# Conventional and high power impulse magnetron sputtering deposition of tantalum nitride films: a molecular dynamics approach

Pascal Brault, Marjorie Cavarroc-Weimer, Sara Fazeli, Nicolas Froloff

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Pascal Brault, Marjorie Cavarroc-Weimer, Sara Fazeli, Nicolas Froloff. Conventional and high power impulse magnetron sputtering deposition of tantalum nitride films: a molecular dynamics approach. European Physical Journal: Applied Physics, 2025, 100, pp.12. 10.1051/epjap/2025012. hal-05057404

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# Conventional and high power impulse magnetron sputtering deposition of tantalum nitride films: a molecular dynamics approach

Pascal Brault<sup>1,2,*</sup> <sup>□</sup>, Marjorie Cavarroc-Weimer<sup>3,**</sup> <sup>□</sup>, Sara Fazeli<sup>1</sup> <sup>□</sup>, and Nicolas Froloff<sup>1</sup>

Received: 10 January 2025 / Accepted: 10 April 2025

**Abstract.** For understanding and controlling film growth parameters of various sputtering deposition conditions, molecular dynamics simulations are carried out to describe Tantalum Nitride conventional Magnetron Sputtering and High Power Impulse Magnetron Sputtering (HiPIMS) film growth and structure. It includes full atomic and ion energy distribution for a realistic account of experimental conditions, notably for HiPIMS deposition technique. Results are well compared with available experimental results in the literature, demonstrating that the present method is well suited for a very broad set of experimental conditions. The effect of the sputtered ion to neutral ratio on the film crystallographic structure is addressed using simulated X-ray diffraction and polyhedral template matching methods. It is shown that hcp phase predominates at moderate ion flux, and always coexists with fcc phase. The present molecular dynamics simulations, are therefore a powerful tool for correlating the predicted thin film structure to experimental conditions.

**Keywords:** Molecular dynamics simulations / HiPIMS / sputtering deposition / thin films / nitride

## 1 Introduction

Transition metal nitrides have garnered significant interest due to their remarkable chemical and physical properties [1]. Among these, tantalum nitride (TaN) has emerged as a material of choice for a wide range of applications, owing to its desirable characteristics such as low electrical resistivity, high hardness, and excellent thermal stability. TaN is notable for its uniform resistivity, low temperature and voltage coefficients of resistivity, high thermal stability, and its role as an effective barrier material in copper interconnects. It also offers the advantage of its high melting point. Recently, TaN films were successfully used in electrochemical devices [2,3], in electrocatalysis [4] and photocatalysis [5]. Tantalum nitride thin films also find applications in magnetic multilayers and thin-film resistors [6].

Chemically inert, tantalum nitride (Ta-N) exists in various phases, including Ta₂N, Ta₃N₅, Ta₅N₆, and other metastable configurations. Among these, Ta₃N₅ is distinguished by its exceptional electrical properties, making it a preferred choice as a dielectric layer in semiconductor devices. In contrast, Ta2N exhibits metallic-like

resistivity. Typically, Ta-N phases such as θ-TaN, Ta₅N₆, β-Ta₂N, η-TaN, δ-TaN₁-x, Ta₃N₅, and Ta₄N₅ are utilised depending on the application requirements [3,7]. Recently there have been efforts to grow high-quality TaN films using radio-frequency or dc magnetron sputtering (MS) deposition [8], and especially the high power impulse magnetron sputtering (HiPIMS) [3]. Such experiments were conducted at different argon/nitrogen flux ratios, operating pressures, leading to various structures and phases, in addition to targeted functional properties. On the other hand simulations at the atomic level, especially the molecular dynamics simulation technique have made progress and are now able to give insights into magnetron sputtering growth phenomena and resulting atomic structure for direct comparison with experiments. Especially, accounting for the ion and atomic energy distribution (AED and IED) functions allows to get closer to experimental deposition conditions [9]: initial velocities of all depositing species at the substrate. The interest of High Power Impulse Magnetron Sputtering (HiPIMS) operation is to produce sputtered ions that participate to the film growth. An important parameter, though not always determined, is the sputtered ion to neutral ratio, which can reach up to 90% [10–12]. This short communication aims at studying TaN deposition in MS and HiPIMS modes and comparing resulting atomic structures for two different ion-to-neutral ratio.

<footnote n="1">¹ MS4ALL, 1 avenue du Champ de Mars, 45100 Orléans, France</footnote>

<footnote n="2">² GREMI, CNRS, Université d'Orléans, 14 rue d'Issoudun, 45067 Orléans, France</footnote>

<footnote n="3">³ Safran Tech, rue des jeunes bois, Châteaufort, CS 80112, 78772 Magny-les-Hameaux, France</footnote>

<footnote>* e-mail: pascal.brault@cnrs.fr</footnote>

<footnote>** e-mail: marjorie.cavarroc@safrangroup.com</footnote>
## 2 Material and methods

The molecular dynamics simulations consist in solving Newton's equations of motion:

$$m_i \frac{d^2 \vec{r}_i(t)}{dt^2} = \vec{F}_i = -\nabla V(\vec{r}_1(t), \vec{r}_2(t), \dots, \vec{r}_N(t)) \quad (1)$$

where $\vec{r}_i(t)$ is the position of atom i at time t with mass $m_i$, and V is the interaction potential between all N involved species. This equation requires the knowledge of two initial conditions: positions and velocities at the initial time t = 0, and the forces between all species at each instant. Initial positions refer to the geometry/topology of the particles at the beginning of the simulation. Velocities are selected (randomly) from a velocity distribution consistent with the studied phenomena, e.g. selected from a Maxwell-Boltzmann distribution, or from any relevant velocity distribution obtained experimentally (e.g. from mass spectrometry), or from any other dedicated simulations.

The simulation box is an iron substrate with an empty zone above it, from which the incident species, N, N⁺, Ta and Ta⁺, are injected, as described in Figure 1.

The iron substrate is of size 20 × 20 × 16 a₀³(Fe), with a₀ (Fe) = 0.287 nm, the lattice parameter of bcc Fe at 300 K. The species are randomly selected according to targeted composition, and injected in sets of 10, at least separated by 1 nm, from a height of 1.5 nm above the substrate. Each set is injected after 20000 timesteps at a height of 0.5 nm above the previous one. Between 20000 and 40000 species are injected per run. After the last injection, a relaxation run is applied during 500000 timesteps. The integration time (one timestep) dt = 0.1 fs. Interaction potentials appearing in Equation (1) are described by Morse functions [13]:

$$V(r_{ij}) = D \left[ e^{-2\alpha(r_{ij}-r_0)} - 2e^{-\alpha(r_{ij}-r_0)} \right] \quad (2)$$

where V is a pair potential energy function, $r_{ij}$ is the distance between atoms i and j, $r_0$ is the nearest atomic distance at equilibrium, D is the bond energy and $\alpha$ is the potential stiffness. Cross-interaction parameters are calculated using the Lorentz-Berthelot mixing rules via the following equations [14,15].

$$\begin{aligned} D_{A-B} &= (D_A D_B)^{1/2} \\ \alpha_{A-B} &= \frac{1}{2}(\alpha_A + \alpha_B) \\ r_{0A-B} &= (\sigma_A \sigma_B)^{1/2} + \ln\left(\frac{2}{\alpha_{A-B}}\right). \\ \sigma_{A,B} &= r_{0A,B} - \ln\left(\frac{2}{\alpha_{A,B}}\right)n \end{aligned} \quad (3)$$

All Morse parameters used in this research are listed in Table 1.

It should be noted, use of embedded atom method (EAM) [16] many-body potentials for Fe(Fe⁺)-Fe(Fe⁺), Ta(Ta⁺)-Ta(Ta⁺) and Fe(Fe⁺)-Ta(Ta⁺) interactions does not improve the results.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Simulation box used for the calculation. The first set of atoms to be injected is present on the diagram.</figcaption></figure>

<table><caption>Table 1. Morse interaction potential parameters for the Fe-Ta (Ta⁺)-N(N⁺).</caption><thead><tr><th>Aatom pair<fnref n="1" /></th><th>r₀(Å)</th><th>D(eV)</th><th>α (Å⁻<fnref n="1" />)</th></tr></thead><tbody><tr><td>Ta-Ta</td><td>3.346</td><td>0.7504</td><td>1.1319</td></tr><tr><td>N-N</td><td>1.8316</td><td>0.2</td><td>6.087</td></tr><tr><td>Ta-N</td><td>2.0503</td><td>0.3872</td><td>3.6094</td></tr><tr><td>Fe-Fe</td><td>2.849</td><td>0.4216</td><td>1.3765</td></tr><tr><td>Fe-Ta</td><td>3.0857</td><td>0.5623</td><td>1.2542</td></tr><tr><td>N-Fe</td><td>1.7948</td><td>0.2903</td><td>3.7317</td></tr></tbody></table>

The next step is to include an energy distribution function for each atom (ion) type. First, ions are treated as fast neutral as they are neutralised at the substrate surface [17]. For the MS process, only Ta and N species are considered. N species are considered instead of N₂ since N₂ should dissociate for reacting with the surface and then growing film. N AED is defined by a thermal distribution at 300 K. On the other hand, Ta AED [9], issued from SRIM calculation, is propagated through the gas phase at pressure P = 0.5 Pa, along the target to substrate distance d = 7 cm [3]. For HiPIMS process, Ta, Ta⁺, N, N⁺ are considered. AED of Ta an N are the same as those used for MS. For Ta⁺ a bi-Maxwellian IED [18] is considered. Hecimovic et al. [18] demonstrated that, within a certain pressure range, the bi-Maxwellian IED approximation is valid. This IED is defined as:

$$F(\varepsilon) \approx C_1 \sqrt{\frac{\varepsilon}{(k_B T_1)^3}} \exp(-\varepsilon/k_B T_1)n \\ + C_2 \sqrt{\frac{\varepsilon}{(k_B T_2)^3}} \exp(-\varepsilon/k_B T_2) \quad (4)$$

<footnote n="1">¹ Interaction cutoff distance is $r_c = 10$ Å.</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Plots of the AED and IED a) Ta, b) Ta⁺, c) N, d) N⁺. Both plot energy and magnitude scales are different, for better view of the A,I-ED shapes.</figcaption></figure>

$k_B T_{1,2}$ are the peak energies of the low- and high-energy Maxwellian IEDs. The lower one ($T_1$) corresponds to thermalised ions accelerated in the sheath. A typical value is 0.35 eV. For the highest energy, $T_2$, a 10 times larger value is retained [18]. $C_{1,2}$ are fitting parameter. A ratio of $C_1/C_2 = 0.5$ is chosen accordingly to previous works [9,18]. Finally, $N_+$ ions are expected to have a constant energy corresponding to the potential drop at the substrate. A typical value of 6 eV is applied here. Figure 2 summarises the selected AED and IED distributions.

The $\frac{Ta}{Ta+N}$ is fixed to 40 atomic %, for ensuring high enough nitride composition, and $\frac{Ta^+}{Ta+Ta^+}$ takes values of 0.9 (high ion flux) and 0.25 (moderate flux).

Such shapes of IED and AED, being typical of the chosen deposition process, allow to run simulations matching as close as possible experimental deposition conditions. Simulations were performed using the LAMMPS software [19,20]. X-ray diffraction patterns were calculated using the Debye method included in LAMMPS [21]. Snapshots were generated using OVITO software [22,23]. The crystalline phases of the simulated films were identified using the Polyhedral Template Matching (PTM) method [24] implemented in OVITO.

## 3 Results and discussion

Figure 3 displays the final film structures for MS and 2 HiPIMS (moderate and high ion flux) processes. The snapshots show ordered films which have respectively N/Ta ratios of 19%, 6%, and 11% for MS / moderate / high Ta⁺ ion flux. Moreover the highest ion flux leads to a thinner film compared to the other process. Additionally, the highest Ta⁺ ion flux leads to greater Ta and N species diffusion in the substrate (Figs 3d-3f). This condition also

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Snapshots of the deposited films: a) MS (Ta and incoming species), b) HiPIMS moderate ion flux, c) HiPIMS high ion flux and the same without the substrate for observing the diffusion of incoming species, d) MS (Ta and incoming species), e) HiPIMS moderate ion flux, f) HiPIMS high ion flux.</figcaption></figure>

<table><caption>**Table 2.** Crystallographic phases of the three films determined by polyhedral template matching method.</caption><thead><tr><th>Films</th><th>Hcp (%)</th><th>Fcc (%)</th><th>Disordered<sup>1</sup> (%)</th></tr></thead><tbody><tr><td>MS</td><td>20</td><td>25</td><td>55</td></tr><tr><td>Ta<sub>75</sub>Ta<sub>25</sub></td><td>29</td><td>28</td><td>43</td></tr><tr><td>Ta<sub>10</sub>Ta<sub>90</sub></td><td>22</td><td>30</td><td>48</td></tr></tbody></table>

induces a flatter film surface. These results are in agreement with established experimental and numerical findings [9–11,25,26].

Identified crystallographic phases using PTM method are reported in Table 2.

Table 2 shows that MS deposition results in the highest degree of disorder while fcc phase dominates hcp ones. Using HiPIMS process leads to a reduction of disorder, while for moderate ion flux fcc phase predominates and for high ion flux hcp is the main phase. In this two latter cases, disorder is reduced compared to MS.

For deeper insights of phase identification, x-ray diffraction (XRD) patterns and radial distribution functions (RDF) are calculated and reported in Figure 4. The XRD patterns are very complex. Comparison with Material Projects database (mp-xxxx sheets) [27,28] allows to observe 3 TaN hcp possible structures, including ε-TaN (mp-1279) and mp-1459, mp-1642. These three hcp phases have been considered since they have the lowest formation energy. The fcc δ-TaN phase is also present as well as Ta₂N trigonal structure. There is no peak in the range $2\theta = 45–60°$. This suggests that fcc δ-TaN phase is present since it lqo has no peak in this region. One should note that bcc-Ta is not present since it would have a peak in this region. Other regions 30–45° and 60–80° present peaks of all other expected phases. RDF plots (Figs 4e-4g) provides the

<footnote n="1">¹ Disordered means that PTM method does not match with any structure.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Plots of the simulated XRD a) MS, b) HiPIMS moderate ion flux, c) HiPIMS high ion flux films, d) predicted diffraction peak positions and RDF g(r), e) MS, f) HiPIMS moderate ion flux, g) HiPIMS high ion flux films.</figcaption></figure>

positions of the nearest neighbours. The first peak at 2.05 Å corresponds to TaN in ε-TaN. This peak is a bit broad and could include the 2.2 Å distance corresponding to TaN separation in δ-TaN. In the two phases ε- and δ-TaN, Ta-Ta separation are respectively 2.91 and 4.44 Å being the second and fourth peaks in the calculated RDF.

Such results are in agreement with experimental findings [3,26] for which both fcc and hcp phases are obtained using radiofrequency, dc MS and HiPIMS processes.

## 4 Conclusion

Molecular Dynamics simulation of TaN deposition from conventional MS and HiPIMS has been carried out. Realistic initial velocity conditions of incoming species at the substrate are used for all species. A bi-maxwellian velocity distribution was applied for describing $Ta^{+}$ incoming ions. Comparing moderate and high flux results in tuning fcc/hcp structure balance. While conventional MS deposition favours fcc structure growth, HiPIMS deposition favors hcp structure. Such balance is in agreement with experimental results. This then allows the method to be applied for any other kind of deposition method, provided AED and IED are known.

## Funding

The article processing charges (APC) were funded by Centre National de la Recherche Scientifique.

## Conflicts of interest

The authors declare no conflicts of interest in relation to this article.

## Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

## Author contribution statement

Conceptualisation, P.B. and M.C.W.; Methodology, P.B. and M. C.W., Validation, P.B. and M.C.W., S.F. and N.F.; Formal analysis, P.B. and M.C.W.; Investigation, P.B. and M.C.W.; Data Curation, P.B. and M.C.W.; Writing – Original Draft Preparation, P.B.; Writing – Review & Editing, P.B., M.C.W., S. F. and N.F.; Project Administration, M.C.W. and N.F.

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**Cite this article as:** Pascal Brault, Marjorie Cavarroc-Weimer, Sara Fazeli, Nicolas Froloff, Conventional and high power impulse magnetron sputtering deposition of tantalum nitride films: a molecular dynamics approach, Eur. Phys. J. Appl. Phys. **100**, 12 (2025), https://doi.org/10.1051/epjap/2025012