Morphology of Thin Films Formed by Oblique Physical Vapor

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Morphology of Thin Films Formed by Oblique Physical Vapor Deposition Christoph Gruener, Susann Liedtke, Jens Bauer, Stefan G. Mayr, and Bernd Rauschenbach ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.8b00124 • Publication Date (Web): 22 Feb 2018 Downloaded from http://pubs.acs.org on February 25, 2018

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ACS Applied Nano Materials

Morphology of Thin Films Formed by Oblique Physical Vapor Deposition Christoph Grüner1,*, Susann Liedtke1, Jens Bauer1, Stefan G. Mayr1,2, Bernd Rauschenbach1,2 1

Leibniz Institute of Surface Engineering (IOM), Permoserstraße 15, 04318 Leipzig, Germany

2

Felix-Bloch-Institute for Solid State Physics, University of Leipzig, 04103 Leipzig, Germany

*E-Mail: [email protected] Oblique Angle Deposition, Physical Vapor Deposition, Nanostructures, Tilt Angle, Porosity, Self-Organization

Abstract Physical vapor deposition is a fundamental tool to create thin films for countless applications. Deposition at oblique vapor incidence angles can lead to the growth of thin films with dramatically changed morphological features. Techniques as oblique angle deposition (OAD) and glancing angle deposition (GLAD) utilize this fact to create self-organized nanostructures on surfaces. The changed columnar microstructure of such thin films significantly influences the film properties. The film density, for instance, influences the refractive index and therefore has impact for optical applications, like filters or anti-reflection coatings. Understanding the influence of the incidence angle in physical vapor deposition is an important step that allows

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tailoring the nanostructured surfaces for specific applications not only in optics, but also for catalysis or bio-sensing usage. In order to investigate thin film growth at oblique deposition conditions, silicon, germanium and molybdenum nanostructured thin films were deposited at different angles of incidence by electron beam evaporation. Additionally, a 3D ballistic offlattice simulation was applied to understand self-shadowing and growth competition, which are the crucial mechanisms for the self-organized growth of nanostructures under oblique particle incidence. Based on the observations, a model is proposed that allows to obtain accurate predictions for the growth rate and density of obliquely deposited thin films. Special attention is paid to the tilt angle of the columnar film morphology, as it is under discussion since decades. The developed model predicts the tilt angles for the grown thin films accurately over the complete angle of incidence range. In the model, material properties and deposition conditions are combined into a single parameter, the fan angle. Since perfectly normal deposition is an idealized case, the observed results have impact on nearly all applications that utilize thin films grown by physical vapor deposition.

Introduction Physical vapor deposition (PVD) is a widely used method to generate thin films on substrate surfaces. Commonly, it is assumed for the description and modelling of PVD that the deposition of the thin film is realized vertically on smooth substrate surfaces.1-3 This is an idealized condition and not given in the practice of applied thin film deposition. On the one hand, the divergence of the generated particle flux, the local extension of the substrate and of the source and a non-parallel arrangement of the deposition source to the surface of the substrate lead to an oblique (non-normal) deposition. On the other hand, curvature and the topography of the substrate surface cause a local deviation from the normal deposition process.


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The resulting oblique deposition can lead to dramatic changes of the properties and morphology of thin films. Figure 1a shows the cross-section morphology of molybdenum thin films, deposited at different angles. With increase of the vapor incidence angle, the separation between the columns in the film and their tilt angle are enlarged. Due to the connection of the film properties on its morphology, the mechanical4, electrical5 and optical6 properties depend strongly on the deposition angle. Consequently, this technique, known as oblique angle deposition (OAD) 7,8

was not only used intentionally to create self-organized nanostructures on surfaces9, but has

always influenced nearly the complete field of thin film deposition applications, since true vertical deposition is a very rare case.

Figure 1 (a) SEM cross-section images of obliquely deposited molybdenum thin films, demonstrating significant changes of the film morphology. The arrows indicate the angle of incidence θ. (b) Oblique deposition with an angle of incidence θ leads to the formation of a columnar thin film, where the columns are tilted by an angle β. The film is porous due to the self-shadowing effect as indicated. (c) The predictions of some common models for the tilt


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angles are shown. It can be seen, that the experimental observations for obliquely deposited silicon thin films are only roughly represented. Figure 1b shows a schematic description of the OAD process. The incident vapor flux arrives at the substrate at an angle θ. The morphology of the grown thin film is determined by a geometrical self-shadowing effect and surface diffusion and results generally in the formation of columns that are tilted by an angle β. The possibility to control the morphology as well as the porosity of the complete film opens a wide field of applications. Optical coatings (as antireflection coatings or filters), bio-sensors or catalytic layers are just a few examples of already established applications (see ref. 9 for an overview). For decades it is well known that the tilt angle β of the film columns is not identical with the angle of incidence θ. In fact, the tilt angle is always smaller than the vapor incidence angle (β < θ). In the past various empirical relationships have been suggested to describe this difference (see reviews

10,11

). Most common are the tangent12 and cosine rules13, which rely on semi-empirical

geometric considerations. These rules do not involve different material properties or deposition parameters and in turn cannot be used to describe the growth of real films accurately. A first step to overcome this disadvantage was the fan model.14,15 The fan angle – the angle by which a free standing fan or overhang structure grows away from the incidence direction – is the exclusive parameter in this model and accessible by direct measurements. Nevertheless, with none of the models it is possible to predict the tilt angles accurately, as demonstrated in fig. 1c. Here we show that the competitive nature of the self-shadowing effect plays an important role in the column formation and by this must be taken into account. Considering this, we propose a model that gives a prediction for the growth angles, the films growth rate and the film density for the complete angle of incidence range (0° ≤ θ ≤ 90°). Thereby, it gives a quantitative explanation


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for the more than 50 years old experimentally firmed knowledge that the growth angle β is not identical with the deposition angle θ. The model predictions are supported by experimental OAD as well as a ballistic computer studies.

Observations from experiment and simulation Germanium, silicon and molybdenum were chosen for the deposition experiments. With these materials a wide range of melting points (from about 1200 K to 2900 K) is covered. As a firstorder approximation, a linear relationship between the tilt angle and the angle of incidence β ≅ 0.71 θ can be obtained for OAD of silicon. A similar, linear behavior can be found for obliquely deposited germanium and molybdenum thin films. As the formation of the columnar structure at oblique deposition is obviously linked to overhangs and fan structures, deposition of such structures was carried out for the used materials. For this purpose, material was deposited at normal incidence onto substrates that were pre-patterned with hillock-like structures. This led to fan structures as shown in figure 2a. The average found fan-out angles Φ were 39°, 48° and 74° for germanium, silicon and molybdenum, respectively. The correlation of the fan angle with the materials melting point (found by Zhu et al.16) can be confirmed.


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a

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b

Figure 2. (a) SEM image of germanium deposited at normal incidence onto a pre-patterned substrate. The fan angle Φ is shown. (b) Simulated deposition onto a similar substrate (not displayed). The colors represent different fibers. Concentric circles are provided to indicate the nearly spherical growth front. The fan shape of individual structures developing from protruding nucleation points is a result of the lateral structure broadening caused by overhang particle sticking. In order to understand the growth of such structures, a ballistic model was implemented in a computer simulation. In this off-lattice simulation spherical particles move on straight trajectories until they hit the substrate or a previously deposited particle. After such a collision appeared, the sphere sticks at this point and the next particle is started. So neither surface diffusion, nor attractive forces during the particles flight are assumed. With this simple computer model, columnar thin films can be observed, that resemble experimentally deposited OAD films (see Supplementary Fig. S2).17,18 Fan structures were deposited with this simulation onto different initial geometries. For this, a single particle, a large sphere (d = 500 particle diameters, shown in fig. 2b), and a plateau were chosen. The simulated fan structures show the same inner columnar morphology that is found at the evaporated structures. It can be observed (compare also Supplementary Fig. S3), that (i) for long deposition times, the simulated opening angle of the fans trends always to the same value of Φ = (48 ± 2)° and does not depend on the geometry of the seed point. (ii) With increasing


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distance from the substrate surface, the growth front on all starting geometries tends toward spherical shape, in contrast to the often assumed cos1/2 shape.19,20 Depositing fan structures onto a tilted row of seed points (as in Tanto’s fan model

15

), leads to a film with a similar fiber

structure, as observed in the depositions experiments. In this kind of simulations, the pre-defined separation between the individual fan structures gets lost after some time. When this happens, the individual fibers start to compete with each other. This observation has to be included into a model, capable of describing oblique deposition. Analysis of the structure evolution In Fig. 3a, a schematic of the proposed model is shown. The substrate is considered to be an array of seed points located in an oblique, parallel particle flux. In the initial stage (I) on each seed point an individual fan structure starts to grow into the direction of the incoming material flux. It is obvious that the local tilt angle βI is identical with the angle of incidence θ. This growth stage lasts until the fan structures start to cast shadows onto the structures located behind them. During a transition stage (II) growth of the lower parts of the fan structures stops, due to shadowing. At this time the upper part of each structure is not shadowed and therefore it continues to grow away from the particle trajectories with an angle equal to the half of fan angle. The local growth angle of the structures βII in this stage is smaller than the angle of incidence θ and can be described by the relation found by Tanto et al.15, using the upper, non-shadowed corner of each fan structure. From the observed shape of the nanostructures, however, it can be concluded, that this is not the final stage of the growth process. In fact, the shadowed corner of the individual fan structures still grows faster than the upper corner. Due to this, the shadowed corner will catch up with this upper corner (see Supplementary Fig. S6 for an example) until


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both finally touch each other. Finally, this former shadowed corner will start to cast a shadow onto the first corner, which is now left behind and therefore stops to grow. As of this point, both corners shadow each other in a competitive process, leading to the final growth stage (III). That has the consequence, that the behind-standing columns can partially shadow the front-standing ones. This can also be considered as the origin of the competitive growth which is inherent to all OAD and GLAD processes. Consequently, both corners of each nanostructure have the same tilt angle. The point of the fan that has the largest distance to the substrate never becomes shadowed and therefore determines the tilt angle of the nanostructure.


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a

b

Figure 3. (a) Scheme of the three growth stages. The yellow arrows represent the local growth direction for each stage. In the initial stage (I) the fan structures start to grow into the direction of the incoming particle flux on each individual seed. When shadowing starts to inhibit the growth of the lower parts of the fan structures, a transition stage (II) begins. During this stage the shadowed lower corner grows progressively into the direction of the corner that casts the shadow. At the end of this stage shadowing is reversed so that the rear standing column starts to partly shadow the top edge of the front standing one, leading to a growth competition between


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both corners (III). Both corners of each structure therefore grow parallel then, and therewith define the final growth direction. As only the point with the highest distance to the substrate will never become shadowed, it can be used to calculate the tilt angle of the complete structure. (b) Ballistic simulation of the structure growth. The growth stages are indicated. On the leftmost seed a non-shadowed fan grows. The indicated dotted lines depict the position of the top corners of non-shadowed fans. It can be seen, that rear standing columns grow over this line. Notice that the rightmost structure has no partner for backward shadowing, hence it continues to grow with βII. Figure 3b shows a ballistic simulation of OAD onto isolated seed points. The three growth stages can be clearly distinguished. It should be noticed, that on flat, non-patterned substrates, the starting points for nanostructure growth (given by nuclei or surface roughness) lie close together, so that the initial stage (I) usually cannot be observed and that β < θ is found for the complete growth process. In the past, this observation led to the different suggestions on the relation between the growth angle and the deposition angle (see e.g.

10,11

). On patterned substrates the

transition stage (II) can be observed for a quite long period of time, until the structures start to compete with each other and the pre-defined order becomes smeared out. Furthermore, it can be seen that the rightmost structure in fig. 3b never leaves the transition stage (II), as it has no partner for the ‘backward shadowing’. This effect can also be observed in deposition experiments at the rear edges of the substrates (see Supplementary Fig. S7) and is evidence that the proposed backward shadowing appears in real films too. Finally it should be noticed that each nanostructure is a section from the outer part of a fan structure, which usually is not compact. So the porosity of the films in the competition stage (III) arises from the inner porosity of the fan structures and not from the spacing defined by an assumed pre-pattern.


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Figure 4. Sketch of the angles and lengths used in the model. For the calculation, the half of the full fan angle is used (ϕ = Φ / 2). In the shown orientation, the particle flux comes from the top, leading to an upright fan structure. The substrate is tilted by an angle θ. The green line represents the connection of the fan’s origin with its highest point and therefore the part of the fan structure that is never shadowed. It is tilted by an angle β.

Modelling the morphology In order to calculate the tilt angle β in the final competition stage (III), the position of the highest point of a tilted fan structure is identified. For this, the approximation of the spherical growth front of a non-shadowed fan is used. Using the angles and lengths as shown in fig. 4, the overhang angle ϕ (defined as the half of the fan angle Φ) is given by

tan

(1)

sin sin ,

(2)

and the tilt angle β is given by


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as can be derived from simple geometry on the corresponding triangles. Combining both equations leads to

tan

sin cos + tan

(3)

. 90°

(4)

that can be approximately linearized by

1

These equations describe the tilt angle for the complete angle of incidence range 0° ≤ θ ≤ 90°. Besides the tilt angle, two other properties of the OAD thin film are of interest. These are the growth rate and the porosity (film density). Assuming that all material that reaches the growing film sticks there, porosity and growth rate are linked with each other.21 This means that, for example, no reflection and re-emission occurs, which can safely be assumed for evaporation onto substrates at room temperature. Based on this assumption

≡ 1

!" & 1 cos #$!% ℎ

(5)

describes the density as a function of the relative growth rate h/H. Here, h is the thickness of the porous film deposited onto the tilted substrate, whereas H describes the thickness of a film deposited at the same conditions under normal incidence. Using the proposed model, H corresponds to the length of a non-shadowed fan and h is the height of the tilted fan structure. Thus, the relative growth rate can be expressed as

ℎ ℎ( + cos + & + +

(6)

that, with equation (1), becomes


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ℎ cos + tan . & 1 + tan

(7)

Inserting equation (7) into (5) allows to calculate the film density.

a

b

c

d

Figure 5. Verification of the model predictions. Tilt angles and film thicknesses for silicon (a) and germanium (b) as well as tilt angles and densities for molybdenum (c) and simulated (d) thin OAD films. The directly measured fan angles Φ are 48°, 39° and 74° for Si, Ge and Mo, respectively. For the simulated case, the measured value of 48° directly was used as model input.


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Verification and Discussion With these equations, the growth of obliquely deposited films can be adequately described (see fig. 5). Fitting the model onto the observed tilt angles leads to fan angles Φ (= 2φ) of 50°, 43° and 77° for Si, Ge and Mo, respectively. Comparing this to the directly measured fan angles of 48°, 39° and 74°, respectively, a small deviation can be noticed, only. A verification of the model based on literature data for more materials (MgF2, Ta2O5, SiO2, ITO) can be found in section (D.) of the Supporting Information. One source of error is presumably given by the approximation of a spherical growth front. The shape of the growth front has strong influence on the outcomes of the model. A non-spherical growth front would lead to a loss of the nearly linear behavior of the tilt angles, for example. Additionally, it is unclear whether the shape of the growth front of a fan structure changes if only a small part of it is really formed, as it is the case for the nanocolumns. Furthermore, it is often observed that the nanostructures grow steeper at the beginning of the growth process.22,23 This observation can partly be explained by the transition from the growth stages (II) to (III), as typically the edges of the nanostructures are measured. But examining simulated OAD nanostructures by using their topmost particles for tilt angle calculation reveals that a deviation of tilt angles can still be observed for individual nanostructures during the early stages of growth (see Supplementary Fig. S4). Tracking individual structures reveals that this also influences the tilt angles of structures that survive the competitive growth process. The nanostructures are steeper close to the substrate before the surviving structures bend to their final tilt angle. This is likely caused by the competition conditions at the beginning of growth. The deviation of the fitted fan angles in the framework of the porosity calculation compared to the measured fan angles can be explained by a closer look onto the inner structure of the


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simulated overhangs. Close to the edges the density of the material rapidly decreases (see Supplementary Fig. S5). Therefore, the interior density of the nanostructures is lower than the density of a normally deposited film. Consequently, eq. (5) is not valid in this case, what leads to an incorrect prediction of the model. However, the density in a real overhang is not expected to drop as rapidly as in the simulated case. Neither the model nor the simulation considers coalescence effects that may increase the density of real films, deposited at higher deposition angles.

Conclusion To conclude, our competition model takes the ‘backward shadowing’ of interacting fan structures into account. The model is used to describe nanostructure tilt angles in good agreement with the simulation and evaporation deposition experiments. Additionally, a prediction for the densities and growth speeds of obliquely grown films is made. The identified relations can be used for the complete range of vapor incidence angles, and could further be used to predict the properties of thin films deposited over complex geometries. The only parameter of the presented model – the fan angle – summarizes the material properties (as surface-diffusion coefficient) and deposition conditions (as substrate temperature or beam divergence). It can be measured at the beginning of a sample series for a given material in a given deposition system, and then be used to predict the thin film properties of the obliquely deposited thin films at any deposition angle. Therefore, the model can promote the use of obliquely grown nanostructures in the large variety of possible applications that arise from the large surface area, the controllable density (and within refractive index) and the very special film morphology. The numerous application areas of OAD thin films as catalysis24, anti-reflection coatings25, optical filters26,27,


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photonic crystals28, mechanical sensors29 and bio-sensors30,31 benefit from the possibility to predict the thin film parameters, as many trial-and-error approaches could be avoided.

Methods Procedure of simulation. The film growth by OAD was simulated by a 3D off-lattice simulation, using a hard sphere model without surface diffusion and with ballistic particle trajectories. No attractive forces between the particles and the film are assumed during the deposition. This means that a particle is started from a random point over the substrate, from where it travels on a straight line until it collides with the substrate or a previously deposited particle. The particle sticks at the position of the collision and then the next particle is started above the substrate. Consequently, the refined film is amorphous. Additionally, all particles carry a cluster number. Each particle colliding with the substrate is provided with a new cluster number, whereas particles colliding with a previously deposited one get the cluster number of their collision partner. For details of the simulation algorithm see Supplementary Figure S1 and the corresponding discussion. In order to simulate oblique deposition, a tilted substrate is inserted into such a simulation cell. Nanostructure tilt angles were calculated automatically by using the first and the topmost particle of each cluster. Only the 20 highest structures of each run were used. Fan and overhang angles were measured manually on a graphical output. For all simulated cases the results of ten runs were averaged. Deposition. To verify the results of the proposed model, silicon, germanium and molybdenum films were deposited by OAD in an ultra-high vacuum electron beam evaporation chamber. Deposition rate and time were kept constant at 1 nm/s and 1000 s, respectively, for Si and Ge and at 0.5 nm/s and 2000 s for Mo. So, the total amount of evaporated material was fixed to


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correspond to a 1000 nm thick normally deposited film for all samples, measured by a quartz crystal microbalance during deposition. Consequently, different measured film thicknesses of the OAD films correspond to different film growth rates. The angle of incidence θ was set, using a computer controlled sample manipulator and care was taken to minimize undesired azimuthal tilt during growth and examination. Since the base pressure of the system is about 10-9 mbar, with a working pressure not higher than 10-7 mbar, the particle trajectories can be considered as ballistic. The particle beam divergence can be estimated by the chamber geometry. The molten spot in crucible is about 1 cm in diameter and the distance between melt and sample is about 30 cm, leading to a maximum divergence of 2°. Natively oxidized Si(100) was used as substrate. For analysis, the samples were cleaved and the edges were investigated with a scanning electron microscope. The film thicknesses and the tilt angles of the nanostructures were measured at three different positions for numerous different nanostructures for each angle of incidence. An error of 5% for all measured angles is assumed, even though the statistical deviation is smaller, typically. The density of the Mo films was measured by X-Ray Reflectometry (XRR).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions


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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors gratefully acknowledge the funding of the DFG, and S. Liedtke would like to thank the graduate school BuildMoNa.

Supporting information Details of simulation algorithm, Simulation results for OAD films and fan structures, SEM image of OAD film during transition stage (II), SEM evidence for backward shadowing, verification of model predictions on literature data.

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20. Pelliccione, M.; Lu, T.-M. Self-Shadowing in Ballistic Fan Formation From Point Seeds. Phys. Rev. B 2007, 75, 245431. 21. Poxson, D. J.; Mont, F. W.; Schubert, M. F.; Kim, J. K.; Schubert E. F. Quantification of Porosity and Deposition Rate of Nanoporous Films Grown by Oblique-Angle Deposition. Appl. Phys. Lett. 2008, 93, 101914. 22. Kiema, G. K.; Colgan, M. J.; Brett, M. J. Dye Sensitized Solar Cells Incorporating Oliquely Deposited Titanium Oxide Layers. Sol. Energy Mater. Sol. Cells 2005, 85, 321. 23. Elofsson, V.; Magnfält, D.; Samuelsson, M.; Sarakinos, K. Tilt of the Columnar Microstructure in Off-Normally Deposited Thin Films Using Highly Ionized Vapor Fluxes. J. Appl. Phys. 2013, 113, 174906. 24. Liu, H.; Cheng, G.; Zhao, Y.; Zheng, R.; Liang, C.; Zhao, F.; Zhang, T. Controlled Growth of Fe Catalyst Film for Synthesis of Vertically Aligned Carbon Nanotubes by Glancing Angle Deposition. Surf. Coat. Technol. 2006, 201, 938-942. 25. Kennedy, S. R.; Brett, M. J. Porous Broadband Antireflection Coating by Glancing Angle Deposition. Appl. Opt. 2003, 42, 4573-4579. 26. Robbie, K.; Hnatiw, A. J. P.; Brett, M. J.; MacDonald, R. I.; McMullin, J. N. Inhomogeneous Thin Film Optical Filters Fabricated Using Glancing Angle Deposition. Electron. Lett. 1997, 33, 1213-1214. 27. van Popta, A. C.; Hawkeye, M. M.; Sit, J. C.; Brett, M. J. Gradient-Index NarrowBandpass Filter Fabricated with Glancing-Angle Deposition. Opt. Lett. 2004, 29, 2545-2547.


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28. Kennedy, S. R.; Brett, M. J. Fabrication of Tetragonal Square Spiral Photonic Crystals. Nano Lett. 2002, 2, 59-62. 29. Kesapragada, S. V.; Victor, P.; Nalamasu, O.; Gall, D. Nanospring Pressure Sensors Grown by Glancing Angle Deposition. Nano Lett. 2006, 6, 854-857. 30. Shalabney, A.; Khalaila, I.; Grüner, C.; Rauschenbach, B.; Abdulhalim, I. SERS Biosensor Using Metallic Nano-Sculptured Thin Films for the Detection of Endocrine Disrupting Compound Biomarker Vitellogenin. Small 2014, 10, 3579-3514. 31. Srivastava, S. K.; Grüner, C.; Hirsch, D.; Rauschenbach, B.; Abdulhalim, I. Enhanced Intrinsic Fluorescence From Carboxidized Nano-Sculptured Thin Films of Silver and Their Application for Label Free Dual Detection of Glycated Hemoglobin. Opt. Express 2017, 25, 4761-4772. Competing financial interests The authors declare no competing financial interests.


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Graphical Table of Contents


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Morphology of Thin Films Formed by Oblique Physical Vapor

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