Growth of nanocolumnar thin films on patterned substrates at oblique angles

1 Growth of Nanocolumnar Thin Films on Patterned Substrates at Oblique Angles A. Garcia-Valenzuela1, S. Muñoz-Piña2, G. Alcala2, R. Alvarez1,3*, B. Lacroix4,5, A. J. Santos4,5, J. Cuevas-Maraver3,6, V. Rico1, R. Gago7, L. Vazquez7, J. Cotrino1,8, A.R. Gonzalez-Elipe1, A. Palmero1* 1 Instituto de Ciencia de Materiales de Sevilla (CSIC-Univ. Sevilla). Avda. Américo Vespucio 49. 41092, Seville, Spain 2 Universidad Complutense de Madrid, Dep. Ingeniería Química y de Materiales, Avenida Complutense s/n, Facultad de Ciencias Químicas, 28040 Madrid, Spain 3 Departamento de Física Aplicada I. Escuela Politécnica Superior, Universidad de Sevilla. c/ Virgen de África 7, 41011, Seville, Spain 4 Departamento de Ciencia de los Materiales e Ingeniería Metalúrgica y Química Inorgánica, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510, Puerto Real (Cádiz), Spain 5 Instituto de Microscopía Electrónica y Materiales (IMEYMAT), Universidad de Cádiz, Spain 6 Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012-Sevilla, Spain 7 Instituto de Ciencia de Materiales de Madrid (CSIC), E-28049 Madrid, Spain 8 Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, Avda. Reina Mercedes s/n. E-41012 Seville, Spain Abstract The influence of one dimensional substrate patterns on the nanocolumnar growth of thin films deposited by magnetron sputtering at oblique angles is theoretically and experimentally studied. A 2 well-established growth model has been used to study the interplay between the substrate topography and the thin film morphology. A critical thickness has been defined, below which the columnar growth is modulated by the substrate topography, while for thicknesses above, the impact of substrate features is progressively lost in two stages; first columns grown on taller features take over neighboring ones, and later the film morphology evolves independently of substrate features. These results have been experimentally tested by analyzing the nanocolumnar growth of SiO2 thin films on ion-induced patterned substrates. Email: [email protected]; [email protected] 3 Introduction Nanocolumnar porous thin films deposited at oblique geometries are nowadays receiving much attention due to their unique morphological features and remarkable properties.[1] While their high specific surface can be exploited for the development of gas or liquid sensor devices,[2-4] the possibility to fine tune their density[5] and connectivity among pores[6-7] make them also suitable for other applications in technological fields such as biomedicine, plasmonics, microfluidics, batteries or photonics, among others.[8-13] In all these cases, the relevant specific features of the nanocolumnar structures (e.g. their size, tilt, average distance, anisotropic distributions, preferential direction of coalescence, etc.) are intimately connected to the governing growth mechanisms. In this regard, the surface shadowing phenomenon emerges as a key nanostructuration process mediating the formation of nanocolumns with typical diameters in the order of few tens of nanometers.[14-15] This mechanism takes place whenever gaseous deposition species arrive at a substrate along a preferential oblique direction, whereby taller features on the film surface inhibit the deposition in neighbor regions, giving rise to different nanocolumnar arrays.[16] From an experimental point of view, porous nanocolumnar thin films have been classically grown by evaporating a given material in vacuum and promoting the glancing incidence of gaseous deposition species onto a tilted substrate, in a so-called Glancing Angle Deposition.[1] Yet, and due to difficulties to upscale this technique to typical industrial standards,[17] other alternatives have been analyzed to achieve nanocolumnar structures.[18] Among them, the magnetron sputtering technique operated at oblique angles (MS-OAD), also called magnetron sputtering at glancing angles (MS-GLAD), has emerged as one of the most interesting procedures in terms of efficiency, reliability, reproducibility and potential industrial scalability. It relies on the interaction of a plasma and a solid 4 target to vaporize atomic species from the latter that, emitted preferentially in the normal direction with respect to its surface, are subsequently deposited on a substrate.[19] In this way, when the substrate is tilted with respect to the target, sputtered species may arrive along a preferential oblique direction.[20] In the last decade, MS-OAD has managed not only to reproduce similar film morphologies as those classically obtained by the evaporation technique, but also to widen its possibilities. For instance, in refs. [21-22], we studied the influence of some experimental controllable parameters (e.g. deposition pressure, tilt angle of the substrate, ion impingement, etc.) on the film morphology, finding different tilted nanocolumnar structures with mass densities ranging from 100% to near 30% with respect to the compact layer, or even sponge-like verticallyaligned coalescent structures. The variety of typical porous morphologies that can be achieved by MS-OAD is rich, permitting the customization of film nanostructures with optimum performance in numerous functional applications (see for instance [23-25]). However, to our knowledge, there are important unexplored conditions that require further study and that might widen the possibilities of the method even more. For instance, in ref. [26] we demonstrated that when a thin porous layer is grown on top of a rough nanocolumnar film, the former reproduces the surface features of the latter, in a so-called structural propagation phenomenon, which is of special relevance when growing periodic multilayer structures (e.g. photonic crystals or Bragg reflectors).[9] On the other hand, and even though there has been an increasing amount of publications dealing with the influence of substrate features on the film growth (see for instance [27-30]), to our knowledge, no general framework analyzing the interplay between both has been put forward yet. In this paper we aim at developing such framework by studying how substrate features may affect the film nanostructure when using the MS-OAD technique. In particular, we focus on the effect of one dimensional quasi-periodic patterned substrates, characterized by peak-to-peak distances in the order of few hundred 5 nanometers, very similar to those experimentally obtained by ion beam sputtering.[31-39] To address this problem, we have first used a well-accepted model to theoretically simulate and analyze the growth of a thin film on purely periodic and near periodic patterned substrates at oblique angles and, subsequently, experimentally test these results by analyzing the growth of porous SiO2 thin films on quasi-periodic ion-induced patterned Si substrates. We have chosen this particular film composition because it is a well-known material, whose properties have been widely studied in the literature. However, our aim is general and our results can be easily extrapolated to more general conditions and other materials. Based on this analysis, relevant general conclusions can be achieved on the influence of substrate features on the structural development of porous nanocolumnar thin films. Growth Model The growth model has already been described in detail in refs. [21, 40] and references therein, where it was proven adequate to describe the growth of numerous materials by MS-OAD in the absence of ion bombardment and at low temperatures, i.e. in the so-called zone I of the Thornton Structure Zone Model.[41-42] We describe it here, although for further details refs. [21, 40] are recommended. The model considers the deposition of Si effective particles on a cubic threedimensional NLxNLxNH grid with periodic boundary conditions, whose cells may take the values 0 (empty cell) or 1. Each cell represents a Si atom in the network that becomes fully oxidized once it is deposited. Thus, the size of each cell is assimilated to the typical volume of a SiO2 molecule in the material (i.e., a typical length of ~0.5 nm). A number of deposition particles per unit time and unit surface are thrown towards the substrate from an initial random position above the film, following 6 the direction defined by an incident angle distribution function. This distribution is calculated as a function of the experimental conditions (reactor geometry, tilt angle of the substrate and other geometrical constrains) by the widely accepted SIMTRA code.[43-44] This software describes the collisional transport of sputtered species through the plasma gas by means of binary collisions. The angle and energy distribution of sputtered species at the target are calculated by the software SRIM, [45] which is typically used to describe the ion-assisted sputtering process. An average gas temperature of 350 K and a screened Coulomb potential (Molière type) were considered in the simulations under the assumption of a circular racetrack with a radius of 2 cm. We have run our simulations in small scales (NL and NH up to 2000 cells) to first analyze the general dependence between substrate features and the morphology of the film, and subsequently extrapolate the results to comply with the larger spatial scales of the experimental data (in the order of few microns). Experimental Details Quasi-periodic patterned Si substrates were prepared by irradiation with 500 eV Ar+ ions as described in ref. [46]. Depending on the irradiation conditions, this technique allows the formation of different patterns on the substrate, from surface ripples to elongated islands.[33] The ion beam was extracted from a broad beam Kaufman ion source (3 cm) at a base and working pressures of 5x10-4 and 2x10-2 Pa, respectively, and impinged on the substrates at an incidence angle of 75º with respect to the surface normal. The experiments were performed for an average current density on the target of 300A/cm2 and an ion dose of 2.3x1018 ions/cm2 (irradiation time was 240 minutes). The target was water-cooled during the irradiation, reaching a temperature of 30ºC. 7 A set of amorphous SiO2 thin films were grown on the patterned substrates using reactive MS-OAD. A 3 in. diameter Silicon target was employed for the depositions, placing the substrate holder at a distance of 7 cm and a discharge power of 200 W. Deposition time in each case was chosen to grow films with thicknesses between 200 and 3000 nm, as determined by means of cross-sectional Field Emission Scanning Electron Microscopy (FESEM) images. The base pressure of the deposition reactor was 7x10-4 Pa. The argon and oxygen partial pressures during depositions was kept at 0.2 and 0.05 Pa, respectively, which was enough to operate in the oxidic mode of the discharge and get fully oxidized films.[19] Samples were prepared simultaneously on flat and patterned substrates, tilting them 80º (see figure 1). The morphology of the SiO2 nanocolumns from the film surface to the substrate was studied by transmission electron microscopy (TEM) at the scientific integrated services (SC-ICYT) of the University of Cádiz (Spain). High-angle annular dark-field (HAADF) imaging of the sample was performed in a 200 kV JEOL 2010F microscope using the scanning TEM (STEM) mode with a probe size of about 1 nm. Prior to observation, cross-sectional specimens were prepared using the flattype tripod polishing approach in order to thin the sample down to a few micrometers, followed by a final ion milling step with 3-3.5 keV Ar+ ions up to electron transparency. The surface topography of the substrates and films were imaged by atomic force microscopy (AFM). The measurements were performed in the non-contact dynamic mode with a Nanoscope IIIa equipment (Veeco@) and with PicoPlus 5500 (Agilent). Silicon cantilevers with nominal tip radius of curvature of 8 nm were used. Images were composed of 512 x 512 up to 2048 x 2048 pixels. FESEM pictures were also recorded for each film using a Hitachi S4800 microscope at the Instituto de Ciencia de Materiales de Sevilla (CSIC-US, Seville, Spain). The surface roughness, 𝑤, and correlation length, 𝑙, of the samples were obtained using the Gwyddion freeware package[47] using the formula 8 𝑤 = √∫𝑑𝑥𝑑𝑦 [𝑧(𝑥,𝑦)− 𝑧]2/S, where 𝑥 and 𝑦 denote the position coordinates of the substrate, 𝑆 the surface area under analysis, 𝑧 the height of the film and 𝑧 the mean height. Moreover, 𝑙 has been calculated along the 𝑥 axis (see figure 1) by obtaining the first minimum, 𝑟0, of the (one dimensional) height-height correlation function, ℎ, as a function of the distance, 𝑟, defined as ℎ(𝑟)=∫𝑑𝑥𝑑𝑦𝑑𝑥′𝑑𝑦′(𝑧(𝑥,𝑦)− 𝑧)(𝑧(𝑥′,𝑦′)− 𝑧)/𝑤2 , with 𝑟 = |𝑥 − 𝑥′| and 𝑦 = 𝑦′. In this way, the surface correlation length is defined as 𝑙 = 2𝑟0. Simulation analysis To illustrate the results of the simulations we first assume that the patterns possess a typical sinusoidal shape in the 𝑥𝑦 plane defined as 𝑧𝑠(𝑥,𝑦)= 𝐴[1 + 𝑠𝑖𝑛(2𝜋𝑥/𝜆)], where 𝑧𝑠 is the substrate height, 𝜆 the wavelength and 𝐴 the amplitude of the ripples. For this surface topography, the correlation length of the substrate in the 𝑥 direction, 𝑙𝑠, is 𝑙𝑠= 𝜆, and the surface roughness of the substrate, 𝑤𝑠, is 𝑤𝑠= 𝐴/√2. We have performed different simulations for values of 𝜆 and 𝐴 up to 𝜆=500 and 𝐴=50cells. In figure 2a we illustrate the results by showing the cross-sectional views of four generic cases, when 𝜆=80 and 160 cells and 𝐴=5 and 25 cells. There, different columnar arrangements are visible depending on substrate features, from which three important conclusions can be drawn: i) the column tilt angle is rather independent of the substrate features, ii) each column grows on top of a ripple, and iii) column diameter strongly depends on 𝜆 and very weakly on 𝐴. These three main evidences stem from the fact that surface shadowing promotes the growth of taller surface features over lower ones and thus induces that a column grows on top of each ripple, 9 depicting a tilt angle and diameter that mainly depends on the incident angle distribution of deposition particles and not on any specific substrate feature.[1, 16] In order to further analyze the columnar growth, in figure 2b we also show the evolution of 𝑙 as a function of film thickness, ∆. In this way, for small film thicknesses, the relation 𝑙=𝑙𝑠 is fulfilled, i.e. the film grows following the arrangement of the ripples. Yet, when ∆ reaches a certain critical threshold, the correlation length departs from this value, implying that the typical correlation distances over the film surface do no longer follow that of the ripples. Due to its importance in this work, we dub this thickness oblivion thickness, ∆𝑂. Moreover, according to figure 2b, when ∆> ∆𝑂, the curve converges to that of a film deposited on a flat surface (also shown in figure 2b), i.e. the film growth becomes independent of substrate features. A similar analysis can be performed regarding the evolution of the surface roughness, also depicted in figure 2b. Remarkably, and despite the different original roughness of the substrates, 𝑤 increases with ∆ when ∆< ∆𝑂, mainly due to the preferential development of the columns on top of the ripples. This trend continues until the valleys between columns are no longer visible from the top, decreasing or reaching a plateau for ∆≳ ∆𝑂, when the roughness values converge to those of a film grown on a flat substrate. The two growth regimes described above are illustrated in figure 3, where we show top views of simulated films using flat and periodic rippled substrates (case with 𝜆 = 80 and 𝐴 = 25 cells) for three values of ∆. There, it is apparent that columns arrange according to the ripple pattern when ∆< ∆𝑂. However, when ∆≳ ∆𝑂 the pattern starts to vanish until, for ∆≫ ∆𝑂 , the film surface looks very similar to that of a film grown on a flat substrate. In figure 4 we show the calculated values of ∆𝑂 as a function of 𝐴 and 𝜆, finding a weak and strong dependence on these two parameters, respectively. This relation can be understood as an outcome of a shadowing dominated growth, by which the taller a surface feature is the more species are deposited on it, rapidly amplifying any initial surface protuberance. Hence, a surface with small ripple amplitudes would develop similarly 16 Free Growth regime, where the growth is equivalent to that of a thicker film deposited on a flat substrate. The theoretical framework developed herein has been experimentally tested by performing numerous depositions on flat and ion-induced patterned substrates with height variations, finding an overall good agreement between theory and experiments. Indeed, three growth regimes have been identified, finding a Substrate Driven growth for thicknesses below ~500 nm, a Columnar Aggregation regime for thicknesses between ~500 and ~1000 nm, and a Free growth for thicknesses above ~1000 nm. In this regard, the obtained results do not only explain the influence of substrate features on the film morphology as a function of thickness, but also indicate the importance of the substrate roughness and correlation length on the film characteristics. Acknowledgements We acknowledge the support of the University of Seville (VPPIUS and VI PPIT-US), the European Development Funds program (EU-FEDER), and the Spanish Ministry of Economy and Competitiveness and Agencial Estatal de Investigación (AEI) (projects MAT2013-40852-R, MAT2016- 79866-R, MAT2015-69035-R, 201560E055, and MAT2015-69035-REDC and MAT2017-85089-C2-1- R), and the Comunidad Autónoma de Madrid (S2013/MIT-3029, NANOAVANSENS, IND2017/IND- 7668). Keywords Nanostructures; Thin Films; Oblique Angle Deposition; Magnetron Sputtering; Patterned Substrate. 17 References [1] A. Barranco, A. Borras, A. R. Gonzalez-Elipe, A. Palmero, Prog. Mater. Sci. 2016, 76, 59. [2] X. Xu, M.A.P. Yazdi, J.B. Sanchez A. Billard, F. Berger, N. Martin, Sensors and Actuators B- Chemical 2018, 266, 773-783. [3] C. Charles, N. Martin, M. Devel, Surf. Coat. Technol. 2015, 276, 136-140. [4] M.S. Rodrigues, D. Costa, R.P. Domingues, M. Apreutesei, P.Pedrosa, N. Martin et al. Applied Surface Science 2018, 438, 74-83. [5] S. Liedtke, C. Gruener, J.W. Gerlac, B. Rauschenbach, Belstein Journal of Nanotechnology 2018, 9, 954-962. [6] K. Kim, J.H. Park, H. Kim, J.K. Kim, E.F. Schubert, J. Cho, Appl. Phys. Letters 2016, 108(4), 011910. [7] V. Godinho, P. Moskovkin, R. Alvarez, J. Caballero-Hernández, R. Schierholz, B. Bera, J. Demarche, A. Palmero, A. Fernández and S. Lucas, Nanotechnology 2014, 25, 355705. [8] J. Ollitrault, N. Martin, J.Y. Rauch, J.B. Sanchez, F. Berger, Materials Letters 2015, 155, 1-3. [9] M. Oliva-Ramirez, L. Gonzalez-Garcia, J. Parra-Barranco, F. Yubero, A. Barranco and A.R. Gonzalez-Elipe, ACS Appl. Mater. Interfaces 2013, 5, 6743–50. [10] C. Sengstock, M. Lopian, Y. Motemani, A. Borgmann, C. Khare, P.J.S. Buenconsejo, T.A. Schildhauer, A. Ludwig, M. Koller, Nanotechnology 2014, 25, 195101. [11] Y.J. Yoo, J.H. Lim, G.J. Lee, K.I. Jang, Y.M. Song, Nanoscale 2017, 9(9), 2986-2991. 18 [12] L. Yang, Y. Zhao, Y. Feng, J.S. Shan ; X.Y. Liang , J. Huang, J.H. Mi, L.J. Wang, W.M. Shi, Applied Surface Science 2016, 363, 252-258. [13] D.B. Polat, O. Keles, Thin Solid Films 2015, 589, 543-550. [14] C.Y. Song, G.K. Larse, Y.P. Zhao, Appl. Phys. Letters 2013, 102(23), 233101. [15] D. Toledano, R.E. Galindo, M. Yuste, J.M. Albella, O. Sanchez, J. Appl. Phys. 2013, 46(4), 045306. [16] T. Karabacak, J.P. Sing, Y.P. Zhao. G.C. Wang, T.M. Lu, Physical Review B 2003, 68(12), 125408. [17] R. Alvarez, J.C. Gonzalez, J.P. Espinos, A. R. Gonzalez-Elipe, A. Cueva, F. Villuendas, Applied Surface Science 2013, 268, 507. [18] P. Romero-Gomez, A. Palmero, T. Ben, J. G. Lozano, S. I. Molina and A. R. González-Elipe, Physical Review B 2010, 82, 115420. [19] Reactive Sputter Deposition, D. Depla, S. Mahieu (Eds.), Springer Series in Materials Science, Springer-Verlag, Berlin, Heildelberg, 2008. ISBN 978-3-540-76662-9. [20] R. Alvarez, J. M. Garcia-Martin, M.C. Lopez-Santos, V. Rico, F.J. Ferrer, J. Cotrino, A. R. Gonzalez-Elipe, A. Palmero. Plasma Processes and Polymers 2014, 11, 571-576. [21] R. Alvarez, J.M. Garcia-Martin, A. Garcia-Valenzuela, M. Macias-Montero, F.J. Ferrer, J. Santiso, V. Rico, J. Cotrino, A.R. Gonzalez-Elipe, A. Palmero, J. Phys. D: Appl. Phys. 2016, 49(4) 45303. [22] M. Macias-Montero, F.J. Garcia-Garcia, R. Alvarez, J. Gil-Rostra, J.C. Gonzalez, J. Cotrino, A.R. Gonzalez-Elipe, A. Palmero, Journal of Applied Physics 2012, 111(5), 054312. [23] T. Fujii, Y Aoki, H. Habazaki, Langmuir 2011, 27(19), 11752-11756. 19 [24] R.L. Rodriguez-Suarez, L.H. Vilela-Leao, T. Bueno, A.B. Oliveira, J.R.L. de Almeida, P. Landeros, S.M. Rezende, A. Azevedo, Physical Review B 2011, 83(22), 224418. [25] K.R. Khedir, G.K. Kannarpady, H. Ishihara, J. Woo, C. Ryerson, A.S. Biris, Langmuir 2011, 27(8), 4661-4668. [26] A. Garcia-Valenzuela, C. Lopez-Santos, R. Alvarez, V. Rico, J. Cotrino, A.R. Gonzalez-Elipe, A. Palmero, Nanotechnology 2017, 28, 465605. [27] K. Chen, R. Frömter, S. Rössler, N. Mikuszeit and H.P. Oepen, Phys. Rev. B 2012, 86, 064432. [28] M. Körner, K. Lenz, M.O. Liedke, T. Strache, A. Mücklich, A. Keller, S. Fracsko, J. Fassbender, Phys. Rev. B 2009, 80, 214401. [29] M.O. Liedke, M. Körner, K. Lenz, M. Fritzche, M. Rankan, A. Keller, E. Cizmar, A.A. Zvyagin, S. Facsko. K. Potzger, J. Lindner, J. Fassbender, Phys. Rev. B 2013, 87, 024424. [30] A. Keller, L. Peverini, J. Grenzer, G. J. Kovacs, A. Mücklich, S. Facsko, Phys. Rev. B 2011, 84, 035423. [31] T. Luttrell, M. Batzill, Phys. Rev. B 2010, 82, 035408. [32] M. Kolmer, A.A. Zebari, M. Goryl, F. B. Mongeot, F. Zasada. W- Piskorz, P. Pietrzyk, Z. Sojka, F. Krok, M. Szymonski, Phys. Rev. B 2013, 88, 195427. [33] J. Muñoz-García, L. Vazquez, M. Castro, R. Gago, A. Redondo-Cubero, A. Moreno-Barrado, R. Cuerno, Materials Science and Engineering R 2014, 86, 1-44. [34] R. Gago, L. Vazquez, F.J. Palomares, F. Agulló-Rueda, M. Vinnichenko, V. Carcelén, J. Olvera, J.L. Plaza, E. Diéguez, J. Phys. D: Appl. Phys. 2013, 46, 455302. [35] J. Shen, J. Kischner, Surf. Sci. 2002, 500, 300. 20 [36] C. H. Sun, P. Jiang, B. Jiang. Appl. Phys. Lett. 2008, 92, 061112. [37] B. Kasemo, Surf. Sci. 2002, 500, 656. [38] A. Wellner, R.E. Palmer, J.G. Zheng, C.J. Kiely, K.W. Kolasinski, J. Appl. Phys. 2002, 91(5) 3294. [39] D. Datta, S.R. Bhattacharyya, T.K. Chini, M.K. Sanyal, Nucl. Instrum. Mathods Phys. Res. B 2002, 193, 596. [40] R. Alvarez, J.M. Garcia-Martin, M. Macias-Montero, L. Gonzalez-Garcia, J. C. Gonzalez, V. Rico, J. Perlich, J. Cotrino, A.R. Gonzalez-Elipe and A. Palmero, Nanotechnology 2013, 24, 045604. [41] J.A. Thornton, J. Vac. Sci. Technol. 1974, 11, 666. [42] J.A. Thornton, J. Vac. Sci. Technol. 1975, 12, 830. [43] K. van Aeken, SIMTRA, Available at http://www.draft.ugent.be/. [44] K. van Aeken, S. Mahieu, D. Depla, J. Phys. D. Appl. Phys. 2008, 41, 20530. [45] The Software SRIM, Available at http://www.srim.org. [46] M. Castro, R. Gago, R. Cuerno, J. Muñoz-Garcia and L. Vazquez, Physical Review B 2012, 86, 214107. [47] D. Necasand P. Klapetek, Cent. Eur. J. Phys. 2012, 10, 181-188. 21 Figure caption Figure 1.- Experimental setup and definition of the 𝑥 axis of the patterned substrate. Figure 2.- a) Cross-sectional images of simulated films grown on periodic patterned substrates (𝜆 = 80,160 cells and 𝐴 = 5,25 cells). Note that the substrate ripples appear with different color. b) Surface correlation length and roughness of these films as a function of thickness. Figure 3.- Top views of simulated films grown on a flat substrate , a periodic patterned substrate with 𝜆 = 80 and 𝐴 = 25 cells , a patterned substrate with fluctuating 𝜆, with 〈𝜆〉=80 and 𝐴 = 25 cells, and a patterned substrate with fluctuating 𝐴, with 𝜆 = 80 and 〈𝐴〉=25 cells. The arrows indicate the incidence of the deposition flux. Figure 4.- Oblivion Thickness as a function of substrate pattern amplitude and wavelength. Figure 5.- a) Cross-sectional images of simulated films grown on patterned substrates (periodic substrate with 𝜆 = 80 and 𝐴 = 25 cells, patterned substrate with fluctuating 𝜆, with 〈𝜆〉=80 and 𝐴 = 25 cells, patterned substrate with fluctuating 𝐴, with 𝜆 = 80 and 〈𝐴〉=25 cells and a patterned substrate with fluctuating 𝐴 and 𝜆, with 〈𝜆〉=80 and 〈𝐴〉=25 cells). Note that the substrate ripples are depicted with different color. b) Surface correlation length and roughness of these films as a function of thickness. Figure 6.- Topography of the patterned substrate, as obtained by AFM (the ion beam irradiation to create the patterns was from top to bottom of the image). The arrow indicates the incidence of the deposition flux. A cross-sectional height profile in the direction of the arrow is also shown. 22 Figure 7.- a) Top view SEM images of the films grown on flat and patterned substrates as a function of thickness. The arrows indicate the incidence of the deposition flux. b) Correlation length and roughness as obtained from the surface topography of these films measured by AFM. Figure 8.- a) Cross-sectional SEM image of the 1 𝜇𝑚 thick thin film grown on the patterned substrate. The arrow indicates the incidence of the deposition flux. b) Cross-sectional STEM-HAADF image of the same film. The three stages of growth as a function of thickness are identified: for thicknesses below ~500 nm the film follows the substrate features in a Substrate Driven regime, while for thicknesses between ~500 and ~1000 nm columns merge and form large structures in a typical Columnar Aggregation regime. Finally, for thicknesses above ~1000 nm, columns develop independent of substrate features in a typical Free Growth regime. 23 TABLE OF CONTENTS The influence of substrate patterns on the nanocolumnar growth of SiO2 thin films at oblique angles is studied. A critical thickness has been determined, below which the columnar growth is modulated by the substrate topography. For thicknesses above, pattern height fluctuations are responsible for the appearance of large tilted structures that grow independent of substrate features. 24 Fig 1 25 Fig 2