysis of the competition between these two interactions allows us to select the surfaces most likely to promote wetting of Cu for further study.
Geometries and energies for all adsorption structures are shown in the supporting information, sections S2 (W-doped surfaces) and S3 (Co-doped surfaces). Figure 7 compares Cu-substrate and Cu-Cu interaction energies for each Cu 2 and Cu 4 adsorption structure on Co-and W-doped TaN.
The competition between Cu-substrate and Cu-Cu interaction for the four Co-doped TaN surfaces shows that the Cu-substrate interaction is stronger than the Cu-Cu interaction for all adsorption geometries. This indicates that Cu should wet on all four surfaces, since the growth mechanism that promotes wetting is favoured when the adatom-substrate interaction is stronger than the adatom-adatom interaction. However, the rearrangements of the Co-doped surfaces could impede or complicate the growth process. The most significant differences between the two energy contributions occur for Co 25 and Co 100 , while the magnitude of the interactions is somewhat more competitive for Co 50−S and Co 50−F . Co 25 has the weakest Cu-Cu interactions of all four surfaces and is also the only Co-doped TaN surface that does not undergo significant rearrangements due to having a smaller Co content. The Cu-Cu interactions for the close, apart and line geometries on this surface are positive, indicating that the incorporation of adatoms into the surface layer is able to prevent interaction between the Cu atoms. Combined with the fact that separated geometries are favoured over associated geometries, wetting of Cu should be promoted which makes Co 25 a potential candidate for our target combined barrier/liner material. Co 50−F is also a candidate, showing some of the strongest Cu binding energies and Cu-substrate interactions, but less drastic surface rearrangements than Co 50−S and Co 100 . While Co 100 shows both strong Cu-substrate interactions and weak Cu-Cu interactions, the distortion of the surface CoN layer indicates that this surface is likely not suitable to promote a smooth Cu film. The large gaps in the surface that arise from surface distortion during Cu adsorption provide opportunities for enhanced Cu-substrate interactions. An example of this is observed for the tetrahedron, which flattens and forms a structure that is almost 2D due to incorporation of atoms into this large gap (see figure S20 of the supporting information). Figure 7 shows that the binding energies of Cu on W-doped TaN are weaker than those on Co-doped TaN. We also observe stronger Cu-Cu interactions compared to Co-doped TaN. The Cu-Cu interaction energies are strongest for the rhombus structures on all but the W 25 surface. This is most likely due to the difference in the shape of the rhombus on W 25 which upon relaxation, resembles the line configuration and thus has fewer interactions between the Cu atoms. The tetrahedral configuration has a favourable binding energy on all of the surfaces. On W-doped surfaces, the Cu-substrate and Cu-Cu interaction energies are competitive, while on Co-doped surfaces the Cu-substrate interaction is stronger than the Cu-Cu interaction. Although the tetrahedron is 3D, as the film grows, further tetrahedrons could join into a 2D film, based on this relationship between Cu-substrate and Cu-Cu interaction energies.
On the W 50−F and W 100 surfaces where the 2D rhombus is most favourable, a 2D film could form based on this preference, as the Cu-substrate interactions remain favourable despite the strong Cu-Cu interaction energy. Additionally, the W 25 surface may promote wetting, as this is the only surface where all geometries have a Cu-substrate interaction that is stronger than the Cu-Cu interaction. Based entirely on the competition between Cu-substrate and Cu-Cu interaction Cu should wet on this surface. However, the overall binding energy of Cu on this surface is weaker than that computed for Cu on TaN (see [30]). Additionally, the tetrahedron is the most favourable Cu 4 geometry on this surface. Given that Cu does not wet on TaN, but has a stronger adhesion compared to W 25 , it is not possible to make a conclusive prediction with these models based on the computed binding energies and structures alone. Further study of this surface should provide more conclusive insights and will also show whether the competition between interaction energies or the favouring of a specific geometry is a better indicator of the film morphology. In contrast, the Cu-substrate interaction is more favourable than the Cu-Cu interaction energy for all structures on Co-doped surfaces. This indicates that Cu is likely to wet on all surfaces. However due to the complicated surface rearrangements that occur, the effect of surface stability and morphology on the Cu structure must also be taken into account.

Ab initio MD of Cu 4 on Co-and W-doped TaN
To gain further insight into how the competition between Cu-substrate and Cu-Cu interaction relates to the effects of temperature on small Cu clusters, we carried out a series of aiMD calculations for the relaxed rhombus cluster on all Co-and W-doped surfaces at 500 K. Both Co 50−S and Co 100 are thermally unstable in this stoichiometry during the aiMD simulation. Co 50−S loses N 2 after 0.5 ps at 500 K, while Co 100 loses five N atoms after 0.5 ps at 500 K. Geometries at the relevant snapshot are shown in the supporting information, figure S21.
CoN is the cobalt nitride stoichiometry with the most favourable formation energy [93], closely followed by Co 2 N [94]. Given that CoN is the most favourable stoichiometry, the distortion of the Co 100 surface and its thermal instability likely do not arise from the particular stoichiometry. However, bulk CoN has a cubic unit cell and bulk TaN has a hexagonal unit cell. This leads to different coordination environments for Co when doped into TaN and in bulk CoN. Additionally, there is a lattice mismatch between CoN and TaN. Bulk CoN has lattice parameters of a = b = c = 3.01 Å, while bulk TaN has lattice parameters of a = b = 5.23 Å, c = 2.93 Å. The combination of lattice mismatch and different unit cell symmetry are likely the largest contributing factors to the instability of the Co 100 surface, along with the different ionic radii of Co and Ta. Similarly, Co dopants in the Co 50−S surface are concentrated in two regions. As such, these can essentially be considered areas of 100% Co doping and thus show the same instabilities as Co 100 . Additional analysis on the stable metal nitrides of Ta, Ru, Co and W and the effect this has on the 100% doped surfaces is detailed in section S6 of the supporting information. Table S3 in the supporting information shows formation energies, types of unit cell and lattice parameters for selected Ta, Co, Ru and W nitrides.
Co 25 and Co 50−F are both thermally stable and the geometry of the initial rhombus structure of Cu 4 before and after the aiMD run are shown in figure 8. The results from the aiMD simulations support our initial hypothesis that these surfaces should promote wetting of Cu. On Co 25 , one of the Cu atoms separates from the cluster, as shown in figure 8(A). This is accompanied by some surface distortions, which cause a Ta atom be pushed partially out of the surface layer. The effect such distortions would have on surface roughness and stability require a much larger model and are outside the scope of this study. The other three atoms remain at their original positions from the relaxed starting geometry, however a single atom migrating away from the cluster supports our idea that there is a preference for fewer Cu-Cu interactions on this surface. Similarly, on Co 50−F , the rhombus rearranges into a line configuration along a row of Co dopants, as shown in figure 8(B). This is likely caused by the strong interactions between Co and Cu, allowing the Co dopant to act as a nucleation site in the surface, similarly to Ru dopants as discussed in [29]. It also reduces the number of Cu-Cu interactions.
On W 25 the less favourable rhombus with three atoms in a line rearranges into a square after 5 ps at 500 K. Each atom is adsorbed at a site A, thus increasing the number of Cu-Cu interactions compared to the 0 K geometry (see figure 9(A)). Even though the tetrahedron was the most favourable geometry on this surface, no such 3D structure is formed here. The Cu 4 structure on W 50−S remains unchanged after 5 ps at 500 K (see figure 9(B)). On W 50−F , it appears that the atoms migrate across the surface toward the nearest A sites and begin forming into the same square structure observed for W 25 (see figure 9(C)). On W 100 , the rhombus rearranges into a tetrahedron, even though this geometry was not as favourable during the standard geometry relaxations (see figure 9(D)). The tetrahedron was most favourable on W 25 , however the fact that the rhombus structure did not rearrange into a 3D structure at 500 K, as well as the favourable Cu-substrate interaction, indicates that 25% W could be enough to prevent Cu island formation, while 100% W is potentially too high of a doping concentration, in that it will be similar to TaN. Experimental results for W x N y barriers [67] showed that W 2 N has good barrier reliability up to 790 • C while WN breaks down at 500 • C. No study of the liner properties of W-based materials has been carried out to the best of our knowledge; however it is reasonable to propose that a W doped TaN surface might have enhanced barrier reliability compared to W 100 , which is essentially a layer of WN passivation on TaN.

Cu 29 on Co-and W-doped TaN
In our previous work [31], we used a 29 atom model of Cu in order to gain better insight into the behaviour of a Cu model with larger number of atoms at a different stage of the film growth process. We use this model on the most promising Co-and W-doped TaN surfaces from Sections 3.2 and 3.3 and assess our predictions of 2D vs 3D Cu morphology based on Cu-Cu and Cu-substrate interactions obtained from 0 K relaxations and trajectories obtained from the aiMD simulations. The surfaces selected are Co 25 , Co 50−F , W 25 , W 50−F and W 100 .
Similar to Ru-doped TaN surfaces, we observe a transition from the initial single layer of Cu 29 to a two-layered structure on all surfaces. On Co 25 , 7 Cu atoms move to the second layer, while on Co 50−F 6 atoms migrate to form a second layer, as shown in figure 10. On both W 50−F and W 100 , the Cu structure resembles facets on the Cu (1 1 1) surface. This is the desired crystal structure for Cu in interconnects as it has the best electromigration reliability [95]. On W 25 , 6 Cu atoms migrate into the second layer and the overall geometry continues to resemble the original Cu 29 geometry, as shown in figure 12. On W 50−F there are 10 atoms in the second Cu layer and on W 100 there are 9 atoms in the second Cu layer. During the aiMD calculation Cu atoms rearrange to be more close packed on both of these surfaces. There are no transitions to a third layer observed over the course of 5 ps on W 100 , however a Cu atom migrates to the third layer on W 50−F after approximately 2 ps. Further upward migration occurs, creating a 3D cluster structure shown in figure 11(A). The reduced number of atoms in the second layer of Cu 29 on Co-doped TaN compared to W-doped TaN shows that Co doping is better at preventing upward migration, as expected given the more favourable adhesion between Cu and Co as compared to Cu and W.
Cu atoms already begin to migrate into the second layer during the 0 K relaxation on Co 25 and compared to Co 50−F the number of Cu atoms that migrates is larger. However no Cu migration to form a third layer is seen during either the 0 K relaxation or the aiMD simulation. Additionally, during the aiMD simulation, we observe a Cu atom detaching from the Cu cluster and migrating towards a Co dopant, while another migrates along the edges of the cluster, but not upwards to form a 3D structure. This indicates good mobility of Cu atoms over the surface. Such Cu atom detachment from the Cu 29 structure was only observed on two other surfaces, the 1 ML Ru passivated surface discussed in [29][30][31] and the W 25 surface. The favourable Cu-substrate interactions, along with the lack of formation of further Cu layers and the Cu atoms that migrate away from Cu 29 suggest that 25% Co-doped TaN is a strong candidate for a combined barrier/liner material that limits 3D island growth.
The aiMD simulation for Cu 29 on Co 50−F shows that this surface can also promote 2D growth of Cu. Cu atoms appear quite mobile on the surface and split off from Cu 29 as smaller clusters with 4 or 5 atoms, figure 10(B). One such structure begins to incorporate into the surface gaps and resembles the geometry of the Cu 4 rhombus on Co 50−F , shown in figure 8(B). There is an equivalent surface gap underneath the largest remnant of the original Cu 29 structure, however atoms do not incorporate here. This indicates that the regular Cu structure formed here is favoured compared to incorporation into the surface when there is a large number of Cu atoms.
These results additionally show that Cu preferentially migrates towards the areas of higher Co concentration in the surface, which is consistent with Cu 2 and Cu 4 adsorption on Co-doped TaN. In our previous work, we found that Ru also acted as a nucleation site for Cu atoms, however we did not observe such preferential migration during the aiMD runs on the equivalent Ru-doped surface in [31]. While a smooth film can likely be achieved with 50% Co doping, for interconnect applications a surface like Co 25 , where the dopants are more distributed should have an advantage in promoting growth of a 2D Cu film. However, it is possible that area selective growth of Cu on CoN could be achieved by combining CoN and TaN. Based on our results, atoms should selectively migrate towards the Co-rich areas. The stronger adhesion of Cu on the CoN areas present on Co 50−F and on the Co 100 surface compared to the TaN surface also means that it could be possible to selectively remove any unwanted Cu atoms in the Ta-rich areas of the surface. The literature around selective atom removal tends to focus on using irradiation techniques to change the composition of polyatomic materials [96]. Other work on selective removal targets specific surface sites based on localised electronic excitations in the surface with the aim to smooth rough metal surfaces [97]. Meanwhile, processes for selective atomic layer etching are still in development and tend to be material-selective rather than truly area-selective [98].
Although the rhombus rearranged into a tetrahedron during the Cu 4 aiMD simulation in section 3.3, the results of the Cu 29 aiMD simulation and the fact that the Cu 4 rhombus structure was preferred during the geometry relaxation suggest that W 100 acts as a liner. As we see no exchange of Cu and surface atoms combining WN and TaN like this should yield a thermally stable material that can act as a barrier, despite the possible inferior barrier reliability of W x N y compared to TaN [67].
On W 25 , during the aimD simulation, the Cu atoms rearrange into a wire-like structure. Additionally, a single Cu atom breaks away from the cluster and migrates across the surface, indicating enhanced atom mobility. We also observe several transient states throughout the aiMD run-time where the Cu 29 structure separates into smaller clusters, before rearranging into the wire-like structure. This is shown in figure 12. As the W dopants are uniformly distributed throughout the surface, meaning that there are no W-rich areas, this rearrangement is clearly not caused by enhanced interaction between Cu and W. Given that the only difference between the interactions of Cu with W 25 compared to the other W-doped surfaces is an increased Cu-substrate energy, it is possible that the distribution of W-dopants in TaN can strengthen the interaction with Cu. Even though there are no clear indications in our analysis why W 25 behaves differently in this respect, provided that these wire-like structures would join into a smooth thin-film, 25% W-doped TaN may be a candidate for a combined barrier/liner material. This also demonstrates that a favourable tetrahedron configuration is not a strict indicator of a preference for 3D growth and that the Cu-Cu vs Cu-substrate interaction is a more reliable indicator for 2D vs 3D morphology. While the weaker overall adhesion of Cu atoms is of some concern, due to the lack of rearrangements and surface gaps in W 25 this composition may have superior stability compared to Ru-and Co-doped TaN.
The Cu-Cu and Cu-substrate interaction energies for Cu 29 on W 25 , W 50−F , W 100 , Co 25 and Co 50−F are shown in table 2. We find that the Cu-Cu interaction is significantly more favourable than the Cu-substrate interaction for all surfaces. Normally, this would indicate a preference towards 3D growth on all surfaces. However, this does not hold for copper on modified TaN. For example, on W 50−F Cu atoms migrate to a third layer. In contrast, no additional layers are formed on any of the other surfaces, even though the magnitude of the Cu-Cu interaction is independent of the surface on which Cu 29 is deposited, and the Cu-substrate interaction is almost constant on all three W-doped surfaces. This demonstrates two consequences: first, that the overall binding energy of Cu 29 is slightly stronger on Co-doped TaN than W-doped TaN. This stronger binding arises purely from the Cu-substrate interaction, as indicated by the more favourable Cu-substrate interaction on Co-doped TaN. Second, for very large Cu structures the competition between the two interactions is no longer a useful indicator of the probable growth morphology of copper because the Cu-Cu interaction becomes independent of the substrate and the shape of the Cu cluster.  (1)), Cu-substrate interaction energies (equation (3)) and Cu-Cu interaction energies (equation (4) We know from the literature that the final growth morphology is controlled by the favoured growth mechanism which is controlled by the competition between the metal-metal and metal-substrate interactions, as described in references [38,45,[47][48][49][50]. Mean field Monte Carlo methods have been used to determine the preferred growth morphology of homoepitaxial growth of metals and this approach together with experiment has been used to directly probe 2D vs 3D growth of Ru on different substrates [47]. However, to the best of our knowledge, our findings provide the first detailed atomistic study of the key factors driving copper morphology and there is ongoing work in our group to fabricate and test our proposed TaN-based materials. The calculation of explicit activation energies for Cu atom migration is obviously important to assess preferred growth morphology, as in [31], where activation energies confirmed our morphology predictions for both 2D and 3D growth from aiMD. Based on this, despite the limitations of our model discussed above, we can propose with good reason a model using aiMD calculations to validate predictions based on metal-substrate/metal-metal interactions avoiding extremely resource intensive activation energy calculations. By extension, the study of the competition between the interactions provides a useful tool to gain initial insights into the likely film morphology.
Discussion of the electronic properties of these surfaces based on Bader charges and DOSs plots are included in the supporting information, section S7. The DOS is metallic for all structures studied. Given the comparatively smaller number of Cu, Co and W atoms compared to the TaN slab, the DOS is dominated by metallic TaN. We find that the contributions of Co to the total DOS are stronger than those of W and Cu for the same dopant distributions and concentrations. The Bader charges show, that Cu atoms tend to be more oxidised on the Co-doped surfaces compared to Ru-and W-doped TaN. On all thermally stable surfaces, as for systems we previously studied, Cu atoms are only oxidised if they interact directly with the surface, while all other Cu atoms remain metallic. Based on the metallic character of the adsorbed Cu atoms on each TaN surface, we expect modified TaN films to promote deposition of Cu interconnect with sufficiently low Cu resistivity essential for Cu interconnects.

Conclusion
In this paper, we showed how incorporation of Co and W into the surface layer of TaN can be used to control morphology of deposited Cu. In particular we show how a preference for 2D vs 3D stability is driven by the competition between Cu-substrate and Cu-Cu interactions which control the preferred growth mechanism. To promote 2D growth, the Cu-substrate interaction energy should be more favourable than the Cu-Cu interaction energy. Additionally, 2D vs 3D growth can be modelled using a Cu 29 cluster which has a sufficient number of atoms to form distinct layers. Ab initio MD simulations at finite temperature of such a cluster on a given surface provide insight whether a 3D cluster with more than two layers would be formed or if that metal film become 2D. We are able to show consistently that for surface compositions where the Cu-substrate interaction is stronger than the Cu-Cu interaction, no more than two distinct layers are formed, indicating 2D film growth. Based on this, we determined that 3D growth of Cu should be inhibited and wetting of Cu should be promoted in the following compositions: 25% Co-doping, 25% W-doping, 50% Co doping (in the more favourable dopant distribution) and 100% W-doping. Interestingly, two Co-TaN compositions are thermally unstable: the 100% and the less favourable 50% Co-TaN surfaces as a result of the ionic radius mismatch between Co and Ta.
The favourable Cu-substrate interactions on the 25% Co-doped surface, along with minimal surface rearrangements due to the lack of possible Co-Co interactions in the surface layer, make it a promising candidate for a combined barrier/liner material-we see migration of only a small number of Cu atoms into a second layer during the relaxation and the aiMD at 500 K, indicating that it should inhibit formation of 3D islands. Meanwhile, 25% W doping does not improve the binding energy of Cu compared to TaN, but it improves the Cu-substrate interaction significantly compared to the other W-doped TaN surfaces. This leads to 2D Cu structures, however the inferior adhesion of Cu and the wire-like structures formed may not be favourable for the manufacturing process. 50% W doping does not prevent 3D growth. This is partially due to the lack of surface gaps formed as a result of the similar ionic radii of Ta and W and which are therefore not available to enhance the Cu-substrate interaction. This property could however be an advantage, as it seems to improve the thermal stability compared to Ru and Co. Additionally, the interactions between Cu and W-doped TaN with W concentrations above 25% are quite strong, indicating that 100% doping, or essentially passivation with WN can create a combined barrier/liner material. To the best of our knowledge this is also the first time that possible liner properties of WN have been studied.
Due to the gaps created in the surface by Ru and Co doping and the subsequent incorporation of Cu into this layer, these combined barrier/liner materials must be at minimum made up of two atomic layers (one layer of TaN and one layer of doped TaN) to retain their integrity as diffusion barriers. While this is not an issue for W doping, tungsten nitrides have been shown to have inferior barrier properties. For this reason, the '100% W-doped' layer of WN likely cannot be used on its own and will require an additional layer of TaN.
Comparing the conclusions drawn based on results from different sizes of Cu clusters we are able to evaluate the limits of our models. In general terms, the more favourable Cu-substrate interactions compared to the Cu-Cu interactions, allowed us to directly predict the likely growth mechanism and thus film morphology of Cu on W 25 , Co 25 and Co 50−F . On W 50−S , W 50−F and W 100 the results were somewhat more ambiguous, as the favoured interaction changed for different adsorption geometries. The likely growth mechanism and surface morphology could only be determined using a larger Cu model.
Overall, we find that the competition between Cu-Cu and Cu-substrate interactions is a better indicator of the likely film morphology than a preference for a particular cluster geometry for few atom clusters as in the case of rhombus vs tetrahedron stability of Cu 4 . Additionally, the competition between the Cu-substrate and Cu-Cu interactions is no longer as useful for larger models where many more Cu-Cu interactions are present, causing the Cu-Cu interaction to become independent of the surface and the Cu geometry. Given this information, we now know that Cu 4 models are most useful for predicting the film morphology and that a large model such as the Cu 29 cluster combined with finite temperature ab initio MD simulations is best used to confirm results or gain additional insight where the results obtained by comparing metal-metal and metal-substrate interactions of smaller clusters are ambiguous.
This approach facilitates screening of many surfaces as it significantly reduces the computational cost and overall time needed to predict thin film morphology, avoiding explicit computation of activation barriers. This provides a rapid method to screen a material selection for specific applications.

Data availability statement
The data that support the findings of this study are openly available at the following URL: https://github. com/MMD-group/VASP.