Growth dynamics of nanocolumnar thin films deposited by magnetron sputtering at oblique angles

Nanotechnology PAPER • OPEN ACCESS Growth dynamics of nanocolumnar thin films deposited by magnetron sputtering at oblique angles To cite this article: R Alvarez et al 2024 Nanotechnology 35 095705 View the article online for updates and enhancements. You may also like Synthesis of WO3 nanoblades by the dealloying of glancing angle deposited W- Fe nanocolumnar thin films Chinmay Khare, Aliaksandr Stepanovich, Pio John S Buenconsejo et al. - Microstructural Evolution and ORR Activity of Nanocolumnar Platinum Thin Films with Different Mass Loadings Grown by High Pressure Sputtering Busra Ergul-Yilmaz, Zhiwei Yang, Mike L. Perry et al. - AZO nanocolumns grown by GLAD: adjustment of optical and structural properties L G Daza, R Castro-Rodríguez and A Iribarren - This content was downloaded from IP address 150.214.182.236 on 02/01/2024 at 12:38 Growth dynamics of nanocolumnar thin films deposited by magnetron sputtering at oblique angles R Alvarez 1,2,∗ , A Garcia-Valenzuela 1 , G Regodon 1 , F J Ferrer 3 , V Rico 1 , J M Garcia-Martin 4 , A R Gonzalez-Elipe 1 and A Palmero 1,∗ 1 Instituto de Ciencia de Materiales de Sevilla (CSIC-US), Américo Vespucio 49, E-41092 Seville, Spain 2 Departamento de Física Aplicada I. Escuela Politécnica Superior, Universidad de Sevilla, Virgen de África 7, E-41011 Seville, Spain 3 Centro Nacional de Aceleradores (CSIC-US), Thomas A. Edison 7, E-41092, Seville, Spain 4 Instituto de Micro y Nanotecnología, IMN-CNM, CSIC (CEI UAM+CSIC), Isaac Newton 8, E-28760 Tres Cantos, Spain E-mail: [email protected] and [email protected] Received 8 September 2023, revised 30 October 2023 Accepted for publication 30 November 2023 Published 15 December 2023 Abstract The morphology of numerous nanocolumnar thin films deposited by the magnetron sputtering technique at oblique geometries and at relatively low temperatures has been analyzed for materials as different as Au, Pt, Ti, Cr, TiO 2 , Al, HfN, Mo, V, WO 3 and W. Despite similar deposition conditions, two characteristic nanostructures have been identified depending on the material: a first one defined by highly tilted and symmetric nanocolumnar structures with a relatively high film density, and a second one characterized by rather vertical and asymmetric nanocolumns, with a much lower film density. With the help of a model, the two characteristic nanostructures have been linked to different growth dynamics and, specifically, to different surface relaxation mechanisms upon the incorporation of gaseous species with kinetic energies above the surface binding energy. Moreover, in the case of Ti, a smooth structural transition between the two types of growths has been found when varying the value of the power used to maintain the plasma discharge. Based on these results, the existence of different surface relaxation mechanisms is proposed, which quantitatively explains numerous experimental results under the same conceptual framework. Supplementary material for this article is available online Keywords: magnetron sputtering, oblique angle deposition, nanocolumns, hyperthermal processes 1. Introduction Porous thin films produced by physical vapor deposition (PVD)techniques at oblique angles have been extensively studied in the last years due to their singular structural features and properties [1]. These films are formed by wellseparated tilted columnar structures with diameters of a few tens of nanometers that provide singular morphological features, e.g. large specific surfaces, high surface roughness, open/embedded porosity, etc [2,3]. Thanks to these features, nanocolumnar thin films have found applications in numerous fields, such as microfluidics, plasmonics, sensors, medicine, solar cells, aerospace industry or hydrogen storage, among others [4–14]. Moreover, they are also useful to perform fundamental studies, as any relevant atomistic mechanism Nanotechnology Nanotechnology 35 (2024)095705 (17pp)https://doi.org/10.1088/1361-6528/ad113d ∗ Authors to whom any correspondence should be addressed. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s)and the title of the work, journal citation and DOI. © 2023 The Author(s). Published by IOP Publishing Ltd1 during growth may leave specific traces on the morphology of the nanocolumns (e.g. affecting the tilt angle, columnar shape, preferential coalescence, typical separation distance, etc)[1]. In general terms, the nanocolumnar growth emerges thanks to a particular experimental arrangement, the so-called oblique angle configuration, by which vapor deposition species are made to arrive at the substrate along a preferential oblique direction, inducing surface shadowing mechanisms. These processes are responsible for the appearance of shadowed regions on the film surface, i.e. regions behind each mound where the deposition is inhibited and that eventually become large intercolumnar pores upon growth [1]. Classically, nanocolumnar films were grown by the evaporation technique at glancing angles, in which the deposition species stems from a sublimated solid source in a vacuum reactor [15]. Last decade, however, has witnessed the development of more versatile and industrially scalable methodologies, such as the magnetron sputtering technique at oblique angles (MS-OAD), by which the interaction between a plasma and a solid target causes the sputtering of species from the latter, preferentially in the direction perpendicular to its surface, that are subsequently deposited on a substrate [16,17]. In this case, the two key conditions to operate at oblique angles are: (i)the sputtered species must arrive at the substrate following a common preferential direction of movement, and (ii)the arrangement in the deposition reactor must allow the oblique angle incidence of sputtered species on the substrate. The first one is usually achieved by working at relatively low pressures, in a typical ballistic transport regime, thus minimizing the number of elastic scatterings of sputtered particles on plasma heavy species [1]. The second condition, on the other hand, is usually achieved by tilting the substrate with respect to the target, although other alternatives have been presented in the literature [18,19]. Interestingly, and despite the similarities between films grown by evaporation and MS-OAD under equivalent geometrical conditions, the atomistic phenomena in either case is known to be very different: while deposition species in the gas phase possess typical kinetic energies below 0.1 eV in evaporation, in MS-OAD they may reach few tens eV, above the binding energy of surface atoms in the film [16,17]. This means that, unlike in evaporation, hyperthermal (HT)mechanisms can be triggered in MS-OAD, i.e. mobility processes of film surface atoms induced by the incorporation of film forming species with relatively high kinetic energy [20–22]. In addition to these processes, key quantities regarding the film growth and nanostructural development are the so-called normalized energy and momentum fluxes, also known as energy per atom (EPA)or momentum per atom (MPA)[23]. They are defined as the total energy or momentum flux deposited in the film, no matter the particular source or transfer mechanism (absorption of photons, ion impingement [24], impingement of fast neutrals, etc), divided by the flux of deposition atoms. Using these quantities, many different energy-related and momentum-related phenomena in classical non-oblique growth conditions have been explained: while the EPA has been linked to microstructural changes in the film, the MPA has been associated to changes in film density and stress [25,26]. For instance, Abadias et al [27]found a straightforward connection between these fluxes and the type of stress in TiN thin films, from tensile to compressive values, while Xia et al demonstrated that these fluxes defined the texture of Y 2 O 3 thin films, finding a smooth shift in the crystalline texture from a monoclinic B phase (111)orientation to a minority cubic C phase, as well as a shift in film density and residual stress [26]. Furthermore, Konstantinidis et al found that the phase constitution of TiO 2 is intimately correlated to the value of these fluxes [28]. Indeed, there are numerous examples in the literature that indicate that the energy and momentum fluxes towards the film in magnetron sputtering depositions affect the dynamic state of surface atoms and the growth process [23], although the affected atomistic mechanisms are yet to be identified and understood [28], a fact that has discouraged their inclusion in growth simulation models. The intrinsic connection between HT processes and the tilt angle of the nanocolumns in MS-OAD was demonstrated in [29]. There, we showed that Ti thin films deposited by evaporation and MS-OAD under equivalent geometrical conditions were formed by nanocolumns with very different morphologies: while those in the evaporated film were thin and highly tilted, those produced by MS-OAD were thick and almost vertical. This difference was explained by means of a well-tested growth model, thanks to which it was demonstrated that HT processes were responsible for triggering numerous displacements of surface atoms in the direction of the arriving particles, thus straightening the columns up [30]. The inclusion of HT processes in the model did not only quantitatively reproduce the tilt angle of the columnar structures by MS-OAD but also their shape and film density under numerous experimental conditions [30]. Moreover, the solutions of the same model in absence of HT processes reproduced quite well the morphological features and density of evaporated Ti thin films, a result that is congruent with the low energy of the deposition species and the inhibition of HT processes when employing this technique [29]. Even though the influence of HT processes in MS-OAD was demonstrated in [30], there are still many issues unsolved that require further research and explanation. For instance, in [29]it was found that the sole increase of the power employed to maintain the sputter plasma during the deposition of Ti caused the progressive tilt of the nanocolumns from almost vertical to angles very similar to those obtained by evaporation. This agrees with some studies in the literature that report nanocolumnar structures deposited by MS-OAD as tilted as those grown by evaporation [31–33], a remarkable result that demands a thorough explanation. Based on all the ideas above, in this paper the growth and nanostructure of numerous materials deposited by MS-OAD are analyzed: for a primary assessment, the growth of Au, Pt, Ti and W is studied in detail and, subsequently, a broad set of data taken from the literature on Ti, TiO 2 , Cr, Al, HfN, Mo, V, WO 3 and W. As a result, it is demonstrated the existence of two different growth modes that lead to two different characteristic nanostructures, despite the similar deposition conditions. While some films are rather dense and defined by highly tilted and symmetric nanocolumnar structures, some others possess much lower 2 Nanotechnology 35 (2024)095705 R Alvarez et al densities and depict rather vertical and asymmetric nanocolumns. With the help of a model, these two growth modes are linked to different surface relaxation schemes upon the arrival of deposition species with relatively high kinetic energy during growth. Moreover, and under the light of the obtained results, in the final part of the paper the morphological transition of the Ti nanocolumns with power reported in [29]is analyzed, and the origin of the two relaxation schemes is discussed. 2. Experimental The experimental data have been explicitly obtained for this paper or taken from the literature for films deposited by DC MS-OAD at (i)relatively low pressures, and (ii)low substrate temperatures. The first condition was imposed to make the mean free path of sputtered species in the plasma as long as possible and minimize collisions with plasma heavy species, responsible not only for their scattering and loss of a preferential direction of movement, but also for reducing their kinetic energy and thus the influence of HT processes. The second condition was imposed to minimize the influence of any thermally-induced mobility process in the film that may overlap with the HT mechanism [34,35]. Consequently, the deposition conditions have been chosen to enhance the role of HT processes in the film growth and to minimize the influence of any other potentially competing mechanism that could produce atomic mobility. Four different materials have been analyzed in detail in terms of columnar morphology, tilt angle (b)and density ( r ): Ti, Au, Pt and W, deposited under different configurations and in different reactors to avoid any system-biased results (see table 1). The depositions of Pt and W thin films were specifically carried out for this work: a cylindrical vacuum reactor was employed, equipped with 1 and 3 inch diameter sputtering targets of Pt and W respectively. The plasma gas in both cases was Ar (purity 99.995%)and the working pressure was set to the minimum value at which the plasmas was stable: 0.4 Pa in the case of Pt depositions, and 0.2 Pa in the case of W. The substrate holder was placed at 7 cm from the target and rotated an angle aof 0°,50°,65°,75°,85°and 90° in the case of Pt, and 0°,45°,70°,80°,85°,90°and 100°in the case of W. Please note that arefers to the rotation angle of the substrate, which can be different form the angle of incidence of the sputtered species. In general terms, these species arrive at the substrate following an incident angle distribution function due to the non-punctual shape of the racetrack and to their different collisional transport in the plasma gas, which depends on quantities such as the gas pressure, the shape of the target, the target-substrate distance, etc. A relevant quantity when operating in typical OAD conditions is the angle aligning the racetrack and the substrate, a. bThis angle defines the angle of arrival of sputtered species that have experienced no elastic scatterings with plasma species and, hence, it provides information on the angle of arrival of ballistic species. In the case of circular targets, and when the substrate is placed along the central axis of the target, aand abare related by aa=-D, bwith D =RLarctan ,()/ L being the target-substrate distance and R the radius of the racetrack [18]. In the case of Pt, it amounts to ~ D 5 , while in the case of W to ~ D 15 . Preparations were carried out using a DC power supply at a constant value of 40 W (Pt)and 300 W (W). The deposition time was taken to obtain films with thicknesses of ~ 300 nm (Pt)and ~ 1000 nm (W). The morphology of the Pt and W nanocolumns was analyzed by means of field emission scanning electron microscopy (FESEM). In addition, Rutherford backscattering spectroscopy (RBS)was employed to assess their atomic areal density: experiments were carried out in the 3 MV tandem accelerator of the National Center for Accelerators (Seville, Spain)with a beam of 1.5 MeV alpha particles and a passivated implanted planar silicon (PIPS)detector located at 165°scattering angle, with accumulated doses about 1.5 μC, and ~ 1 mm beam spot diameter. The RBS spectra were simulated with the SIMNRA code [36], whereas r was calculated by dividing the areal density by the film thickness, as obtained from the crosssectional FESEM image at a location next to the RBS beam spot. The uncertainty of r has been estimated to be between 5% and 10% of its numerical value, given the uncertainties of the RBS measurement and of the thickness determination of columnar films with high surface roughness. The data from the Au thin films were taken from [37] (see table 1for deposition conditions). As mentioned above, only the set grown at the lowest pressure value in that paper (0.15 Pa)was chosen, with aset to 0°,45°,60°,70°,80°,85° and 87.5°, with a negligible value of D .Moreover, in [37]the focus was on the tilt angle of the nanocolumns as a function of the deposition conditions. That is why, in this paper, the density of these layers was explicitly measured following the same procedure as for the Pt and W films described above. The data regarding the Ti thin films considered in this paper were taken from different sources (see table 1): (i)Reference [30], where the films were deposited far from the plasma, and where the nanostructure and density of the films were presented. Following the same approach as before, the low-pressure cases (0.15 Pa)were analyzed for aset to 0°,45°,60°,70°,80°and 85°, with a negligible value of D .Although the columnar structures were rather vertical, the tilt angle of the columns with respect to the substrate normal, b , was not specifically measured in [30]. Therefore, for this work, this angle has been measured using the FESEM images. Also, in [30]a full analysis on the crystalline features of these films is performed. (ii)The films studied in [29], where the deposition was carried out using collimators to maximize the deposition of ballistic high energy atoms, keeping the same geometrical conditions (a=95 , with ~ D 15 )while increasing the power supplied to maintain the plasma. There, a complete analysis on the film nanostructures and densities were carried out. (iii)For comparison purposes, Ti thin films were also grown by evaporation at glancing angles on Si substrates, with a set to 0°,65°,70°,80°and 85°in an experimental setup 3 Nanotechnology 35 (2024)095705 R Alvarez et al Table 1. List of experimental conditions employed to deposit the films and analyze both, tilt angle, b,and density, r ,of the nanocolumnar structures, together with the references from which the values were taken. The experimental data required to solve the model are also included in the framed region. The symbol fdenotes the target radius. The data containing ( * )have been estimated (the gas temperature was set to 3 50 K in all the cases, while the racetrack was placed at a position half the radius of the target). Film p g (Pa) Target-Film distance (cm)Target diameter (inches)Target potential (V)Substrate rotation angle (°)DC Power (W)b(°)r(%) Evaporated Ti 10 −4 50 ——0–85 —This Work This Work Au 0.15 (Ar)19 f=1.5 150 0–87.5 100 [37]This work Ti 0.15 (Ar)22 f=2 150 0–85 300 This Work [30] W 0.2 (Ar)7f=3 300 0–100 300 This Work This Work Pt 0.4 (Ar)7f=1 100 0–90 40 This Work This Work TiO 2 0.2 (Ar), 0.05(O 2 )7f=3 300 60–85 300 [38][38] Cr 0.53 (Ar)8.5 f=2 300 * 0–80 N.A. [39][39] Ti 0.15 (Ar)7f=3 300 95 25–400 [29][29] 4 Nanotechnology 35 (2024)095705 R Alvarez et al already described in [15]. These films were characterized by FESEM as well as by RBS to obtain the tilt angle of the nanocolumns and their density as a function of a(in this case, arefers to the angle aligning the evaporation source and the substrate with respect to the substrate normal). In addition to these 4 materials, data from the literature on Cr and TiO 2 (see table 1)were taken to complete the discussion. Results on TiO 2 thin films grown by MS-OAD were taken from [38], where both film density and tilt angle of the nanocolumns were measured as a function of a(values set at 60°,70°,80°and 85°)following the same procedure described above. Moreover, data on Cr thin films for aset to 0°,30°,60°and 80°were taken from [39], where bwas obtained from the SEM images and r by means of x-ray reflectivity measurements at grazing incidence. Since no uncertainty is mentioned in that reference for r, 10% error bars have been included here. Finally, the growth of different materials by MS-OAD has been analyzed, such as Al, Cr and Ti [32], HfN [40], Ti and Mo [41],Ti[31],V[42,43],WO 3 [44], and W [45,46]. 3. Growth model and surface relaxation schemes 3.1. Growth model The growth model, which was presented in [30], does not consider any thermally-induced mechanisms, and has already been tested under numerous low temperature growth situations. However, some modifications have been introduced regarding the surface relaxation schemes, which will be explained and discussed below. For the sake of clarity, next we describe its fundamentals (please, check figure 1for a scheme of the model). In a first stage, the model makes use of the SRIM code [47], which provides the momentum distribution of sputtered species from the target due to the plasma ion impingement,  Fp,()given the target material, the ion chemical nature (which is argon in all the presented cases)and the ion energy, estimated as eV , 0with ethe charge of the electron and V 0the target voltage. Effectively, the SRIM output is a list of different sputtered particles that includes the ejection direction and kinetic energy, from which the corresponding distributions functions can be obtained. However, given the important correlation existing between these two magnitudes, it is more adequate to describe the ejection of sputtered particles by means of a momentum vector distribution. The SRIM output is then introduced into the SIMTRA code [48,49] along with the geometrical quantities that define the vacuum reactor and the transport of species from the target towards the film, such as the target size, the position of the racetrack, the target-film distance, the substrate rotation angle, the pressure in the reactor as well as the temperature, which are dependent on the particular deposition system and conditions. From these input quantities, the SIMTRA code simulates the transport in the gas phase of the species sputtered from the target until they are deposited at the substrate, thus providing the linear momentum distribution function of the deposition species at the substrate,  fp.() Here, it is important to notice that SIMTRA also provides a list with the kinetic energies and directions of arrival of numerous deposition atoms at the substrate, although due to the important correlation between these quantities, in the proposed model, the momentum vector distribution is again employed instead of two uncorrelatedenergy and angular distribution functions.  fp( ) is then introduced as an input into a home-made Monte Carlo model of the film growth. This code simulates the incorporation of different deposition species on a flat substrate that defines the XY plane, whereas the z axis corresponds to the direction perpendicular to it. The space is then divided into a ´´ N NN xyz cubic grid, where each cell has the value 1 if it contains a deposited species and 0 otherwise. For metals, each cell represents the typical atomic volume in the material, with a typical length of ~0.4 nm. The deposition species are considered to approach the substrate from a random initial location over the substrate and to follow a straight trajectory defined by  p,which is randomly calculated using  fp.() Consequently, in the model, the angular distribution that defines the direction of movement and the kinetic energy distribution function of the deposition species are strongly correlated through  fp.()The movement continues in the cubic grid, using periodic boundary conditions in the XY plane, until the arriving species land on the substrate or try to move into an occupied cell. In this latter case, the following processes are considered: •Kinetic energy-induced mobility: If the energy involved in the collision between the arriving and surface atoms, pM2, 2/where Mis the mass, is above certain energy threshold, e , kboth atoms are allowed to move into the film network according to a given surface relaxation scheme (see below)[20–22]. •Biased diffusion: If the kinetic energy-induced mobility process is inefficient, either because the kinetic energy is below e kor because there are no available neighbor sites where to relax, it is considered that the incident atom keeps part of its momentum in the direction parallel to the film surface,  p,and slide over it until it finds an obstacle, where it gets deposited. As stated in [20,30], this process takes place if the energy associated to that component of momentum,  pM2, 2/is above certain threshold value, e, BD and the angle of incidence is above certain angular threshold with respect to the normal to the surface, q . BD Consequently, this process is introduced in the same way as in [30]without alterations. •If none of the abovementioned processes takes place, the arriving atom is deposited at the landing position and no subsequent mobility processes are considered. The model is therefore solved by knowing the features of the deposition reactor, the deposition conditions, as well as e k, e BD and q BD (see figure 1). These quantities were estimated as follows: e kwas taken as the surface binding energy of the material, estimated as the enthalpy of sublimation, whereas 5 Nanotechnology 35 (2024)095705 R Alvarez et al the biased diffusion energy and angular thresholds were estimated as e ~1 BD eV and q ~  30 BD [20,30]. Moreover, the remaining input data in the model have been taken from table 1(and table S1 in the supplementary material)for each simulation condition. It is important to underline that the model does not contain any aditional input quantity or adjustable parameter, and that it only employs the data explicitly mentioned in this paper as an input. The size of the simulations was == N N2500, xy i.e. a base of mm~´1m 1m , and a value of N zto match the thickness of the experimental films. 3.2. Surface relaxation schemes The HT relaxation of the arriving and surface atoms in the film network is a complex phenomenon that involves (i)the breaking of surface bonds, (ii)the interaction of both incoming and surface atoms, and (iii)the mobilization of these atoms (relaxation)on a growing surface to a final position in the surface network, whose detailed analysis is far beyond the scope of this manuscript. Instead, in this paper, a similar approach as in [30]was followed, where a simplified, effective scheme was presented. There, this process is simplified by introducing a so-called relaxation region, which contains all possible neighbor positions where both atoms may migrate to. In [30]it was introduced as a cone-shaped volume with its apex located at the position of the collision, opening angle of p4/and its axis aligned with the momentum of the arriving atom. In this way, all neighbor positions both empty and coordinated within this region are considered potential destinations for these atoms (see figure 2for a 2D illustration of a single relaxation process). Based on this simple idea, the two following surface relaxation schemes are considered: •Random position relaxation (RR), where the final destinations of both atoms are randomly chosen among all the positions available in the relaxation region, and •Most coordinated position relaxation (MCR), where the destinations of both atoms are the two most coordinated positions available in the relaxation region, determined as follows: for each of the positions in the relaxation region, a coordination number is calculated. The relaxing atom will then end at the position with the highest coordination number. In the case that there is more than one position with the same highest coordination number, one of them is randomly picked. The two surface relaxation schemes described above are introduced ad-hoc into the calculations and must be understood as effective processes that combine numerous elemental processes affecting the dynamics of surface atoms. Despite their similarities, these two schemes introduce profound differences in the simulation of the growth dynamics and in the morphological development of the films. In the final part of the paper (section 4.5), and based on the results of the model and their comparison with the experimental data, their physical nature and origin are discussed. However, it is worth to mention that the RR scheme was already implemented in [30,45]as a basic relaxation mechanism, and, hence, our model is identical to the one employed in these references whenever this scheme is considered. However, the solutions of the model using the MCR scheme are presented and discussed here for the first time. Figure 1. Scheme of the different modules of the growth model, and the different input quantities required to solve it. 6 Nanotechnology 35 (2024)095705 R Alvarez et al 3.3. Influence of the surface relaxation schemes on the simulations The introduction of a particular surface relaxation scheme in the simulations strongly influences the calculated results. Actually, the use of a given scheme alters the distribution of empty positions on the film surface and affects the efficiency of other mechanisms, such as the biased diffusion or even surface shadowing processes, the latter responsible for the nanocolumnar growth. In fact, all of them are strongly interdependent, and a variation in one of them results in a completely different growth dynamic and film nanostructure. In order to illustrate how the use of a particular surface relaxation scheme affects the film nanostructure, a simulation has been run as follows: as a case example, the model has been solved according to the conditions defined in [30](see third row in table 1)when a=  80 and for a total film thickness of 300 nm. Moreover, in this simulation, all HT processes have been inhibited during the first 150 nm of growth to illustrate the film nanostructure in absence of HT processes and under the solely influence of surface shadowing mechanisms. Subsequently, the HT processes have been activated during the following 150 nm, up to a total film Figure 2. Illustration of the surface relaxation schemes. For clarity reasons, a 2D illustration of a single relaxation process is presented. In the actual model, the relaxation process takes place within a 3D relaxation cone and both atoms (incident and surface atoms)are allowed to relax. Figure 3. Influence of the HT processes in the results of the model. The simulations correspond to the deposition of Ti, in the conditions of [30], for a=80 , with film thickness of 300 nm. The first 150 nm of growth have been carried out with all HT processes inhibited, and subsequently activated during the remaining 150 nm according to different relaxation schemes. Top images: results of the simulation illustrating the change in density and in tilt angle of the nanocolumns. Bottom images: a one-atom slice of the same simulated material as above, illustrating the influence of HT processes in the porosity. 7 Nanotechnology 35 (2024)095705 R Alvarez et al thickness of 300 nm. The results appear in figure 3: there, typical tilted nanocolumnar structures with b=  48 are obtained for thicknesses below 150 nm, with a film density of 29%. Remarkably, when the HT processes are activated according to a RR scheme, columns sharply become more vertical due to the appearance of relaxation processes in the direction of arrival of the deposition species, i.e. in the direction of the incoming momentum, in a process already reported in [30]. This also translates into a small increase of the film density, from 29% to 3 5% in this region, that is clearly appreciable when showing a 1 cell-depth slice of simulated material (see bottom part of figure 3). Remarkably, when the MCR scheme is imposed, only a slight variation of column tilt angle is noticeable, from b~  48 to b~ 52 . Yet, the film density shifts from 29 % to 60 % , revealing the influence of the surface relaxation processes during growth. This is clearly visible when displaying the 1 cell-depth slice of this simulated material, where the increase of density is noticeable. This suggests that the MCR scheme induces certain surface relaxation dynamics that does not significantly alter the original growth defined by the surface shadowing mechanisms, leaving the column tilt rather unaffected but making the structures denser. Consequently, the introduction of these two relaxation schemes in the model induces profound changes in the simulated growth dynamics, and affects the columnar development, density and tilt angle. 4. Results and discussion 4.1. Growth of Au, Pt, W and Ti thin films by MS-OAD The columnar morphology of the Au, Pt, W and Ti thin films is illustrated in figure 4, where the cross-sectional FESEM images of these films for the same angle aligning the racetrack and the substrate a=  85 b(i.e. for aa= = Au Ti85 ,() () a=  Pt85 , 90() and a=  W100() )are shown. At a glance, important structural differences are apparent despite the similar deposition conditions: Au and Pt nanocolumns are clearly more tilted that those of Ti and W. Moreover, the shape Figure 4. Center)FESEM images of Au, Pt, Ti and W thin films grown by MS-OAD when the angle aligning the racetrack and the substrate is a=  85 b(i.e. aaa= = =  Au 85 , Ti 85 , Pt 90() () () and a=W 100 .() Sides)Results of simulations using the two hyperthermal relaxation schemes: Random Relaxation (left)and Most Coordinated Relaxation (right). The arrow indicates the direction of arrival of the deposition flux. Simulations are in the same scale as the experiments. 8 Nanotechnology 35 (2024)095705 R Alvarez et al deposited under numerous and different conditions, some of them carried out specifically for this paper and others taken from the literature. This evidence strongly suggests that, no matter whether the two relaxation schemes represent elemental processes or effective mechanisms, the model accurately reproduces the growth dynamics of the studied nanocolumnar thin films under the conditions explained in the experimental section. Moreover, it is also found that when the HT processes are switched off in the model, the solutions reproduce the morphology of evaporated thin films, suggesting that the model is physically coherent. Based on the ideas above, and on the fact that each surface relaxation scheme may involve the confluence of many elemental processes, we postulate the following hypothesis to rationalize the presented results: while the HT process is triggered in a first (knock-on)stage caused by the arrival of deposition species at the film surface with relatively high kinetic energies, the relaxation scheme represents a subsequent process mediated by the state of the growing film surface, which conditions whether the atoms involved end up at most energetically stable locations or not. This is in line with the experimental results presented in [50,51], where Shaginyan et al found that increasing values of the energy flux towards the film in classical magnetron sputtering depositions promoted the formation of a so-called hot thin solid layer on the top of the growing surface that modifies the way gaseous atoms get deposited, from a classic gas  solid to a gas  liquid  solid scheme, in a clear parallelism with our results. Moreover, this would explain why an increase of power involves a transition in the surface relaxation scheme in the case of Ti, as this quantity greatly influences the energy flux towards the film during growth [52]. The proposed hypothesis above also agrees with current ideas on the influence of the normalized energy and momentum fluxes towards the film during growth: as mentioned in the introduction, these fluxes are known for causing mobility of surface atoms and for affecting the film nanostructuring in magnetron sputtering depositions in classical non-oblique geometries. In our case, the introduction of a particular surface relaxation scheme produces particular growth dynamics: under a RR scheme, the movement of the atoms in the film network takes place in the preferential direction of the momentum of the deposition species in the gaseous phase, being the most remarkable effect the straightening up of the nanocolumns, while the film density changes very little. Under a MCR scheme, on the other hand, the relaxation seems to adapt to the growth direction defined by the surface shadowing mechanisms, causing the densification of the nanocolumns and a slight variation in the tilt angle. Therefore, from a global perspective, our model obtains a ‘momentum-driven relaxation process’, linked to relaxation processes in the preferential direction of the incoming momentum of the deposition species, or an ‘energy-driven relaxation process’, linked to an increase of the film density and of the coordination of the deposited atoms. These results are in line with those found in [23], where the influence of the normalized momentum and energy fluxes are described. Given the analysis above, one would think that the logical next step is the study of the surface relaxation schemes by means of Molecular Dynamics or First Principles simulations. However, these approaches are not evident due to the lack of specific quantitative information on different phenomena, such as the appearance of the hot thin solid layer or the influence of the energy/momentum fluxes on the film growth. Actually, these phenomena encompass numerous elemental processes and mechanisms at an atomic level that promote a collective behavior of the surface atoms, and that end up causing specific growth dynamics. In this regard, the model presented here proposes a set of mechanisms, either elemental or effective, that quantitatively reproduce this growth dynamic for numerous thin films in scales of tens of nanometers, thus shedding some light on the different surface phenomena affecting the film growth. Yet, it is worthy to mention that the model does not explain structural features in atomic scales, such as crystalline orientation or film stress, or whether the surface relaxation schemes represent transient or thermal mobility processes [53]. An interesting aspect regarding the physical coherence of the proposed hypothesis relies on the potential existence of a structural transition between relaxation schemes for materials other than Ti. Yet, typical operational range of magnetron sputtering conditions may restrain the appearance of a transition. To study this phenomenon, W thin films have been explicitly grown for this work at higher powers than those presented in figure 6, but no structural transition could be found. The same occurs for Pt, where the deposition system was operated at the lowest possible power to maintain the plasma, but no structural transition was found either in comparison with the cases presented in figure 6. Yet, it is remarkable that, while W and Ti seem to follow a RR scheme in figure 6, the WO 3 and TiO 2 films reported in figure 9do follow a MCR scheme. This suggests that, as mentioned above, the oxidation process of W and Ti atoms during growth alters the relaxation scheme, in a phenomenon that will be studied in the future. 5. Conclusions Morphological aspects, such as column tilt angle, column shape and film density of numerous nanocolumnar materials grown by the magnetron sputtering technique at oblique angles at low pressures and temperatures have been compared, demonstrating the existence of two distinct growth modes. With the help of a well-accepted deposition model, these changes have been linked to two different effective surface relaxation schemes upon the arrival of deposition species with kinetic energies above the surface binding energy. From an experimental point of view, we have primarily employed four different materials to illustrate the phenomenon: Au, Pt, Ti and W grown under different conditions and reactor configurations. The first relaxation scheme has been dubbed Random position Relaxation, and accurately explains the main features of films such as W or Ti, while the second scheme has been dubbed Most Coordinated position 15 Nanotechnology 35 (2024)095705 R Alvarez et al Relaxation, and explains the features of films such as Pt or Au. Moreover, it has also been demonstrated that the materials grown by magnetron sputtering are very different to those grown by evaporation, i.e. in absence of hyperthermal processes. Furthermore, the analysis of numerous additional cases taken from the literature on materials as different as Au, Pt, Ti, Cr, TiO 2 , Al, HfN, Mo, V, WO 3 and W, grown by MSOAD in different conditions and reactors, is congruent with the existence of the two proposed effective surface relaxation schemes. Remarkably, this analysis demonstrates that Ti may grow following either one scheme or the other, indicating that the dominating surface relaxation scheme is not only linked to the chemical nature of the material but also to the deposition conditions. Furthermore, data in the literature regarding a structural transition of nanocolumnar Ti deposited by magnetron sputtering at oblique angles when increasing the DC power employed to maintain the sputter plasma have been studied. Based on this analysis, it has been found that this transition can be explained by introducing a smooth and progressive shift between surface relaxation schemes. A discussion has been carried out on the main features of these relaxation schemes and their influence on the morphology of the growing films. Based on these results, a hypothesis has been put forward on the nature of the surface relaxation mechanism linking it with the state of surface atoms. The obtained results are in line with experimental data in the literature regarding the influence of the normalized energy and momentum fluxes on the film nanostructure, or the appearance of a hot thin solid layer during growth. Overall, and based on the two surface relaxation schemes defined in this paper, a plausible hypothesis that explains the growth of numerous materials under a wide number of experimental conditions has been put forward. Acknowledgments The authors acknowledge projects PID2020-114270RA-I00, PID2021-126524NB-I00, PID2021-123879OB-C21 and PID2020-112620GB-I00 funded by MCIN/AEI/10.13039/ 501100011033, project TED2021-130124A-I00 funded by MCIN/AEI/10.13039/501100011033 and the European Union NextGeneration EU /PRTR, projects US-1380977 and US-1381045 funded by Fondo Europeo de Desarrollo Regional (FEDER)and Consejería de Transformación Económica, Industria, Conocimiento y Universidades de la Junta de Andalucía, within Programa Operativo FEDER 2014- 2020, project P18-RT-3480 funded by Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (PAIDI-2020), the H2020-EU.1.2.1-FET OPEN program (Grant 899352, project SOUNDofICE, and the EFRE Infra-Pro project ChAMP), and the University of Seville (VI PPIT-US). Guillermo Regodón would like to acknowledge funding from the European Comission-Next- GenerationEU through the ‘Plan de Recuperación, Transformación y Resiliencia’from the Spanish Government. Data availability statement The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors. ORCID iDs R Alvarez https://orcid.org/0000-0002-1749-4946 A Garcia-Valenzuela https://orcid.org/0000-0002- 5238-6465 V Rico https://orcid.org/0000-0002-5083-0390 J M Garcia-Martin https://orcid.org/0000-0002- 5908-8428 A R Gonzalez-Elipe https://orcid.org/0000-0002- 6417-1437 A Palmero https://orcid.org/0000-0002-1100-6569 References [1]Barranco A, Borras A, Gonzalez-Elipe A R and Palmero A 2016 Prog. 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