Thin film nanostructuring at oblique angles by substrate patterning

Surface & Coatings Technology 436 (2022) 128293 Available online 1 March 2022 0257-8972/© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Thin film nanostructuring at oblique angles by substrate patterning S. Mu˜ noz-Pi˜ na a , A.M. Alcaide b , B. Limones-Ahij´ on c , M. Oliva-Ramírez b , d , V. Rico b , G. Alcal´ a e , M.U. Gonz´ alez c , J.M. García-Martín c , R. Alvarez b , f , * , D. Wang g , P. Schaaf g , A. R. Gonz´ alez-Elipe b , A. Palmero b , ** a Nano4Energy SLNE, C/Jose Guti´ errez Abascal 2, 28006 Madrid, Spain b Instituto de Ciencia de Materiales de Sevilla (CSIC-US), Am´ erico Vespucio 49, 41092 Seville, Spain c Instituto de Micro y Nanotecnología, IMN-CNM, CSIC (CEI UAM +CSIC), Isaac Newton 8, 28760 Tres Cantos, Madrid, Spain d Departamento de Física At´ omica, Molecular y Nuclear, Universidad de Sevilla, Avda. Reina Mercedes, 41012 Seville, Spain e Departamento Ingeniería Química y Materiales, Universidad Complutense de Madrid, Avenida Complutense s/n, Facultad de Ciencias Químicas, 28040 Madrid, Spain f Departamento de Física Aplicada I, Escuela Polit´ ecnica Superior, Universidad de Sevilla, c/Virgen de ´ Africa 7, 41011 Seville, Spain g TU Ilmenau, Institute of Materials Science and Engineering and Institute of Micro- and Nanotechnologies MarcoNano®, Gustav-Kirchhoff-Str. 5, 98693 Ilmenau, Germany ARTICLE INFO Keywords: Magnetron sputtering Nanostructured thin films Substrate patterning Oblique angle deposition Porous thin films ABSTRACT It is demonstrated that, besides classical nanocolumnar arrays, the oblique angle geometry induces the growth of singular structures in the nanoscale when using wisely designed patterned substrates. Well-ordered array of crosses, cylindrical nanorods or hole structures arranged in square or hexagonal regular geometries are reported as examples, among others. The fundamental framework connecting substrate topography and film growth at oblique angles is presented, allowing the use of substrate patterning as a feasible thin film nanostructuring technique. A systematic analysis of the growth of TiO 2 thin films on 4 different lithographic patterned substrates in 4 different scale lengths is also presented. A first conclusion is the existence of a height-based selective growth in the initial stages of the deposition, by which the film preferentially develops on top of the tallest substrate features. This behavior is maintained until the film reaches a critical thickness, the so-called Oblivion Thickness, above which the film topography becomes gradually independent of the substrate features. A general formula relating the spatial features of the pattern, the coarsening exponent and the Oblivion Thickness has been deduced. 1. Introduction Last decades have witnessed the introduction of important modifications in well-established thin film deposition methodologies aiming to widen their nanostructuration possibilities and make them more versatile [1–3]. This is the case of the so-called plasma-assisted magnetron sputtering technique, a classical Physical Vapor Deposition (PVD) procedure that relies on the interaction between a plasma and a solid target to sputter species from the latter that, upon deposition, make the thin film grow [4]. In the classical configuration, the substrate is placed parallel to the target, resulting in the deposition of well-known dense and compact homogeneous layers [5–7]. However, if the substrate is tilted, in a so-called Oblique Angle configuration, a wide range of new possibilities emerge, enabling the growth of layers formed by nanocolumnar structures for tilt angles above a threshold value [8]. These nanostructured films have found applications in fields as different as sensors, biomedicine, microfluidics and plasmonics, to name a few, [9–18] thanks to their unique morphological features, e.g. high specific surface, tunable density, high porosity or high pore connectivity [19–21], which have motivated an intensive research to attain precise nanostructural control and optimum functionality. The aim of this paper is to demonstrate the profound connection between substrate topography and film growth when operating at oblique angles, as well as deducing the main principles describing the interplay between these elements. In this way, and based on the large number of reported possibilities, it is suggested that substrate patterning methods may effectively act as a feasible thin film nanostructuring technique. In general terms, the oblique incidence of ad-species on a substrate * Correspondence to: R. Alvarez, Instituto de Ciencia de Materiales de Sevilla (CSIC-US), Am´ erico Vespucio 49, 41092 Seville, Spain. ** Corresponding author. E-mail addresses: [email protected] (R. Alvarez), [email protected] (A. Palmero). Contents lists available at ScienceDirect Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat https://doi.org/10.1016/j.surfcoat.2022.128293 Received 22 December 2021; Received in revised form 6 February 2022; Accepted 24 February 2022 Surface & Coatings Technology 436 (2022) 128293 2 induces the so-called surface shadowing mechanism and the appearance of shadowed regions, i.e. parts of the growing surface where the deposition is inhibited due to the presence of mounds that capture most adspecies [22]. This causes a surface selective and competitive development that ends up in the formation of tilted nanocolumnar structures separated by large pores [8]. Consequently, the nanocolumns are always found in the form of large arrays with strongly interdependent heights. The main experimental control parameters defining the columnar development in oblique angle depositions with magnetron sputtering (MS-OAD) are the tilt angle of the substrate with respect to the target, α , and the working pressure in the deposition reactor [23]. While the former defines the angle of incidence of ad-species and the efficiency of the surface shadowing mechanisms, the latter influences the transport of sputtered species in the plasma from the target to the substrate. In this way, at very low pressures (or, likewise, for large mean free paths of deposition particles in the plasma gas) the sputtered species move according to a ballistic diffusive regime from the target to the film, while at very high pressures (short mean free paths) their movement becomes Brownian-like due to the large amount of collisions with heavy plasma species, thus arriving at the substrate along any possible angular direction. In real conditions, both types of transports coexist depending on the target-film distance and the mean free path value [24]. Different characteristic film morphologies have been reported when the growth takes place on a flat substrate and at relatively low pressures: compact (when α <60◦), compact with tilted mesopores that percolate from the top of the film to the very substrate (when 60 ◦≲ α ≲ 80◦), and tilted nanocolumnar structures (when α ≳ 80◦). Moreover, at relatively high pressures, sponge-like vertically aligned and coalescent structures are promoted, no matter the tilt angle of the substrate, due to the nonpreferential arrival of sputtered species along any specific oblique direction [23]. The influence of both, deposition pressure and α , has been thoroughly studied in the literature for numerous materials and conditions (see for instance refs. [23,25–27] and references therein). Yet, to our knowledge, no systematic study has appeared analyzing the interplay between the film columnar arrangement and the topography of the substrate at oblique geometries. Indeed, it is known that any pattern carved on the substrate strongly modifies the surface shadowing mechanisms and affects the resulting film nanostructure: in ref. [28], for instance, it was found that the morphology of a SiO 2 thin film grown by MS-OAD on a 1D rippled surface tends to mimic the ripples' features, up to a critical thickness, called Oblivion Thickness, Δ O , above which the pattern progressively vanishes from the film surface. Moreover, in ref. [29] these results where corroborated by growing W thin films on different stainless-steel polished substrates by MS-OAD, finding that the nanocolumnar arrangement mimicked the substrate topographical features up to a film thickness of few microns, above which the film surface started to evolve independently of such features. These ideas were also tested using as substrates the self-arrangement of nanosphere beads on a surface [30], alumina [31–40] or porous silicon membranes [41,42], finding that the nanocolumnar films replicate the main features of these substrate patterns for small film thicknesses. Remarkably, this substratedriven nanostructuring mechanism has been applied just relying on an empirical basis, without any well-founded general formulation describing the interplay between the substrate geometrical features and the nanocolumnar growth. This is the scope of this work, to theoretically and experimentally develop some basic principles by which the aforementioned phenomenology can be rationalized. For this study numerous depositions have been carried out on 4 different periodic patterned substrates in 4 different scale lengths, below and in the order of 1000 nm. For simplicity, and due to the large number of potential applications based on it, TiO 2 has been employed, although the results are widely applicable to other materials. 2. Fundamentals of thin film growth on patterned substrates at oblique angles In this section, some fundamental principles of MS-OAD when the substrate topography is tailored according to a certain pattern are discussed. For this purpose, a well-tested model of the deposition has been used. This model has been successfully applied in numerous cases for oxides and metal thin films grown by MS-OAD on flat substrates, and its details can be checked in refs. [23,28]. For instance, as a case example, in Fig. 1a–b the cross-sectional and top views, respectively, of a simulated film grown under the experimental conditions of this paper on a flat substrate for a film thickness of 300 nm are presented. There, it is evident the existence of tilted and well-separated nanocolumnar structures whose tips can be seen at the top-view image in Fig. 1b. This model was used to determine which particular geometrical feature of a given substrate pattern gives rise to the nanocolumnar arrangement. To do so, simulations were run on substrates formed by numerous coalescent rectangular prism-shaped platforms, with different base area and height defining their topography. Consequently, the particular geometrical aspect of these platforms that may prompt a faster/slower vertical development during the early stages of growth could be identified. The followed procedure is described next: •A substrate with a lateral size of 250 nm was formed by coalescing several platforms with random base area and height (see Fig. 2a for an example). •For a given substrate, and under the experimental conditions described in the experimental setup section, the deposition of an individual atom was simulated and the particular location where it landed on the substrate was calculated. •The features of the landing location (base area and height of the platform) were saved for statistical purposes, after which the deposited atom was removed from the simulation to maintain steady substrate topography. Only the atoms deposited on the top surface of the platforms were considered to contribute to the vertical growth. This process was repeated for a total amount of 10 8 atoms. •For a given substrate, similar statistics were performed assuming different angles of incidence of deposition species. •The process described above was carried out using 10 4 different randomly generated substrates containing different configurations of platforms. The representation of the vertical growth rate per unit area as a function of the area of the base of the platform, irrespective of height, and for different angles of incidence (see Supplementary figure S1), indicates that the vertical growth rate does not depend on the size of the base: in other words, the area of the base of the platforms does not play a role in determining how faster or slower the vertical development of the platform is. In addition, the plots in Fig. 2b, corresponding to the vertical growth rate per unit area as a function of height, irrespective of the area of the base, depict a clear trend: in classical non-oblique depositions (angle of incidence of 0◦), Fig. 2b indicates that the growth rate is independent of the height of the platform. Yet, as soon as the incidence is oblique, a clear preferential growth of taller platforms is found in detriment of lower ones. This has been checked for different pattern geometries finding similar results for 1D walls or cylinders instead of rectangular prims (results not shown). This numerically demonstrates a general rule, that from now forth we dub the height-based selective growth principle, by which the taller certain geometrical elements are on the substrate, the faster they will vertically develop in the initial stages of growth, implying that the nanocolumns will initially arrange according to the tallest features of the substrate pattern. Yet, it is noteworthy that, according to Fig. 2b, the more oblique the incidence is, the more selective the growth becomes and, hence, the criterion by which a certain feature is tall enough or not to develop would depend on the angle of incidence of the deposition species. In practical conditions, where the S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 3 incidence is defined by a probability distribution [2], this means that, for a given substrate pattern and in the absence of any further detail on the growth conditions, the proposed principle only provides qualitative information on key pattern elements, especially when these show large dispersion of heights or smooth slopes (see the Results and discussion section for more details on this issue). The height-based selective growth principle sheds some light on the connection between substrate features and thin film morphology at oblique geometries during the first stages of growth. Interestingly, this principle is implicitly assumed in many works in the literature using the concept of shadowed region (i.e. the area behind each mound where the deposition is inhibited thanks to the shadowing mechanism), which takes into account that the larger this region is, the more atoms would be deposited on the mound that casts the shadow and, thus, the faster it will develop [8]. In this regard, both aspects, the height of a certain mound and the size of the shadowed region, can be taken as equivalent for our purposes, as both quantities are proportional. To our knowledge, the height-based selective growth principle deduced herein has not been quantitatively demonstrated in the literature before, nor the particular morphological aspect defining its efficiency. Once the height-based selective growth principle is established, the subsequent film development on a patterned substrate for increasing thicknesses is discussed. Here, it is important to notice that, upon growth, the nanocolumns increase their diameter and merge, forming either larger nanocolumns or closely-packed clusters of nanocolumns. This process introduces a characteristic length in the plane of the substrate, λ c , that relates to the size of these features that grow as a whole and not as independent elements (see Fig. 1b and d for a visual representations of λ c ). Consequently, the film development on a patterned substrate implies the accommodation of such features, defined by λ c , into those defining the pattern. λ c can be calculated by analyzing the growth on a flat substrate, i.e. in the absence of any other relevant characteristic lengths, using the concept of correlation length, a statistical quantity that, given a surface topography, can be obtained through different statistical methods, e.g. Fourier or surface self-correlation analyses [43]. Remarkably, λ c is known to increase with film thickness, Δ, as a power law λc=CΔ1/z,(1) where C is a proportionality constant and 1/z the so-called coarsening exponent. Both C and 1/z are process- and material-dependent quantities that, together with the growth and roughness exponents, characterize the film growth [43,44] (for simplicity, an isotropic behavior was assumed for λ c ). According to the ideas above, the comparison between λ c and the typical lengths defining the pattern determines the different stages of growth, which are described next (in the audiovisual information of this manuscript we present a video that illustrates these stages): •In agreement with the height-based selective growth principle above, in the initial stages of growth, the film surface tends to mimic the pattern defined by the tallest substrate elements. •For increasing thicknesses, the nanocolumnar arrangement at the edges of tallest regions will spread towards contiguous lower regions, progressively covering them, at a pace defined by λ c . In this way, if λ min is the shortest length between the tallest elements of the pattern, the Oblivion Thickness, Δ o , introduced as the critical thickness above which the pattern starts to vanish from the film surface, would be defined by the condition λ c (Δ o )~λ min , which using Eq. (1) yields the relation Δo∼(λmin C)z ,(2) that links three key quantities: Δ o , λ min and the coarsening exponent, z. •As the film develops, columns will continue to spread over the surface, progressively covering the different valleys between taller surface features. If λ max is the longest characteristic length between these features, the critical thickness above which they will no longer be visible from the film surface, Δ FG , can be similarly found when λ c (Δ FG )~λ max , which using Eq. (1) results in ΔFG ∼(λmax C)z (3) Fig. 1. Cross-sectional and top view images of a film deposited on a flat surface under the experimental conditions of this paper. a) Simulation. b) Experimental. The characteristic length of the film features, λ c , and the film thickness, Δ, are also depicted. S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 4 In agreement with ref. [28], this growth stage is denoted as free growth regime. When there is only one characteristic length separating the tallest parts of the pattern, λ min =λ max =λ 0 , Δ o coincides with Δ FG . Moreover, dividing Eq. (2) by Eq. (3) gives a general relation between the pattern features and the two critical film thicknesses as Δo ΔFG ∼(λmin λmax)z ,(4) an expression that connects the geometrical features of the pattern, the critical thicknesses defining the different growth stages and the coarsening exponent characterizing the nanocolumnar growth. At this point it is important to note that Eq. (2) is formally equal to an empirical equation found in ref. [28] through a numerical fit. There, the growth of a SiO 2 thin film by MS-OAD was analyzed when the substrate contained a sinusoidal pattern with wavelength λ, finding the relation Δ 0 ∝ λ γ with γ =1.55 ±0.04 under those deposition conditions. Remarkably, by considering that the distance between the lower parts of the sinusoidal pattern is ~λ/2, the comparison with Eq. (2) gives away the relation γ =z. Unfortunately, the value of z was not specifically calculated in ref. [28] under their conditions, precluding a direct comparison with the calculated value of γ. Yet, this parameter could be easily obtained using the data displayed in Fig. 2a in the same publication, finding z =1.53, which compares fairly well with the fitted value of γ. Based on the discussion above, a general framework describing the influence of a given substrate pattern on the growth of a nanocolumnar thin film at oblique geometries has been developed. In this way, the vertical and horizontal dimensions of the geometrical elements defining the substrate pattern affect the growth very differently: while the vertical ones (heights) define the initial stages of growth and the regions of preferential vertical development, the typical horizontal distances (in the plane of the substrate) define the subsequent columnar development and the Oblivion and Free Growth Thicknesses. As a final comment, it is important to underline that for simplicity an isotropic behavior has been assumed for λ c . However, the presented ideas can be easily generalized to anisotropic conditions, by solely considering the power law defined by λ c in the particular direction that connects two contiguous tallest surface features. 3. Experimental setup TiO 2 thin films were grown in a semi-industrial scale reactor that operates at the company Nano4Energy SLNE. The target is rectangular with a size 20 ×7.5 cm 2 with a balanced magnetic configuration, exhibiting a racetrack with the shape of a rectangle (the long and short sides being 13.5 and 4.2 cm, respectively) with lines that are about 3 mm wide. The base pressure in the reactor was 2 ×10 −6 mbar. The DC electromagnetic signal to maintain the plasma was generated by a Pinnacle Generator source set at 400 W and current intensity of 1 A, being the argon and oxygen fluxes 18.1 and 2.5 sccm respectively, and the total deposition pressure 3.3 ×10 −3 mbar. The OAD configuration was achieved as described in reference [45]: the substrate holder was located 10 cm away from the target and parallel to it, while the substrate was placed perpendicular to both, in such a way that atoms stemming from the racetrack may reach the substrate along an averaged oblique angle of ~80◦(a scheme of the reactor is shown in Fig. 3). As demonstrated in ref. [45], this configuration ensures that both momentum and kinetic energy distributions of sputtered species deposited at the substrate coincide with those found in laboratory reactors when tilting the Fig. 2. a) Example of a substrate employed for the simulations. The pattern is formed by coalescent platforms with the shape of rectangular prisms with random base area and height. For a better visual appreciation, the platforms are presented in different colors. b) Calculated vertical growth rate per unit area as a function of the height of the platform (height percentage calculated with respect to the maximum value). Fig. 3. Scheme of the experimental setup employed to carry out the depositions. S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 5 substrate holder. Indeed, in Fig. 1c–d the cross-sectional and top electron microscopy images of a TiO 2 thin film with thickness ~300 nm, deposited on a flat substrate using this configuration, are shown. There, it is apparent not only the clear nanocolumnar morphology of these films, but also the good agreement with the simulations presented in Fig. 1a–b. The TiO 2 thin films were grown on patterned substrates: different patterns were defined on (100) oriented Si wafers by using substrate conformal imprint lithography (SCIL) with SiO 2 sol-gel as photoresist [46,47]. Then the residual layer of the imprinted photoresist was removed with inductively coupled plasma – reactive ion etching (ICPRIE, Sentech SI 500) with a CHF 3 plasma. The structures were further transferred into Si substrate using reactive ion etching (RIE, Oxford Plasmalab 100) with a CF 4 plasma. After that, the imprinted sol-gel layer was removed by diluted HF solution. A total amount of 4 different patterns in 4 different scale lengths were imprinted, each with a size of 100 ×100 μ m 2 , and separated 100 μ m from each other. The four simple regular geometries were: i) lines perpendicular to the deposition flux (#Line1–#Line4), ii) lines parallel to the deposition flux (#ParLine1–#ParLine4), iii) cylindrical holes in a hexagonal pattern (#Hex- a1–#Hexa4), and iv) cylindrical holes in a square pattern (#Square1–2 and #Mound1–2). These 4 geometries represent different possibilities of azimuthal orientation between the incident deposition flux and the elements defining the pattern: perpendicular (#Line1–4), parallel (#ParLine1–4), perpendicular and parallel (#Square 1–2 and #Mound1–2) as well as perpendicular, parallel and tilted (#Hexa1–4). Moreover, the 4 scale lengths were taken from few hundred nanometers to nearly 1 μ m to check whether the film growth is affected in these scales. The central (flat) region of the substrate was taken as a reference for a growth on a flat surface topography. A scheme of the substrate pattern distribution appears in Fig. 4 (individual SEM images of each pattern appear in the supplementary information). The patterned substrates and the deposited films were analyzed by Field Emission Scanning Electron Microscopy (FESEM), using an FEI Verios 460 equipment at different magnification scales. Moreover, the Atomic Force Microscopy (AFM) technique was used prior to the film deposition to analyze the topography of the substrates with a Hysitron TS77 Select nanoindenter system manufactured by Bruker and available at the Complutense University of Madrid. In this way, the analysis of the topography of each pattern revealed that all carved parts were at least 100 nm deep, while the in-plane length of the lower carved regions in each substrate were measured and listed in Table 1. Overall, each Fig. 4. Scheme of the substrate employed for the deposition, containing 4 patterns in 4 different scale lengths. The central part was taken as a reference for a film grown on a flat surface. Table 1 Values of the typical length between the tallest regions of the substrate pattern, λ 0 , along with the calculated and measured values of Δ 0 , Δ FG using Eqs. (2) and (3), respectively. Note that in all the patterns except #Mound1 the relation λ min =λ max =λ 0 holds. The values marked with the symbol (*) are presented and discussed in the Results and discussion section. Pattern label λ 0 (nm) Calculated Δ 0 , Δ FG (nm) Experimental Δ 0 ,Δ FG (nm) #Line1, #ParLine1 550 ~5900 Δ 0 ,Δ 0 =Δ FG >2000 #Line2, #ParLine2 450 ~4300 Δ 0 ,Δ 0 =Δ FG >2000 #Line3, #ParLine3 350 ~2900 Δ 0 ,Δ 0 =Δ FG >2000 #Line4, #ParLine4 250 ~1700 Δ 0 =Δ FG ~2000 #Hexa1 550 ~5900 Δ 0 ,Δ 0 =Δ FG >2000 #Hexa2 400 ~3600 Δ 0 ,Δ 0 =Δ FG >2000 #Hexa3 250 ~1700 1500 <Δ 0 =Δ FG <2000 #Hexa4 150 ~780 500 <Δ 0 =Δ FG <1000 #Square1 550 ~5900 Δ 0 =Δ FG >2000 #Square2 400 ~3600 Δ 0 =Δ FG >2000 #Mound1 λ min ~50* λ max =250 Δ 0 ~140* Δ FG ~1700 100 <Δ 0 <300, 1500 <Δ FG <2000 #Mound2 λ min ~150* λ max =150 Δ 0 ~750* Δ FG ~750 500 <Δ 0 =Δ FG <1000 S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 6 pattern possesses the following features: •Lines Perpendicular to the deposition flux (#Line1–#Line4): These patterns contain carved 1D lines azimuthally perpendicular to the deposition flux. The typical size of the carved region for each pattern ranged from λ 0 (#Line1)~550 nm to λ 0 (#Line4)~250 nm (see Table 1). In order to illustrate these cases, in Fig. 5a the SEM image of pattern #Line1 taken at the border between the patterned and the flat regions of the substrate is displayed (the images of all #Line1–4 substrates appear in the supplementary information). •Parallel Lines (#ParLine1–#ParLine4): These patterns are equal to #Line1–#Line4, but rotated 90◦. In this way, the deposition flux is azimuthally parallel to the carved lines instead of perpendicular. •Cylindrical Holes with Hexagonal distribution (#Hexa1–#Hexa4): This pattern consists of cylindrical holes with radius ranging from λ 0 (#Hexa1)~550 nm to λ 0 (#Hexa4)~150 nm (see Table 1), distributed according to a hexagonal geometry. This type of substrate is illustrated in Fig. 5b and c, where the top view SEM image of patterns #Hexa1 and #Hexa4, respectively, is displayed. Interestingly, in this latter case, the short typical distance between holes and their small radius induces numerous defects in the pattern, as it is apparent in Fig. 5c. •Cylindrical Holes with Square Geometry (#Square1–#Square2): This pattern is made with cylindrical holes with radius λ 0 (#Square1)~550 nm and λ 0 (#Square2)~400 nm (see Table 1), in a square geometric distribution, as illustrated in Fig. 5d, where the SEM image of pattern #Square1 is displayed. •Square geometry with mounds (#Mound1–#Mound2): this pattern emerged when carving the substrate with cylindrical holes in a square geometry, just like the #Square1–2 cases above. Yet, the holes were so close that they overlapped, being the small region in the center of four neighbor holes the only surviving tall region. In Fig. 6a–b a scheme of the hole distribution to produce such patterns, the SEM images of the substrates, and the AFM measurement of these structures are shown. In this way, the pattern #Mound1 represents the case where neighbor holes barely touch, resulting in the formation of a square distribution of mounds connected by smooth slopes (see AFM topography in Fig. 6a). The existence of these smooth slopes makes difficult to determine the size of the lower parts in the pattern. In the case of #Mound1, however, the value of λ max (#Mound1)~250 nm can be determined (see Table 1), while the value of λ min will be discussed later on. In case of pattern #Mound2 a similar behavior was found (see Fig. 6b), although now the mounds are smaller and present sharper slopes due to the overlapping of the holes. As in the #Mound1 case, the value λ max (#Mound2)~150 nm was identified (see Table 1) while the value of λ min will be discussed later on. Given the patterns above, it is important to mention that, according to their topographical characterization, the carved regions in all the cases are defined by a single characteristic length, except in the #Mound1 and #Mound2 patterns. Moreover, in all the cases (see Figs. 5a–d and 6a–b) numerous small holes with diameter below 100 nm can be seen in both the region containing the pattern and the contiguous flat parts. These small holes appear as a side effect of the lithographic technique and have not been considered in the discussion. In any case, they clearly disappear from the film surface for film thicknesses above 50 nm (see results below). Each TiO 2 deposition was progressively carried on using the same sample as substrate (i.e. the newly deposited film grows on top of the previous film), thus allowing to incrementally analyze the film topography with thickness. In this way, after each deposition, the sample was taken out of the reactor, its surface characterized, and put back inside for the following run. To better monitor the film growth, for each deposition the same flat Si substrate was placed next to the substrate containing the patterned regions, along with a fresh Si flat substrate to determine the incremental thickness. The deposition time was set to achieve progressive film thicknesses of ~50, 100, 300, 500, 1000, 1500 and 2000 nm, respectively. Depositions were stopped when the film thickness was 2000 nm, as it was enough to illustrate the different growth stages in most studied cases (see Section 4). 4. Results and discussion In Fig. 7a the top view SEM images of the film grown on the flat substrate for thicknesses ranging from 50 to 2000 nm are shown. There, a clear granular morphology is depicted, typical of MS-OAD, where each grain represents the tip of a nanocolumn (see also Fig. 1b), whose size increases with thickness. From these images, the correlation length was obtained by calculating the first minimum of the height-height Fig. 5. SEM Images of four different patterns. a) #Line1, b) #Hexa1, c) #Hexa4, and d) #Square1. S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 7 correlation function: the representation of λ c as a function of thickness, Δ, is depicted in Fig. 8, where a clear power law between both quantities is found, in agreement with Eq. (1), with λ c =2.12 ×Δ 0.64 , being λ c and Δ in nanometers. The relation between λ c and Δ is of relevance as it provides the values of C =2.12 and z~1/0.64 =1.56 in our conditions. Here, it is noteworthy that, in general, λ c may show an anisotropic behavior, i.e. it may show a different trend depending on the particular direction under consideration. However, in this case, the value of λ c has been checked to be rather isotropic, and therefore an averaged value of this parameter over the whole surface is presented. Next, the growth of the film deposited on each pattern, depending on its geometry, is discussed. 4.1. Growth on patterns #Line1–#Line4 In Fig. 7b the top SEM images taken for the films grown on #Line1 Fig. 6. Analysis of the patterns #Mound1–2, including a scheme on how the mounds are produced (left), SEM image (center) and AFM characterization of the surface (right). a) #Mound1, and b) #Mound2. Fig. 7. Top view SEM of the deposited films as a function of thickness on different patterns. a) Flat surface, b) #Line1, c) #ParLine4, d) #Square2. S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 8 are shown for different values of Δ. For comparison purposes, the images were taken at the very border between the patterned and the flat regions of the substrate. At a glance, it can be noticed that the nanocolumns grow at the tallest parts of the substrate, in agreement with the heightbased selective growth principle deduced in the previous section. Moreover, nanocolumns tend to disorganize with thickness, even though, in the studied range, the pattern is always visible from the top. This implies that the Oblivion Thickness has not been surpassed for film thicknesses below 2000 nm. In this regard, pattern #Line1 is defined by a single length for the lower pattern features, λ 0 =550 nm, which according to Eq. (2) results in Δ o ~5900 nm, a value that agrees with the experiments (see Table 1). Fig. 9a shows a detail of this film morphology when its thickness is 100 nm: there, a small amount of deposited material can be seen inside the grooves, caused by those sputtered species that move as Brownian-like particles in the plasma, and that may arrive at the film surface from any possible direction, thus reaching the bottom of the grooves. The results for patterns #Line2–#Line4 are very similar to those of #Line1 and appear in the supplementary information. 4.2. Growth on patterns #ParLine1–#ParLine4 Fig. 7c shows a set of top SEM images of the films grown on the pattern #ParLine4 for different film thicknesses. These images illustrate the depositions on these geometries (the images for patterns #ParLine1–#ParLine3 are similar to those presented in Fig. 7c, and appear in the supplementary information). There, it can be appreciated again how the film mimics the tallest features of the pattern for small thicknesses, in agreement with the height-based selective growth principle. Moreover, it can be clearly seen how nanocolumns laterally spread out from tallest regions, progressively covering the grooves (i.e. the lower regions of the pattern), in a clear illustration of the fundamental mechanism discussed in the previous section. Remarkably, for a thickness of 1500 nm, it seems that the nanocolumns have completely covered the grooves, even though some order is still visible. The pattern seems to have vanished from the film surface for a thickness of 2000 nm, where the disorder is even higher, which agrees with the calculation of Δ 0 by Eq. (2), that results in Δ 0 ~1700 nm (see Table 1). Fig. 9b presents a top view SEM image of the film grown on this pattern for a thickness of 100 nm. Again some deposition of material is noticeable at the bottom of the grooves, even though it is negligible in comparison with the amount of material deposited at the tallest regions. 4.3. Growth on patterns #Square1–#Square2 The top SEM images of the films deposited on the pattern #Square2 as a function of thickness are depicted in Fig. 7d, again taken in the border region between the pattern and the flat region of the substrate. This figure illustrates once more how the nanocolumnar arrangement accommodates on top of the tallest features of the substrate pattern. As in the previous cases, a small amount of deposited material is visible inside the holes (see detail of a hole for a film thickness of 100 nm in Fig. 9d), which can be again attributed to the existence of Brownian-like diffusive species in the plasma. Moreover, the Oblivion Thickness seems to be above 2000 nm, despite the fact that columns seem to become well disordered for the highest thicknesses, 1500 and 2000 nm. Yet, even for this last case they possess some evident alignment suggesting that the thickness remains below the Oblivion Thickness. This agrees with Eq. (2) where a value ~3600 nm is obtained (see Table 1). Similar results are Fig. 8. Correlation length of the film deposited on a flat surface as a function of film thickness in a log-log representation. The numerical fit of the data to the power law in Eq. (1) is also included. Fig. 9. Close-up SEM images of the deposited films a) #Line1 for a film thickness of 100 nm, b) #ParLine4 for a film thickness of 100 nm, c) #Hexa3 for a film thickness of 300 nm, d) #Square2 for a film thickness of 100 nm. S. Mu˜ noz-Pi˜ na et al. Surface & Coatings Technology 436 (2022) 128293 9 obtained for #Square1, which are displayed in the supporting information of this manuscript. 4.4. Growth on patterns #Hexa1–#Hexa4 The film growth on the pattern #Hexa3 is illustrated in Fig. 10a, where the top SEM images of the films with thicknesses ranging from 50 nm to 2000 nm are shown. There, it is clear that the tilted columnar growth mimics the tallest features of the substrate pattern up to a thickness of 1500 nm. Indeed, it is noticeable how the holes progressively close (see Fig. 9c for a detailed image of the holes for a film thickness of 300 nm) until the Oblivion Thickness is surpassed, an event that, according to Fig. 10a, must take place for a film thickness between 1500 and 2000 nm. Remarkably, Eq. (2) yields a value of ~1700 nm, which is in good agreement with the experiments (see Table 1). Similar results are obtained when the film grows on patterns #Hexa1 and #Hexa2, although this time the Oblivion Thickness is never reached in the studied range (see supplementary information for a complete set of images of the surface evolution of these films). The growth on pattern #Hexa4 is depicted in Fig. 10b, presenting a hexagonal array of cylindrical holes with numerous defects which, as commented before, are due to the substrate patterning process. In any case, the Oblivion Thickness is found for a thickness between 500 and 1000 nm, which agrees with the calculated value using Eq. (2) that gives away a value of ~780 nm (see Table 1). 4.5. Growth on patterns #Mound1–#Mound2 The evolution of the surface morphology of the films grown on pattern #Mound1 is depicted in Fig. 10c. Again, the top view SEM images are displayed as a function of the film thickness. Moreover, Fig. 11a shows a close-up detail of the morphology of this film for a thickness of 50 nm, 100 nm and 300 nm, respectively, where it can be observed how, for a thickness of 50 nm, the height-based selective growth does not only make nanocolumns develop at the apex of the mounds but also at the top parts of the slopes, forming cross-shaped periodic structures. Based on Fig. 11a the value λ min can be now estimated as the distance between closest parts of the crosses, which gives λ min ~50 nm. This trend develops with thickness until individual elements touch one another and eventually merge (Fig. 11a), resulting in a characteristic square pattern, very similar to that found on pattern #Square2 in Fig. 7d. This suggests an Oblivion Thickness between 100 and 300 nm, in agreement with our calculations using Eq. (2), which, using the estimated value λ min ~50 nm, yields a value of Δ 0 ~140 nm (see Table 1). As in the previous cases, Fig. 10c shows that for increasing thicknesses, the nanocolumns progressively cover the holes defining the pattern until they disappear, giving rise to a free growth regime for a thickness between 1500 and 2000 nm. This result agrees with Eq. (3), that renders a value of Δ FG ~1700 nm for the λ max value corresponding to this pattern (~250 nm - see Table 1). The morphology of the films grown on the pattern #Mound2 is displayed in Fig. 10d as a function of thickness. There, it is remarkable the selective growth of the film on top of each mound, obtaining an ordered array structure with the shape of nanorods. This morphology defines the substrate for thicknesses below 1000 nm, at which the Oblivion Thickness is already surpassed. However, a closer look to these structures for a film thickness of 50 nm (see Fig. 11b) reveals an important aspect: contrary to the film grown on #Mound1, the sharper change of the slopes in this pattern causes the sole development of the apex of the mounds (Fig. 11b), indicating that in this case λ min =λ max = λ 0 . In this way, the film morphology evolves as an array of well-ordered nanorods in a square geometrical arrangement, until these become wellpacked for a thickness of 300 nm (Fig. 11b). This behavior continues even when the film is 500 nm thick in Fig. 10d, up to a thickness of 1000 nm for which the pattern is no longer visible on the film surface. This suggests that the Oblivion Thickness has been surpassed, in agreement Fig. 10. Top view SEM of the deposited films as a function of thickness on different patterns. a) #Hexa3, b) #Hexa4, c) #Mound1, d) #Mound2. S. Mu˜ noz-Pi˜ na et al.