iii Titre : Développement de composants grande surface à nanostructures résonantes pour systèmes de réalité augmentée Mots clés : metasurface, nanofabrication, nanoimpression, plasmonique, facteur de structure, réalité augmentée Résumé : Récemment, les systèmes de visualisation et en particulier la réalité augmentée, ont connu une utilisation accrue pour les applications telles que les affichages tête haute dans l'automobile ou les afficheurs montés sur tête tels que les Google Glass. En raison des contraintes de coût des applications industrielles, des solutions technologiques sont nécessaires pour améliorer l'efficacité de ces dispositifs. Notamment ces systèmes incluent une lame de grande surface qui doit être à la fois transparente dans le visible et réfléchissante pour certaines longueurs d'onde. Elle peut également réaliser la fonction de focalisation ou défocalisation. Dans ce contexte, les métasurfaces réfléchissantes sélectives en longueur d'onde sont considérées comme de bonnes candidates. Ce type de dispositifs a attiré beaucoup d'attention ces dernières années en raison des propriétés uniques qui peuvent être obtenues mais néanmoins, des améliorations significatives sont encore nécessaires pour en faire une option viable. Dans ce travail, nous abordons deux domaines principaux que nous souhaitons améliorer.

Le premier est la fabrication de dispositifs de grande surface. Nous présentons ici un procédé basé sur la nanoimpression par timbre souple (Soft NIL-UV) pour fabriquer de grandes surfaces à faible coût. La principale amélioration est une nouvelle technique pour la fabrication de timbres PDMS basée sur l'auto-assemblage de nanosphères de polystyrène combiné à la gravure directe du PDMS. La seconde est le développement d'outils pour étudier l'impact du niveau d'ordre de la métasurface sur l'effet optique obtenu. Dans cette thèse, nous proposons d'utiliser le facteur de structure en raison de son applicabilité aux structures quel que soit leur niveau d'ordre, et de sa bonne adaptabilité aux grandes surfaces lorsque combiné à des programmes de vision par ordinateur. Nous montrons ainsi la faisabilité de la fabrication d'une métasurface grande surface, dont les propriétés optiques sont évaluées avec différents outils (facteur de structure, transmittance, transparence macroscopique).

Title : Development of resonant nanostructures large area device for augmented reality Keywords : metasurface, nanofabrication, nanoimprint, plasmonics, structure factor, augmented reality Abstract : Recently, visualisation systems, and in particular augmented reality, have seen increased use in applications such as automotive head-up displays or head-mounted displays such as Google Glass. Due to the cost constraints of industrial applications, technological solutions are needed to improve the efficiency of these devices. In particular, these systems include a large surface blade that must be both transparent in the visible range and reflective at certain wavelengths. It can also perform the function of focusing or defocusing. In this context, wavelength-selective reflective metasurfaces are considered good candidates. This type of device has attracted a lot of attention in recent years due to the unique properties that can be obtained but nevertheless, significant improvements are still needed to make it a viable option. In this work, we address two main areas that we aim to improve.

The first is the fabrication of large area devices. Here we present a process based on nanoimprint based on soft stamps (Soft NIL-UV) to fabricate large areas at low cost. The main improvement is a new technique for the fabrication of PDMS stamps based on the self-assembly of polystyrene nanospheres combined with direct etching of PDMS. The second is the development of tools to study the impact of the order level of the metasurface on the obtained optical effect. In this thesis, we propose to use the structure factor because of its applicability to structures of any order level and its good adaptability to large surfaces when combined with computer vision programs.

Due to the nature of my work, which was mostly focused on nanofabrication, I had the luck of interacting with more people than it is usual in a PhD. This network of researchers, engineers, post-doc and PhD students was fundamental in the completion of my work that went through multiple technical problems and pandemic. As I cannot name them all in this page I would like to start with expressing my gratitude to everyone who will identify themselves in this amazing group of people.

First, I must adress my deepest thanks to my supervisor Prof. Béatrice DAGENS, for always helping me push through the obstacles along the way and finding a solution in the face of any problem. You have made this work a great experience were I felt accompanied while being free to explore my own hypotheses and ideas. I learned a lot of about the field of nanoscience but most importantly about what it is to be a researcher.

Futhermore, this work would not have reached the results presented here without the invaluable experience of my technological tutor Dr. Frédéric Hamouda. I would like to express my great thanks for the time dedicated to my work. Thank you, for listening me to my propositions and being open to try them even when you thought their chances of success were low (and you were usually right). All the experience of this 3 years will most certainly help me in my career ahead. I must also thank the personnel in the cleanroom that helped through all my recipes and processes. I would like to give my apprecition, particularly to Abdelmounaim HAROURI, Christophe DUPUIS and Étienne HERTH. A special and very deep thank you to Xavier LE ROUX who passed away shortly after the end of my PhD, you will be missed by everyone at C2N. Thank you all for the invaluable conversations in front of the machines, in the cleanroom SAS and during coffee breaks.

Thank you aswell to Navy YAM, Frédéric POMMEREAU from III-V Lab and Serge RAVAINE from CRPP whose contribution was fundamental to this work.

A big thank you to all of the CIMPHONIE team, Marius CROUZIER, Kimhong CHAO, Emilien GADOUX and Fei MAO, for listening to me during all the lunches, coffee breaks and other moments when I needed to talk. And a very special thank you to Sevag ABADIAN, you were always there by my side since the first day and even after you finish your own PhD.

On a more personal note I would like to express my gratitude to Maria for all the love and understanding and to my family for the the support through all my life.

Finally, I need to adress a special thank you my aunt, who inspired with her work to follow research and my parents for allways being there for me in the most important and difficults moments of my life. ix Pour cela cette lame doit être à la fois réfléchissante et transparente. À première vue, cela semble paradoxal car ces deux fonctions sont couplées et complémentaires. Si on prend l'exemple des VTH (Vision Tête Haute) des avions de chasse la lame de combinaison a un revêtement qui la rend réfléchissante à 30 %. Étant donné que 70 % de la lumière extérieure traverse le combineur, celuici est essentiellement transmissif et ne constitue pas un obstacle pour que l'utilisateur puisse observer le monde réel et réagir en conséquence. Néanmoins, le fait de n'avoir qu'une réflectivité de 30 % signifie que la majeure partie de la puissance optique de la source lumineuse est perdue et dans certains cas d'utilisation (par exemple luminosité extérieur élevée) la puissance émise doit être très élevée pour que l'utilisateur puisse voir correctement les images virtuelles [1].

Soft UV-NIL gravitationnel

Ce timbre a ensuite été utilisé dans un procédé Soft UV-NIL gravitationnel, c'est-à-dire, où seul le

Caractérisation des métasurfaces

Dispersion de tailles

Ce procédé a été utilisé pour fabriquer des métasurfaces sur deux substrats différents : une sur Si et une sur silice, ce qui démontre l'adaptabilité du procédé à différents matériaux. Pour la métasurface sur Si, nous avons utilisé un total de 10 images MEB. Au total, plus de 49000 NPs ont été mesurées, pour une surface totale de 2300 µm 2 (Figure 6). La taille moyenne des NPs obtenue à partir de la mesure est de 132,4nm avec un maximum à 136nm avec 3,6% des NPs. 50% de toutes les NPs se trouvent dans un intervalle de 16nm, entre 128 et 144nm.

Pour la métasurface sur le substrat en silice, nous avons utilisé un total de 11 images MEB. Plus de 55000 NPs ont été mesurées, pour une surface totale de 2760 µm 2 (Figure 7). xv Ceci est très probablement dû au fait que la silice est non-conductrice et peut se charger positivement pendant la gravure résultant en une augmentation de l'isotropie de ce procédé.

Transmittance

Comme nous avons établi précédemment, l'objectif principal de l'utilisation de structures résonantes plasmoniques est de générer une réflexion sélective en longueur d'onde. Afin de caractériser la sélectivité en longueur d'onde de la metasurface sur silice, nous avons mesuré sa transmittance (Figure 8).

Facteur de structure

La réponse optique en champ lointain de toute structure est liée à deux phénomènes principaux : la diffraction et la diffusion. 9). xvii Si nous calculons le facteur de structure de nos metasurfaces fabriquées, nous obtenons le facteur de structure présenté dans la Figure 10. Nous pouvons conclure que la transparence de la métasurface est suffisante pour notre application. Cette méthode a été utilisée pour caractériser la diffraction et la diffusion des structures fabriquées.

Les résultats obtenus ont été confirmés par l'effet visuel de la métasurface sur silice.

1

Chapter 1 : Here we first give a short overview of the domains of interest before introducing the main objectives and the structure of the thesis.

General introduction

Augmented reality

Definition and history

With the evolution of technology and its blending into our daily lives, augmented reality (AR) is, in a sense, the ultimate step of this merging of the real with the digital.

One of the proposed definitions of AR technology is that of systems that are capable combining virtual and real images (e.g. making a virtual lamp appear on a real table), registering virtual images with the real world (e.g. if the table is moved the lamp will appear in the same place on it) and allow interaction in real-time (e.g. the user can move the lamp) [1].

This sort of technology may seem quite futuristic but since the invention of the first augmented reality device, called "Sword of Damocles" (Figure 1.1), in 1968 by Sutherland and his team, this technology has attracted a lot of attention and has seen very fast improvements in the last few decades to the point of starting to appear in day-to-day applications such as touristic guided tours and car displays.

Display types

In AR devices the blending of real and virtual images can be done in two ways: by video or optically.

The video method consists in filming the real-world scenery, adding the virtual objects to it, and then replaying a live video of the combination of the two.

The optical method is based on a see-through display, so the user can observe the real world directly, while virtual objects are superimposed over reality on the display, as is exemplified on the right, on Figure 1.2, by a Head-Up Display (HUD) in a fighter jet.

The first method allows for a much better blending of real and virtual object. Since the real world is available in a digital format it can be easily edited to make the integration of virtual object more realistic. An example of the use of this technique is touristic applications such as virtual guided tours and videos since they can be easily done with a smartphone. An example of this type of blending is presented in Figure 1.2, on the left.

Despite this, the optical method, shows more potential in many applications that require a better responsive system. This method is simpler to implement and does not have time delay between reality and the video shown to the user, since it does not require real-world video recording and editing. Furthermore, real objects do not suffer from a resolution limitation due to the use of a display.

Within optical methods, we can again distinguish two types of displays.

Emissive displays have their light source integrated directly onto the display through which the observer see the real world. This is the case for µLED and µOLED displays, where very small light emitters are encased in a transparent membrane. This type of devices have great potential but remain very difficult to fabricate.

Reflective displays, have a projector like light source, that emits light to a combiner plate. The plate has the functionality of reflecting the virtual objects to the user while at the same time allowing him to directly observe the real world. Thanks to this simple working principle these devices are easier to fabricate and use for real applications, with commercial devices such the Google glasses (working principle presented in Figure 1.3).

Reflective display combiners

The combiner plates that have specific transmittivity and reflectivity properties are a fundamental element of a reflective display for AR since it will have a strong impact on the efficiency of the device (at first this clearly seems paradoxical as these two functions are opposite).

We can take as an example HUD for fighter jets which was the first widely used AR device (Figure 1.2, right). The combiner plates in these devices have a coating that makes them 30% reflective. Indeed, with 70% of light from the exterior passing through the combiner, it is mostly transmissive and is not an obstacle for the user to observe the real-world and react accordingly (Figure 1.4). However, this means that most of the optical power from the light source is lost.

In consequence, in situations with a lot of sunlight the power emitted must be very high (30,000 Cd/m2) for the user to be able to properly see the virtual images [2]. A solution to this problem is to have more selective wavelength reflection. If the reflection of the combiner plate at the wavelength of the light source is, for example, 60%, while staying mostly transmissive for the rest of the visible spectrum, the user will still have a view of the exterior and the power output of the light source will be halved.

One of the solutions proposed to obtain this type of selective reflection are multilayer filters.

These multilayer stacks that alternate between high-index and low-index dielectric materials work as interference filters, reflecting a very narrow band set of wavelengths [3].

The disadvantage of this solution is that, to have a good filter, many tens of layers can be required, and the composition of each stack must be very well controlled, implying the use of technologically advanced techniques which make their fabrication expensive.

To maintain fabrication costs acceptable for industrial scale low-cost methods for wavelength selective reflectance need to be developed. The first scientific description of SPPs happened in 1902 when R. W. Wood [4] noticed a surprising phenomenon while studying the spectra obtained using an optical grating of a continuous light source. He found that the presence of specific narrow bright and dark bands was dependent on the polarization of light, but R. Wood did not have any explanation for this phenomenon. So, for a few decades, the study of plasmonics was the study of grating anomalies. Following this first description of the plasmonic effect a lot of contributions were made with a unified theory coming about at the end of the 60's.

As for LSPs, the phenomena of interest in this work, its history dates back over two-thousand years.

It's first known use was indeed optical, as roman glass makers used it to color glass cups [5].

Tiny gold nanoparticles (NPs) were mixed with the glass giving it a bright red color when looking at it in transmission and green when looking at it in reflection. Unknowingly these artisans were using the resonance of the metallic particles at wavelengths corresponding to red in the visible spectrum to give the glass this particular property. A famous example of this is the Lycurgus cup which is depicted in Figure 1.5 which can be found in the British museum.

The theoretical description for this phenomena only came much later based on the work of Mie in 1908 [6].

We know today that this phenomenon is related to the resonant oscillation of surface charge density at the interface between the particle and the dielectric. This oscillation can be induced by the incident electromagnetic field applied by light.

Applications

It was only almost a century after Mie's theorical model that the scientific community started to look into applications for this phenomena, with the publication of Ebbesen et al. in 1998 [8]. In his publication Ebbesen was able to demonstrate that, for certain resonant wavelengths, the total power transmitted by a metallic nanohole arrays was superior to the incident power, when normalized for the nanoholes size. The SPPs modes excited on the grating were leading to a concentration of the electromagnetic field at the top of the aperture that made up the structure. The modes were then guided through the holes and reemitted on the other side resulting in enhanced transmittance for the selected wavelength.

This capacity of plasmonics to concentrate light into very small volumes, providing very strong field enhancement, is one of the main reasons of interest for this phenomenon. Many applications that make use of this have been developed such photoemission [9], energy transfer [10], vibrational spectroscopy [11], molecular fluorescence [12], polarizers [13],

nanoscale microscopy [14] and color generation [15,16].

In previous work from our team, a structure using plasmonic NPs has been proposed to achieve high reflectance for selected wavelengths on a transparent substrate [17].

The NPs were design to support LSP resonance at a specific wavelength in the visible spectrum making them reflect more optical power. The off-resonance wavelengths do not interact with the NPs and are transmitted resulting in wavelength selective reflectance, the exact characteristics required to improve the performance of reflective combiner plates for AR displays.

Metamaterials and metasurfaces

Overview

For a long time, the development of new devices was limited by the materials that scientist and engineers had available. Meaning the properties achievable were controlled by the atomic and molecular level structuring of the material.

By structuring materials with subwavelength elements called meta-atoms and controlling their composition, size, shape, and periodicity, enabled the possibility of tuning the optical contribution of each of the constituting elements. These structure materials are what we call metamaterials.

This increased control of the material properties has allowed for the fabrication of metamaterials that go beyond what is possible with natural materials. Indeed these structures have allowed the development of negative refraction index materials [18,19] and near-zero-index materials [20,21] which are not possible with natural materials.

The start of this field is difficult to define but the first use of the term metamaterial was in 2000 by Smith and his team [22]. Nevertheless this field was in development long before, with the first metamaterial, by the modern definition, being made by Bose in 1898 [23].

In fact, metamaterials and their 2D version, metasurfaces, came from a steady improvement of our knowledge of light matter interaction starting with the invention of antennas for the manipulation of electromagnetic signals in the radio frequencies. These were then scaled down to reach shorter wavelengths and eventually used in arrays to improve performance.

The development of nanofabrication fueled by the semi-conductor industry made it possible to reach nanometric scale structured devices and so the first metamaterials (for visible range applications) as we know today could be fabricated.

Due to the complexity of fabrication of 3D metamaterials, metasurfaces, which are much easier to make, have attracted a lot of attention from the scientific community making this field one of the most active today. Many applications that make use of these unique properties of this devices have been demonstrated from holography [24], to polarizers [25] or even metalenses [26]. The difference between transparent and translucent objects is that, in the former incident waves are all deviated at the same angle or not at all, which allows our eye to reform the image behind the object. Translucent objects will deviate incident wave in different directions due to non-periodic variation in the optical index of the surface. Light can still travel through the surface but the information about the image behind it is lost. This optical phenomenon of deviating light at multiple angles is known in optics as diffusion, for this reason we refer to object presenting this property as diffusive.

Overall, a transparent object becomes diffusive due to a random structuring of its surface which deviates incident waves in multiple directions. When we fabricate metasurfaces on transparent substrates, by controlling structure of the meta-atoms, we can control the rate of diffusion and, in consequence, the transparency.

Generally, periodic structures will be transparent and disordered structure will be diffusive.

Since AR devices require transparency, periodic structures are the preferential candidate, but this periodicity can create diffraction, meaning, very strong emission of specific wavelengths at specific angles. The consequence of this optical effect is that if the angle of observation of the user matches an angle of diffraction, the user may be "blinded" by this strong emission effectively deteriorating its capacity to see objects behind the display.

The structure proposed by our team [17], solved this problem by using correlated disorder structures, which is a sub-type of hyperuniform structures (structures with no density fluctuations at very long ranges) [27,28]. This type of structures is characterized by having long-range order but short-range disorder. The result is that diffraction will be strongly suppressed due to the short-range disorder without giving rise to diffusion thanks to the longrange order.

Another way to get around this problem is to use sub-wavelength periodic structures so that diffraction occurs at wavelengths shorter than the visible regime as we shall discuss in more detail throughout this thesis.

Thesis objectives

To summarize, the use of AR has become more and more prevalent, but technological improvements are required to make them efficient and usable regardless of the environment conditions. In the case of reflective display this means improving the reflectance without deteriorating the transparency of the combiner plate.

The best way to obtain both characteristics is to use wavelength selective reflective structures. Plasmonic metasurfaces are a good candidate for this type of devices.

Plasmonic NPs can present strong resonances in the visible regime which allow for wavelength selection. By assembling them in metasurface on a transparent substrate we can obtain a wavelength selective reflection.

The structuring of the metasurface, meaning, the position of plasmonic NPs, will determine the properties of diffusion and diffraction of our device, and in consequence, its transparency.

Correlated disorder and subwavelength structures are two examples of structures that can be used to suppress both diffusion and diffraction to ensure the display is transparent.

Within this context the aim of this work is to develop essential techniques in two important areas for the development of this type of technologies.

The first is a low-cost fabrication process for large area plasmonic metasurfaces for wavelength selective reflective displays for AR. Demonstrations of concept have been done

and show the potential of this technology [17,29,30], but the main limitation is its fabrication at acceptable cost due to the use of expensive nanofabrication techniques.

The second is a tool for analyzing the optical phenomena of diffusion and diffraction of metasurfaces. We know that periodic structures are diffractive and disordered structures are diffusive but cases in between such as correlated disordered structures are harder to analyze and there are currently no tools that can be applied to all types of metasurfaces regardless of their level of order.

Structure of the thesis

This thesis is divided into seven chapters:

Chapter 1 has given us an overview of the subject and the technological objectives along with some historical context. We discussed the main requirements for a working device and the optical phenomena that can be exploited to achieve them. We also presented the main objectives of the work presented in this thesis.

Chapter 2 covers the state of the art on two different subjects: processes that can be used for the fabrication of large area metasurfaces at a low cost and plasmonic metasurfaces with potential use for transparent displays. We conclude the chapter with the objectives for this work considering the state of the art.

Chapter 3 presents the tools developed and used to characterize the optical properties of the fabricated structure. In this work we present the structure factor (and a program for its calculation), a tool that we can use to analyze diffusion and diffraction as well as the level of order of any type of ensemble of particles. Other tools required for the numerical analysis of fabricated structures are also presented (particle position identification and size measurement). We also detail our program for the generation of correlated disorder structures.

At the end of the chapter, we present the two optical benches used for sample characterization: an Optical Fourier Transform bench, used to experimentally validate the structure factor, and an Angulo-spectral bench used to characterize the transmittance of fabricated metasurfaces.

Chapter 4 details a novel fabrication technique, based on Polydimethylsiloxane (PDMS)

etching with a Polystyrene (PS) Nanosphere (NS) mask, for stamps to be used in Soft UV Nanoimprint Lithography (NIL) nanofabrication processes. We analyze different parameters that affect different steps of the fabrication process. We show the parameters that work best for our fabrication process and propose improvements to this novel technique.

Chapter 5 covers the fabrication of large area plasmonic metasurfaces by Soft UV-NIL using PDMS stamps fabricated with the technique detailed in the previous chapter. This process is presented using the same stamp for the fabrication of metasurface on Si and fused silica

substrates. An analysis of the size dispersion of the NPs that constitute the metasurfaces is presented for both substrates, followed by improvement propositions.

Chapter 6 presents the characterization of the metasurfaces fabricated using the tools presented in chapter 3. The structure factor is experimentally validated using Optical Fourier Transform (OFT) figures. The diffusion and diffraction of the structures fabricated are analyzed by means of the structure factor. We then present a method for controlling the NP density of structures and study its impact on optical properties.

We end the chapter with an optical characterization in transmittance of the metasurface fabricated on silica and its use in a HUD system is validated.

Chapter 7 provides a conclusion to the work presented in this thesis as well as a discussion on future work that should be done to improve the tools developed.

Chapter 2 : In terms of the organization of metallic nanostructures two main approaches can be found: random deposition of colloidal plasmonic NPs onto a substrate [1,2] or NP fabrication by means of a patterned mask using a lithographic techniques [3,4].

State of the art

The first method does not allow for the control of the organization and will mostly result in a disordered structure. The second method allows for a very good control of the structure but usually relies on expensive nanofabrication processes, such as electron-beam lithography, for nanometric scale structures, which is not scalable for large area devices nor industrial scale fabrication.

In consequence, methods compatible with large area fabrication that maintain the control of the organization of nanometric structures are required.

One method that has been developed for large area fabrication is Nanosphere Lithography (NSL). This technique was first proposed in 1995 by Hulteen & Van Duyne [5], and used selfassembled Polystyrene (PS) Nanospheres (NS) as a mask for a metallic deposition. From inception, NSL was able to produce structures with sub-100 nm dimensions over-large areas.

Another good candidate is Nanoimprint lithography (NIL). This process was first proposed by Chou et al. in 1995 [6]. The method consisted of using a hard mold to imprint onto a thermoplastic material which was heated up. In 1996 J. Haisma [7] proposed a method using a UV-curable polymer instead of a thermoplastic material solving the problems caused by the thermal expansion and contraction of the materials. This first version of NIL with a hard mold has good performances as works have shown that this technique can reach the sub-10nm range [8,9]. The main drawback of this technique is that it requires flat and low rugosity substrates due to the hard mold.

In order to improve the mold's conformity to rough or even curved surfaces a process was developed by Xia & Whitesides [10] where the hard mold was replaced by a polymer based soft mold (to avoid ambiguity we shall refer to it as "stamp"). This technique is capable of fabricating subwavelength structures with a high throughput, good scalability for industrial process and has an adaptive nature.

In this global context, we will try to position the present work with respect to different technological approaches enabling large area metasurfaces fabrication. For this purpose, we present the state of the art regarding: self-assembled PS NSs used as a lithographic technique, polydimethylsiloxane (PDMS) structuration (which could be useful for soft UV-NIL), soft-UV NIL using nanostructured PDMS, plasmonic metasurface fabrication, and finally designs of plasmonic metasurfaces for transparent displays.

Self-assembly of PS NSs and size reduction

As discussed in the introduction of this chapter, self-assembled PS NSs as a lithographic technique was first used in 1995 by Hulteen & Van Duyne [5]. In their work, 264 nm PS NSs were spin coated on various substrates, forming monolayers and bilayers that were then used as masks for a metallic deposition, obtaining triangular or circular shaped NPs. This method showed promising results by reaching 32 nm dimensions. Nevertheless, it has the disadvantage of both the distance between particles and particle size being determined by PS NSs diameter and a limited amount of NP shapes being possible to fabricate. This lack of flexibility makes it only useful for a few specific types of structures.

Haginoya et al. [11] proposed a different approach. In this publication, a monolayer of 200 nm PS NSs was fabricated by dropping colloidal solution onto an angled hydrophilic Si wafer.

The NSs were then reduced by an O2 RIE plasma, followed by a metallic deposition and a liftoff of the NSs resulting in a metallic mask which was used to perform an etching of Si substrate. With this method the inter-NP distance is controlled by the PS NSs size and the diameter of the structure components (in this case nanoholes, Figure 2.1.1) is controlled by the reduction of the NSs allowing for more control of the structure obtained. Improvements have been proposed to reach smaller dimensions with this technique such as the use of lowfrequency plasma, to reduce the damaging of the NSs during etching [12] and highly isotropic plasma etching to maintain the particle shape [13]. Notably, this second technique was able to reduce 100 nm particles down to 25 nm (Figure 2.1.2).

Other methods have been proposed to fabricate non-hexagonal, non-compact structures without doing particle reduction. Piechulla et al. [14] proposed to deposit negatively charged polymethylmethacrylate (PMMA) NSs onto a positively charged substrate. Due to the negative charge on the surface of the NSs these formed a non-compact correlated disorder structure.

The deposition method for compact structures, has been subject of a lot of variations, with the objective of depositing structure with larger areas on a multitude of substrates.

A promising method to fabricate large area hexagonal structures on substrates with different shapes and sizes was proposed by Born et al. [15] in 2011. This method was then combined with NS reduction by Bauer et al. [16]. In this method the colloidal solution is placed between the substrate and a glass slide which are placed close and parallel to each other with the solution being kept in place by capillary forces. By moving the glass, the PS particles are deposited on to the substrate forming hexagonal monolayer. This method uses the same physical mechanism for the deposition as dip coating, but the substrates size and shape are not limited by the solution container size and shape and requires much lower amount of colloidal solution. Nevertheless, this approach requires substrates that are particularly hydrophilic, limiting the materials that can be used.

To solve this limitation Weekes et al. [17] proposed a technique where the monolayer were formed at the surface of water and is then lowered onto the substrate. In this method, the colloidal solution is introduced onto the surface of the water by a glass slide placed at 45°, where it forms a monolayer. The water solution is then emptied out from the bottom lowering the self-assembled structure onto a substrate that was previously placed inside the solution We should note that even though these methods permitted the use of materials with lower levels of hydrophilicity, they are not compatible with highly hydrophobic materials.

As far as self-assembled PS NS structures on Polydimethylsiloxane (PDMS) are concerned this technique has not been widely used due to PDMS being characteristically hydrophobic. In Table 2.1 we present some instances found of deposition of self-assembled PS NS structures on PDMS, without any further process on the NSs [19][20][21]. No one mentions size reduction of the PS NS after deposition.

Reduction not performed

Reduction not performed

Self-assembled PS NSs structure as an etch mask

In the publication by Haginoya et al. [11], the PS NS structure was used as a mask for a metallic deposition. The particles were then lifted off resulting in a patterned metallic mask for etching. This technique can reach small dimensions [13], but from experience (see annex 1)

we know that the lift-off step can be a major obstacle for dimensions in the 100 nm range.

An adaptation of this technique has been proposed, where the PS NSs are used directly as a mask of wet [22] or, more commonly, dry etching [23][24][25][26].

In Table 2.2 we present the state of the art for structures fabricated using a PS NSs selfassembled structures as an etch mask.

PDMS etching

PDMS has become a very used material in different areas such as microfluidics and nanofabrication due to, among other properties, its biocompatibility, elasticity, and transparency at visible wavelength.

This wide use of the PDMS has pushed the development of means to structure it to fabricate devices, with a lot of attention being given to it in microfluidic applications [27][28][29][30].

The most standard technique for fabrication of these devices is molding [27] of liquid PDMS into a master. One of the limitations of this technique is it is not possible to create via holes in the PDMS during the molding. PDMS can be pierced mechanically but with limited resolutions [28,[START_REF] Chen | Photolithographic surface micromachining of polydimethylsiloxane (PDMS)[END_REF]. This, coupled with the motivation to use PDMS with standard micro and nanofabrication processes, pushed the development of PDMS structuring by dry etching, on its own or coupled with wet etching to increase etch rates [START_REF] Balakrisnan | Patterning PDMS using a combination of wet and dry etching[END_REF].

In Table 2.3 we present the state of the art for PDMS dry etching. All the mask structures were fabricated by photolithography. The metal masks were obtained by wet etching with a resist mask [28,[START_REF] Hwang | Dry etching of polydimethylsiloxane using microwave plasma[END_REF] or electroforming of the metallic layer [START_REF] Balakrisnan | Patterning PDMS using a combination of wet and dry etching[END_REF] after the lithographic step. We can see that sub-micrometric dimensions have not been reached since the application is microfluidics which does not require smaller dimensions.

Electron beam lithography on PDMS has been explored, by using the PDMS itself as a resist [START_REF] Constantoudis | Roughness characterization in positive and negative resists[END_REF][START_REF] Bowen | Direct e-beam lithography of PDMS[END_REF][START_REF] Szilasi | Selective etching of PDMS: Etching as a negative tone resist[END_REF]. The structures obtained stayed in the micrometer range.

Patterning of a resist on PDMS in the 100 nm range has been demonstrated by using laser interference lithography [START_REF] Wu | The fabrication of nanostructures on polydimethylsiloxane by laser interference lithography[END_REF], but the structure was not transferred to the PDMS substrate. [33] using a metallic mask for dry etching. 3) Hexagonal array of 6 µm diameter holes in PDMS etched using optical resist as mask by Hill et al. [30].

Soft UV-NIL using PDMS stamp

PDMS stamp for sub-micrometric structure fabrication

With PDMS becoming one of the preferred polymers for Soft UV-NIL stamps a lot of research has been done to structure its surface with smaller and smaller dimensions.

Even though dimensions as low as 2nm have been demonstrated [9], the height obtained in stamps with such dimensions is not sufficient to obtain a good pattern transfer (Figure 2.4.1).

Since the height of the pattern for stamps obtained with classical molding techniques is limited by the viscosity of the PDMS, a lot of work has been done with the idea of lowering the PDMS viscosity. One approach is diluting it in solvents [START_REF] Koo | Improved mold fabrication for the definition of high quality nanopatterns by Soft UV-Nanoimprint lithography using diluted PDMS material[END_REF][START_REF] Zhou | Replication of mold for UV-nanoimprint lithography using AAO membrane[END_REF] which allows for sub-100 nm resolutions (Figure 2.4.4). On the other hand, the dilution in solvents changes the properties of the PDMS after reticulation and makes it more fragile. For this reason, this option is unreliable for large scale fabrication processes.

Another approach is to treat the master mold with solvent to improve the wetting of the mold surface by the PDMS [START_REF] Con | Effect of mold treatment by solvent on PDMS molding into nanoholes[END_REF]. This technique proved successful at reducing the dimensions that the PDMS could fill but it was unable to go beyond 150 nm.

In 2000 Schmid and Michel [START_REF] Schmid | Siloxane polymers for high-resolution, high-accuracy soft lithography[END_REF] developed an alternative to the classical PDMS called Hard-PDMS. This polymer presents much lower viscosity before reticulation, meaning it can fill holes in the master with smaller dimensions. In 2010, Cattoni et al. [START_REF] Cattoni | Soft UV-NIL at 20 nm scale using flexible bi-layer stamp casted on HSQ master mold[END_REF] demonstrated that this polymer can reach 20 nm dimensions by molding it in a master fabricated by electron beam lithography (Figure 2.4.2).

Hard-PDMS presents a higher Young modulus after reticulation. This can be an advantage, since it will suffer less deformations during the imprint process, but it also makes it more brittle and, in consequence, more subject to breaking during fabrication.

One way that has been proposed to improve upon the fragility of this material is to use a back plate of a material with higher elasticity such as standard PDMS [START_REF] Schmid | Siloxane polymers for high-resolution, high-accuracy soft lithography[END_REF][START_REF] Cattoni | Soft UV-NIL at 20 nm scale using flexible bi-layer stamp casted on HSQ master mold[END_REF][START_REF] Plachetka | Comparison of multilayer stamp concepts in UV-NIL[END_REF][START_REF] Hauser | Soft thermal nanoimprint of PMMA doped with upconverter nanoparticles[END_REF][START_REF] Yoon | Single-step manufacturing of hierarchical dielectric metalens in the visible[END_REF].

Nevertheless, other methods have shown that it is possible to obtain smaller dimensions without reducing the viscosity of PDMS. Koo et al. [START_REF] Koo | The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography[END_REF] fabricated standard PDMS stamps with sub-100 nm dimensions by using pressure-assisted molding (Figure 2.4.3). As the name indicates, this process applies pressure on the polymer during molding to enhance the filling of the master. Yet, this technique increases the complexity of the stamp fabrication process and applying pressure on the polymer during molding will inevitably increase the risk of breaking the master making the overall cost of fabrication higher.

In Table 2.4 we present the state of the art for PDMS stamp fabrication. The dimensions presented are the ones transferred to a resist layer unless specified otherwise. [START_REF] Cattoni | Soft UV-NIL at 20 nm scale using flexible bi-layer stamp casted on HSQ master mold[END_REF], onto AMONIL resist for NSs with 20 nm diameter and 60nm pitch. 3) (left) Pressure-assisted molding method developed by Koo et al. [START_REF] Koo | The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography[END_REF] and (right) PDMS stamp fabricated with this method. 4) PDMS stamps fabricated by Koo et al. [START_REF] Koo | Improved mold fabrication for the definition of high quality nanopatterns by Soft UV-Nanoimprint lithography using diluted PDMS material[END_REF] for different percentages of PDMS dilution in toluene.

the process to a transfer into a resist means that, in the case of metasurface fabrication, the composing NPs will be made up of the resist substance. Indeed, Cattoni et al. [START_REF] Cattoni | Soft UV-NIL at 20 nm scale using flexible bi-layer stamp casted on HSQ master mold[END_REF] fabricated a metasurface with AMONIL NPs with 20 nm in dimension and 60 nm in pitch and Lim et al.

[47] proposed a similar approach to obtain TiO2 metasurface. In this work the pattern transfer was made onto a TiO2 resin, which after heat-treatment, transforms into amorphous TiO2.

With this method a TiO2 metasurface was fabricated with 80 nm NPs and 500 nm pitch.

For the case of plasmonic metasurfaces, metallic NPs are required, and, to the best of our knowledge, no metallic based resist exist with potential for industrial scale application. For this reason, metallic metasurfaces require more fabrication steps, such as resist etching, metallic deposition and lift-off which impose further limitations on the dimensions that can be obtained.

The best dimensions reported were obtained by Kontio et al. [START_REF] Kontio | Nanoimprint fabrication of gold nanocones with ~10 nm tips for enhanced optical interactions[END_REF], which fabricated nanocones with 130 nm base diameter and a periodicity of 300 nm using a PDMS stamp.

In the case of structure composed of flat NPs, larger dimensions have been reported. In 2010, were able to reach 200 nm dimensions using standard PDMS and Hard-PDMS respectively.

In Figure 2.5 we present images of those metasurfaces and in Table 2.5 a summary of the works discussed.

Plasmonic metasurfaces for transparent displays

To have a working transparent display, two conditions need to be fulfilled: strong reemission of a specific wavelength and transparency for visible wavelength. It is important to note that when talking about transparency we are considering not only the transmittance but also the fact that the structure is not diffusive nor diffractive for the visible wavelengths. Indeed, any one of these optical effects can block the user from properly seeing objects behind the device.

For reemission of a selected wavelength two phenomena can be used: reflection and diffusive scattering.

In the case of reflection, light is remitted at the complementary angle of the angle of incidence. This emission is very directional since most of the optical power is concentrated in a specific direction. Here, the combiner plate acts as a transparent mirror for the light source, meaning the image will be formed at a distance behind the plate corresponding to the distance between the plate and the light source (Figure 2.7.3).

In the case of diffusive scattering, light is reemitted across multiple angles. This means the emission will not be directional since the optical power will be spread over multiple directions.

The main difference compared with the reflective case is that the image needs to be formed in the plane of the plate, so there will be no notion of depth (Figure 2.7.1-2).

An example of a diffusive display is the one developed by Hsu et al. [1], which used chemically synthesized 60nm silica-core Ag-shell NPs, randomly distributed, to fabricate a display which was highly diffusive at 458nm and transparent for most of the visible spectrum (i.e. at higher wavelengths).

Saito et al. [2] fabricated a transparent display based on the same optical effect. In this work

Ag nanocubes, also chemically synthesized, were deposited on a TiO2 thin layer resulting in a peak of diffusive backscattering of 15% at around 400nm and approximately 5% for the rest of the visible spectrum. This scattering for multiple wavelengths allowed for poly-chromatic images to be formed on the plate, as is shown in Figure 2.7.2.

In the case of non-subwavelength structures, these must be ordered to not become diffusive which will deteriorate the transparency of the device. In this situation diffraction also needs to be considered.

This highly directional emission of light at a specific angle related to the periodicity of the structure can deteriorate the overall properties of the device since the user will see unwanted optical effect at specific angles of observation. This was solved by Bertin et al. [3] by using correlated disordered structures. These structures are disordered in a short-range scale but ordered on long-range scale. The consequence of this mixed type of order is a strong attenuation of the diffraction without the appearance of diffusion.

Arslan et al. [4] used a similar type of structure to obtain selective diffusive scattering at infra-red wavelengths. In this work they used a perturbed array, a square lattice structure to which some low level of disorder is added, composed of Ag disk with 470 nm in diameter and 800 nm inter-NP distance, fabricated by e-beam lithography. This low-level disorder coupled with the resonance of the plasmonic NPs resulted in a selective diffusive scattering at the wavelength of resonance.

Another important property of combiner plates in transparent displays is the balance between the amount of remitted light at the selected wavelength and the overall transparency of the display.

Very few papers mention this problematic since works are more focused on color printing [START_REF] Kumar | Printing colour at the optical diffraction limit[END_REF][START_REF] Tan | Plasmonic Color Palettes for Photorealistic Printing with Aluminum Nanostructures[END_REF][START_REF] Roberts | Subwavelength plasmonic color printing protected for ambient use[END_REF], where only reflection is studied, or color filtering [START_REF] Ellenbogen | Chromatic Plasmonic Polarizers for Active Visible Color Filtering and Polarimetry[END_REF][START_REF] Yoon | Color filter based on a subwavelength silicon grating[END_REF][START_REF] Yokogawa | Plasmonic color filters for CMOS image sensor applications[END_REF], which will be focused on transmission.

Transparent reflective plates for augmented reality were studied notably by Bertin et al. [3] and the balance between the two parameters in function of the particle density is presented in Figure 2.6. The compromise proposed in this work was an average transmittance (for the visible spectrum, 400-800nm) of 60%, which resulted in a reflectance of over 70% at the resonant wavelength (590nm) for a NP density of 16 NP/µm 2 . The structure was composed of 111nm by 98nm Ag disk obtained by e-beam lithography.

By looking at Table 2.6 we can see that most devices proposed presented values close to this reference of 60%. In Table 2.6 we present the state of the art of plasmonic metasurfaces for transparent displays using diffuse scattering or reflection. Both the maximum emission at the selected wavelength and the average transmission are presented. Some publications did not report the average transmission, so this value was estimated from the plots of transmittance for visible wavelengths. Objectives with respect to the state of the art Nanoimprint processes, and especially soft-UV NIL, appear as the most relevant solutions for large area fabrication, thanks to the possibility of replication of a pattern. Nevertheless, the main obstacle in this method is the nanostructured stamp fabrication so that it remains compatible with further technological steps (such as metal lift-off): no realistic solution is available for ~100 nm plasmonic nanostructures on several cm².

Besides, in order to nanostructure large surface stamps (to limit the replication numbers), NS self-assembly seems to be a good solution to generate the initial pattern.

Nevertheless, the pattern obtained with NS self-assembly is inherently ordered and in consequence, the final structure will be non-diffusive but highly diffractive. To avoid this diffraction, we decided to use subwavelength structure by self-assembling 200nm PS NSs. We can see in

Bibliography

Chapter 3 :

Fundamental concepts and numerical tools Furthermore, with the use of metasurfaces with large areas, studying them based on a handful of NPs will give us less reliable results making the development of tools based on statistical analysis for a large amount of data necessary. This is the principal aim of most of the tools, experimental and numerical, that we present in this section.

At the end of the chapter, we also present an angular-spectral bench used for measuring the optical characteristics in transmission of the fabricated metasurfaces.

Structure factor

The far field optical response of any optical structure is related to two main phenomena: diffraction and diffusion of light.

Diffraction comes from a periodic repetition of elements, and it can be predicted from the spatial periodicity orientation and distance of the repeating elements. Diffusion appears when the structure is disordered, meaning that the distance between the elements of a structure is not homogeneous.

But in intermediary cases it is less clear what the optical behavior of the structure will be. That is the case, for example, with correlated disordered structures. These present homogeneous particle spacing but do not have a specific orientation for pattern repetition. For these types of structures, the structure factor can be used to quantify the level of disorder and predict the optical behavior.

This mathematical tool is very used in crystallography, to study the structure of matter, since it gives its scattered intensity: it can also be obtained by measuring the scattering pattern of light (usually X-Ray) or electrons [5].

The structure factor in two dimensions is mathematically defined as:

𝑆 𝑞 , 𝑞 = 1 𝑁 × 𝑒 . . , (3.1)
where 𝑁 is the number of elements that compose the structure, 𝑑 and 𝑑 are the x and y components of the distance between particles, 𝑞 and 𝑞 are the x and y components of the scattering vector 𝑞 which is defined as:

𝑞 = 𝑘 -𝑘 = 4𝜋 𝜆 sin 𝜃 2 (3.2)
Here, λ is the wavelength of incident light and θ is the angle between 𝑘 , the incident wavevector, and 𝑘 , the diffracted wavevector (Figure 3.1).

In 2D, the structure factor depends on the two spatial components of 𝑞 (equ. When looking at the structure factor, diffraction will be represented by a significant increase for a small interval of the scattering vector (indicating an ordered structures) while diffusion will be represented by a small increase for a large interval of the scattering vector. For example, the structure factor of perfectly ordered structure would be a Dirac function while a perfectly diffusive structure would be equal to 1 for all values of the scattering vector since it emits equally at all angles.

Indeed, an Optical Fourier Transform (OFT) gives the projection of the far-field scattering figure, for a beam at normal incidence, onto the focal plane of a lens. This effectively gives us the spatial frequency representation of the structure, as a function of the diffraction wavevector 𝑘 .

The structure factor is a numerical method to obtain the scattering figure of the structure, resulting as well in a spatial frequency representation of it, as a function of the scattering vector 𝑞.

In other words, the OFT is a specific case of the structure factor where the incident wavevector is set and only the diffracted wavevector changes.

Numerical generation of correlated disordered structures

As we saw in chapter 2 there are two main ways to avoid undesired optical effects: using subwavelength structures or correlated disorder structures, which are a sub-type of hyperuniform structures (structures with no density fluctuations at very long ranges) [6,7].

Even though some work has been done on how to fabricate correlated disorder structures experimentally [1], they can also be generated numerically. The structures generated can then be used as mask for standard lithographic processes (such e-beam or photolithography)

to obtain correlated disorder metasurfaces.

The program presented in this section was previously used to generate correlated disorder structures, in our team, by H. Bertin. In this work we focused on improving the program (i.e.

possibility of using periodic boundaries) and using the structure factor, presented in the previous section, to study the influence of multiple parameters in the final structure obtained.

Main principle

As mentioned in section 3.2, correlated disorder structures are characterized by having homogenous distances between particles over the whole structure without preferential orientation of alignment between particles.

The program used to generate these structure uses the following algorithm:

1. Generate a mesh with the dimensions set by the user.

2. Generate N number of particles with completely random coordinates placed over the mesh. The initial state of our structure is fully disordered.

3. Do Voronoi tessellation for the whole structure. This means that it defines regions which consist of all the points of the mesh that are the closest to a specific particle (these regions are called Voronoi cells).

4. Once all the regions are defined, all the particles are moved to the centroid of its corresponding region (Voronoi cell).

5. Repeat steps 3 and 4 the required amount of times

Parameter influence

There are 3 main parameters that influence the result that we will obtain:



Numbers of particles

To verify the influence of the number of particles on the order level of the obtained structure we generate multiple structures with 10000 mesh points per particle with a total of 100 iterations and different number of particles. It should be noted that since the number of mesh points is defined per particle, the precision of the mesh does not decrease with the increasing number of particles. In Figure 3.5 we have the structure factor structures with: 100 particles, 200 particles, 500 particles and 1000 particles. As we can see the number of particles does not significantly impact the final structure factor obtained, for a given mesh per particle.

Numbers of iterations

To see the impact of the number of iterations on the structure obtained, we calculate the structure factor of a structure generated with 1000 particles and 10k mesh points per particle, at different amounts of iterations during its generation (Figure 3.6).

As expected, the more iterations are performed the higher the level of order is reached. The first few iterations create some order, represented by the formation of a circle of lower intensity at the center of the structure factor: large first neighbor-distances have been mostly

eliminated. With more iterations we see the formation of a ring corresponding to the average first-neighbor distance. With even more iterations we reach a level of order that creates a second ring corresponding to the distance to second neighbor particles.

It is important to note that the maximum level of order is limited by the amount of mesh points per particle. Structures generated with few mesh points will require fewer iterations before reaching their maximum level of order. If the structure is generated with a higher amount of mesh points more iterations will be required.

Even if the amount of mesh points is low, we still gain some order per iteration, but this gain will gradually decrease making the program less efficient.

Number of mesh points

To verify the influence of the number of mesh points per particle we generate multiple structures with 1000 particles and different numbers of mesh points. We also analyze the structures at different amounts of iterations. In Figure 3.7 the structures calculated with different amounts of mesh points have similar structure factors after their first 10 iterations, meaning a similar level of order. But after 100 iterations, the structures generated with a higher amount of mesh points present thinner and higher peaks: they are more ordered.

Since the function of the mesh points in this algorithm is to calculate the centroid of each Voronoi cell, the more points in the mesh the more accurate the centroid will be. For this reason, the maximum order a structure can reach is directly related to the amount of mesh points.

Since the structure starts off as a fully disordered arrangement, during the first few iterations the increased precision for calculation of the centroid of Voronoi cell does not have a great impact. But as the structure becomes more and more ordered the structure generated with less mesh points starts reaching a "saturation" level in terms of order and the increase per iteration becomes lesser while structures generated with more mesh points will continue to see their order increase at a higher rate.

Recommended parameters

Following this evaluation, we have chosen the following parameters for the correlated disordered structures generation:

 100 iterations  5 000 mesh points per particle

Peak maximum difference

The structure generated with these parameters presented good levels of order without requiring a lot of computing time.

The total number of particles was adapted to the size and density of the area we wanted to generate.

For small structures (< 500 particles) where the calculation time was not a limiting factor or for structures where we wanted high levels of order, we used 10 000 mesh points per particles and 200 iterations.

Computer vision for fabricated structures analysis  the program receives an image as an input and applies a blur to the image to improve edge detection.

 The image is then binarized (Figure 3.8, left). For each pixel the program calculates the average contrast level of all pixels within a window of a selected size centered on the pixel of reference. If the contrast level of the pixel is higher than this average, the pixel becomes white, if not the pixel become black. This highlights the particles in white and the background in black (Figure 3.8, middle).

 The program then identifies all contiguous areas composed of white pixels and removes areas which are either above or below user specified size thresholds. This is done to remove background noise and very big shapes which can correspond to particle aggregates, objects which are not particles or artifacts due to the image contrast in specific areas (for example due to charging of an area of the structure during SEM observation) (Figure 3.8, middle).

 Lastly the program calculates the geometrical center of each of the areas which are saved onto a file which can be used for structure factor calculation. To know with a good level of confidence the size of the NPs which compose a structure with a large area we cannot rely on measurements of a hand-full of NPs.

When talking about structures with periodicities of 200nm we have NP densities of more than 2 billion per cm 2 . Measurements of a few NPs are not sufficient to properly characterize the structure, thus we require a statistical analysis of its size distribution.

To be able to do this sort of analysis we improved upon the previous program to be able to measure the diameter of thousands of NPs over many images.

The application of a blur and binarization remains unchanged. Following this step, a clean-up of the objects is done to remove defects that could modify the measurement (this is detailed in the next section). Lastly, the diameter is calculated based on the area of each of the shapes.

The diameter is that of a disk with the same area as the shape (Figure 3.9).

Binarized image clean-up

The first step of the image clean-up procedure consists of removing very small objects which correspond to background noise.

Then the program fills the small holes in closed contiguous areas of white pixels (Figure 3.10). This step is important since the edge of the NPs is often brighter than the interior meaning the edge of the NPs becomes white after the binarization, but not the interior.

Following this, very big shapes are removed. This is done to remove patches of fused NPs. Binarized image « Filled » image as white.

 On the right, the apparently hollow NPs are caused by NPs with low contrast levels at the center that extend to the edge. This results in the NPs looking like opened arcs that the program did not fill, since it did not see them as closed area.

These artifacts cannot be solved by simply adjusting the contrasts level of the images as, for example, an increase in contrast would reduce the hollow NPs but increase the fusion of NPs (and vice-versa). Increasing the minimum size and decreasing the maximum size of objects to be removed could remove the unwanted artifacts but would inevitably modify the results of the measurement.

For this reason, the program was set to remove very elongated objects and shapes that were hollow: the program considers an object as elongated when major axis is 50% longer than the calculated equivalent diameter, and as hollow, when less than 10% of the pixels inside the bounding box (smallest rectangle inside which the NP can fit) is white.

Resolution and error calculation

Both the radius inaccuracy and the error in diameter measurement are linked to the size of the pixels used for the measurement. Here we understand radius inaccuracy as being the minimum size variation the program can detect and error as the incertitude associated with our measurement method.

To obtain the radius from the area the program uses a simple formula:

𝐴 = 𝑁 . 𝑝 = 𝜋. 𝑟 𝑟 = 𝑁 𝜋 𝑝 (3.3)
where 𝑁 is the number of pixels that compose an object, 𝑝 is the size of one pixel and 𝑟 is the measured radius.

We can then calculate the radius inaccuracy which is the difference between radii of an object measured with 𝑁 pixel and 𝑁 + 1 pixels:

A plot of the inaccuracy versus the pixel size and the number of pixels in an object is presented in Figure 3.12 on the left. We can observe that the minimum variation in radius we can detect drops very fast with the decrease of the pixel size and increase of the number of pixels in the object.

In this figure, two lines are plotted that represent NPs with radii of 50nm and 100nm, the interval in which we expect most of our NPs to be in. We can see that for pixel sizes smaller than 8 nm our inaccuracy is below 1 nm, which is the resolution of the SEM used for imaging in this work. For this reason, 8nm is considered as a good upper bound for the pixel size used in this program. To know the error when measuring the diameter, we must first know the error we make when measuring the area.

By using this method, we are approximating the circle to a sum of squares, so the first question is how many squares we are using to approximate a NP. We have two different cases:

𝑟 = 𝑟 -𝑟 = 𝑝 √𝜋 ( 𝑁 + 1 -𝑁 ) (3.4)
1. All squares fit entirely inside the circle, so we underestimate the area (Figure 3.13, left)

2. Some parts of the square are outside the circle, so we overestimate the area (Figure 3.13, right)

Taking the same notation as before we have a circle with radius 𝑟 and squares with side corresponding to the pixel size.

In the underestimation case the area which we do not consider, corresponds to the area inside half of the diagonal of each square, meaning the area measured will be:

In the overestimation case the area is essentially the same as the underestimation case of a circle with radius of 𝑟 + 𝑝 , meaning the area measured will be:

In consequence the error in radius measurement will be:

The first thing we can conclude is that the error increases proportionally to the pixel size meaning that if we want to reduce the error, we must increase the resolution of the images used for the measurement.

We can also conclude that the error is larger in the underestimation case than in the overestimation. For this reason, when talking about the error by the program we will always consider the underestimation case. The structure factor is used to numerically calculate the far-field response of the structure related to the positions of the particles that compose it ( § 3.2).

To do the same type of characterization optically we use a Fourier Optics bench to obtain the OFTs of different structures. It's widely understood that if we place an object in the front focal plane of a lens and illuminate it, the image observed at the back focal lens will be the Fourier transform of the object.

For this bench we use a supercontinuum coherent light source (STM100-VIS-IR from Leukos) followed by a spectral filter (tunable spectral width from 5 nm to 100 nm) which allows us to set the wavelength and bandpass of the emitted light.

In this set-up we want to observe the OFT in reflection due to the reflective nature of the fabricated metasurface targeted function. For this reason, the objective used to collect the diffracted light is also used to send the light onto the sample. Hence, a focusing lens is required to focus the beam onto the focal plane of the objective to have a collimated beam incident on the sample. This is required as a non-collimated beam would create distortions on our Fourier transform due to multiple incident wavevectors.

A direct image of the sample is formed by the objective at the back focal length. There we place a diaphragm to avoid parasite light from interfering with our measurement.

A beam splitter is used to send the image into two systems:

The first is composed of two convex lenses which form a direct image of the sample. This is used to verify that the sample is at the correct distance from the objective by observing if the image is in focus.

The second is composed of one convex lens that is placed at one focal length from the direct image to form the OFT of the sample on the camera sensor.

One of the most important parameters for imaging capabilities of our bench is the Numerical aperture (NA). It can be easily calculated with the formula:

𝑁𝐴 = 𝑛. sin (𝛼) ( 3.10)
where 𝑛 is the optical index of the medium and 𝛼 is the half-angular aperture of the objective.

For our use case the medium is air so our optical index will always be 1. The objective used had an NA of 0.8 and was non-infinity corrected with the direct image being formed 160mm behind the objective.

Smaller features of a sample will diffract light at larger angles. Higher numerical aperture and thus larger half-angular aperture, enables to collect diffracted rays at steeper angles and hence image smaller features. The other way to collect the diffracted rays for smaller periodicities is to decrease the wavelength which decreases the angle of diffraction (cf Equ. 3.11).

The angle of diffraction of the first order at normal incidence for a grating of period 𝑝 is given by the formula:

𝜃 = arcsin 𝜆 𝑝 ( 3.11)
The maximum angle we can collect in our objective is α. So, the condition for the diffracted rays to be collected by the objective is simply:

𝛼 > arcsin 𝜆 𝑝 ( 3.12)
which can be simplified as:

sin(𝛼) = 𝑁𝐴 > 𝜆 𝑝 ( 3.13)
Thus, we need the proportion between the wavelength and the spatial frequency of the structure to be smaller than our value of NA (0.8 for our set-up).

If we consider that the shortest wavelength our source can emit is 500nm we conclude that our system can collect diffracted rays for structures with periodicities as small as 625nm.

Periodicity and q vector

Since we use an objective with a magnification of 60 to image our sample, the actual OFT figure is the figure of a structure 60 times larger. This means that the maximum diffraction angle of the magnified image is:

Since we know the maximum proportion between the wavelength and the spatial frequency is NA we obtain.

The maximum angle is now much lower meaning the paraxial approximation is valid.

So, a diffracted planewave incident on our lens at the angle at which it was diffracted will be This is represented in Figure 3.16.

Considering the magnification of our system and using the paraxial approximation Equation (

Focal distance calibration

During the first calibration measurements with this bench, we observed that the Fourier transform did not form exactly at the focal distance of the lens. measurements with this bench.

Angulo-spectral bench (ISOLASER)

The angulo-spectral bench has been developed by P. Gogol and several PhD or postdoctoral fellows, to measure the reflectance and transmittance characteristics of samples with variable angles of incidence over a large spectral band. The bench is referred to as ISOLASER, name of the European project for which it was first developed between 2002 and 2005.

As an "home-made" set-up, it is highly modular and can be easily improved and adapted depending on the measurements to perform and their requirements.

Mechanical description

To be able to measure optical characteristic at different angles of incidence the set-up needs to displace its elements relative to each other. For this reason, it is composed of three parts: The emission arm is fixed in place and the sample holder and reception arm are both motorized. This is done because the light source is connected to the emission arm through an optical fiber. By maintaining the emission arm in place, we reduce the risks of damaging the fiber during measurement.

The sample holder can move rotationally, to set the angle incident required for the measurement, and translationally, to align the light beam with the targeted area on the sample.

The reception arm can move rotationally, with the axis of rotation aligned with the sample holder: this allows us to set it at the required angle to collect the light from the sample.

Each of the arms holds an optical rail so all the elements can move freely in one direction (X axis). Furthermore, each element is attached to two plates with micrometric screw for displacements in the two other direction (Y and Z axis) for optical alignment.

Optical description

The optical system is composed of an initial broadband light source. The light emitted is sent into a monochromator which separates the different wavelengths. The selected wavelength is then injected into an optical fiber which guides the light into an optical adapter connected to a collimator. The collimated light beam of the selected wavelength goes through a beam reducer (composed of two lenses, one concave, one convex) and a polarizer before being focused onto the sample by a lens.

The light reflected or transmitted by the sample is then collected by a lens that focuses it onto a detector (schematic in Figure 3.19).

Monochromator

This system uses a monochromator iHR320. The monochromator takes light in and collimates it with a collimation mirror. The collimated beam of light is then sent onto a diffraction grating which separates the multiple wavelengths remitting them at different angles. By rotating the grating, the monochromator selects the wavelength sent to the exit by means of another collimation mirror.

The grating used for all our measurements has 1200 lines/mm which is ideal for a spectral range from 300nm to 1200nm. The bandpass of the light from monochromator can be controlled by the width of the exit slit. For our measurements we used a slit width of 0.5mm corresponding to a bandpass of 1.16nm.

Furthermore, to avoid the overlap of higher-order diffraction of shorter wavelength with our selected wavelength the monochromator is equipped with optical filters. Measurement of the spectra of light sources with each filter are presented in Figures 3.20 and 3.21.

Filter 1 is used for measurements between 350 nm and 500 nm (it corresponds to no light filter). Filter 2 is used for measurements between 500nm and 1050nm. Filter 3 is used for measurements from 1050nm to 1900nm.

Light source

The light source used in the set-up at the start of my work was a 75W Xenon lamp from Horiba Jobin-Yvon (spectrum in Figure 3.20). As we can see the lamp had a lot of power concentrated in a few peaks in the infrared which is not ideal for our use case as the measurements will be in the visible spectrum.

Another disadvange of this lamp is emission of ozone which meant an air extraction needed to be used to ensure the safety of the user.

For these reasons we decided to replace the Xenon lamp by a 250W Tungsten-Halogen also from Horiba Jobin-Yvon (model LSH-T250). Other than the ozone-free emission, this lamp presents two main advantages:

The first one is that it can be directly attached to the monochromator removing the losses of a connection through an optical fiber.

The second advantage is black body like emission (rated at 3400K), which results on a continuous emission spectrum over the visible and infrared wavelengths without peak emissions for certain wavelengths (spectrum in Figure 3.21).

Certain measurements were done without using the optical filters to maximize the optical power detected and lower the signal to noise ratio. To ensure the validity of these measurement we calculated the impact that higher order diffraction could have on the transmittance at 800nm. This impact should be the highest for this wavelength power proportion between 800nm and its half, 400nm, is the maximum in the 700nm to 800nm range as we can understand my looking at the emission spectra for Filter 1 in Figure 3.21. The relative error was estimated to be 2.3% which allows to have confidence in these measurements. Furthermore, this error is likely overestimated since the calculation done supposes the second order diffraction at 400nm has the same power as the first order, when it is likely lower.

Beam reduction and focusing lens

Another of the changes to the system was removing the beam reduction system. This is used to ensure the spot of light is completely inside the structure we want to characterize, as reflection or transmission outside of the metasurface induces an error in the measurement.

But the use of these two lenses adds complexity to the alignment of the system and due to the large area of our structures the spot of light remained within the structure without any reduction, even at steps angles.

The lens used to focus the beam onto the sample was removed for large area metasurfaces, for the same reasons. It was only added for test samples fabricated by electron beam lithography that, in consequence, have smaller areas.

Detector

We used a Silicon detector for this system, with a Peltier cooler and a preamplification stage.

This detector allows us to do measurement mainly in the visible spectrum, going from 200nm to 1100nm.

Conclusion

As mentioned at the start of this chapter, one of the main objectives was to develop tools for the analysis of disordered structure in a manner that allows for comparison with ordered structure. Here we proposed the structure factor to analyze optical effects which can be used for both ordered and disordered structures. The experimental verification of the results is done using an OFT bench ( § 6.3). Furthermore, the structure factor, coupled with the computer vision program for NP position detection can be used for large amounts of particles, which responds to our second objective of developing tools for analyzing structures with large areas. A use of these three tools for the analysis of the structures fabricated is presented in chapter 6.

The NP diameter measurement program also responds to this second objective since it can measure large amounts of NP quickly and with a low error. In section 5.5 we use this program for the analysis of size dispersion of samples fabricated.

Lastly, we presented the Angulo-spectral bench which is used to optically characterize the fabricated samples in transmission ( § 6.5 and 6.7).

Chapter 4 :

Process development for large area plasmonic metasurfaces

Introduction

The first objective of this work is to propose and demonstrate large area plasmonic metasurfaces for transparent displays, with the targeted application as plate combiners for HUD systems.

The first challenge is their fabrication. One promising method to obtain both nanometric dimensions and large areas is self-assembled nanostructures.

Here, we have focused our work on the combination of self-assembly and NIL. More precisely, we have developed a new approach: it uses PS NSs self-assembly technique directly on PDMS to generate large area stamps for Soft UV-NIL. The PDMS stamp is structured here not by standard molding but by direct etching with PS NSs as a mask.

The object of this chapter is to describe the development of this new approach. The new process includes three main steps (Figure 4.1):

1. NS self-assembly directly on a PDMS substrate 2. PDMS etching using a PS NSs mask 3. Gravitational Soft UV-NIL. After a detailed presentation of these three steps, a short comparison of the 'standard' soft UV-NIL process (using molded PDMS pattern) will be proposed, and then the chapter will be concluded with additional process steps to reduce the NP density of large area metasurfaces.

The target of this fabrication process is to obtain transparent reflective metasurfaces on glass, composed of disk-shape Ag NPs with 130nm in diameter with interNP distances of 220nm (resonance at ~550nm) over a total surface of more than 0.5 cm 2 .

Polystyrene (PS) Nanosphere (NS) self-assembly

The first step of our fabrication process is to form a monolayer of PS NSs by self-assembly and deposit it onto a planar substrate (PDMS or Si). The objective of this step is to easily form a large area structure that can be used as a mask for metallic deposition or etching.

This technique allows us to obtain a hexagonal structure, with a surface reaching many cm 2 , with a pitch equal to the diameter of the used NSs. The process used in this work is based on the one proposed by Vogel et al. [1].

One of the main limits of this process is its sensitivity to external perturbations. Vibrations caused by someone walking nearby or a door closing could easily break the monolayer formed at the water surface. Furthermore, any airflow during the formation, deposition or drying of the monolayer would induce disorder in the structure. For this reason, the process was done in a relatively isolated area within the cleanroom to avoid vibrations, with a specifically fabricated acrylic protection over it to protect from airflow.

Deposition step

To obtain a self-assembled structure with sub-wavelength dimensions we use a 1:1 solution of deionized water and ethanol with a concentration of 13g/l of PS NSs with 200 nm in diameter (the real average diameter is closer to 220nm). The NSs are deposited onto the surface of a solution of deionized water with sodium dodecyl sulfate (SDS) through a glass blade (with the same surface treatment as the substrate) tilted at 45º degrees placed on a blade holder fabricated specifically for this purpose to ensure stability.

The SDS is used to create surface tension and ensure that the NSs form closely packed monolayers. For the 1 µm NSs we use 40 drops and for the 200 nm 10 drops of a 2% solution of SDS for a total of 300ml of deionized water. This parameter is important as an excess in SDS would cause the NSs to form bilayers since the surface tension is too high. If the amount of SDS is too low, the NSs will quickly get dispersed across the water surface and form very small monolayers that break very easily.

The deposition blade allows the NSs to arrive at the water surface at a controlled and constant velocity limiting the dispersion and favoring the formation of monolayers.

The self-assembled layers we obtain with this method have, consistently, around 1cm 2 in area.

Once a monolayer is formed, the hydrophilic substrate is dipped into the water solution, placed under a monolayer, and removed from the solution, recovering it on its surface (Figure 4.2, right).

In Figure 4.2, on the left, we can see the set up used for deposition. The red piece is the blade holder, the blade is attached to it using two screws. In the image in the center, the solution is being deposited onto the glass blade (white drops) and the monolayer formed at the waterair interface (highlighted in red). On the right, a substrate is dipped onto the water solution for a monolayer to be deposited onto it.

Drying step

During the drying step the monolayer is lying on a thin layer of water, on the substrate, and not in direct contact with the substrate making it possible for the NSs to move, increasing the disorder of the structure.

The substrate is placed at a vertical position for water to slide down onto the absorbing paper underneath, reducing the time during which the NSs can move and become disordered. We should note that during drying in a vertical position, the monolayers can slide down due to gravity resulting in depositions near the edge of the substrate. To fix this problem drying can be done with the substrate horizontal with the trade-off of less ordered structures.

Indeed, an analysis of the structure factor extracted from Sem images shows that (Figure 4.3), the structure factor of a horizontally dried structure presents a lower and wider peak indicating less order than the vertically dried one.

Once the substrate is dry, the NSs adhere to it making them unable to move. The total duration of drying is 2 hours.

Deposition onto PDMS substrate

As mentioned above, in the proposed process the self-assembled monolayer of PS NSs is deposited onto a PDMS substrate.

To have a deposition with the lowest amount of disorder, our PDMS film must have the minimum amount of surface irregularities as possible. In consequence, we use RTV 615 from ELECO PRODUITS composed of a specific dilution of 93wt\% PDMS and 7wt\% of reticulating agent. This ratio of PDMS to reticulating agent was chosen to maximize the etch rate of PDMS [2] for the step presented in section 4.4.

The PDMS is spin-coated at 200 rpm on a silicon wafer, degassed at room temperature during 1h and baked at 80ºC for 30 minutes to reticulate. The film is then inverted to do the deposition on the smoother surface which was in contact with the silicon.

PDMS is naturally hydrophobic due to the presence of methyl groups at its surface so it must be treated before deposition to become hydrophilic. The treatment used is as follows:

1. Substrate cleaning in acetone bath with ultrasounds for 20 minutes, 2. O2 plasma treatment at 150W for 20 minutes.

The O2 plasma serves to replace the methyl groups with silanol, which are hydrophilic.

Unfortunately, PDMS becomes hydrophobic again after only a few hours [3]. For this reason, the deposition must be done immediately or very soon after the O2 plasma to ensure the monolayer of NSs can be deposited.

We observed that PS NSs fused together if they are left for a certain duration at room temperature. To the best of our knowledge this effect was not reported in any previous publications on other substrates. The closest behavior reported was the formation of "bridgelike" connections between the NSs [4,5] (this was observed in our deposition on Si, see annex). This is highly unexpected since the glass transition of PS is 100 o C. This fusing can be observed after time periods as short as one day for the 200nm NSs, but the behavior is highly heterogeneous with it happening at very different speeds and even for different areas of the same sample. This is represented in Figure 4.4, with a sample that presents fusion of the entire NS layer only after four days on the left and another sample that presents no fusion after five days on the right.

For this reason, any following fabrication steps with 200 nm NSs should be done within two days after the deposition to minimize the risk of fusing of the layer.

PS NSs size reduction on PDMS

As mentioned in section 4.2 the PS NSs monolayers are used as a mask for the PDMS etching

days after deposition 5 days after deposition

process. To control the masked area per NS, we use dry etching to reduce the size of each NS.

The etching method used for reducing the PS NSs will have an important impact on the resulting structure. A more anisotropic method, such as RIE, will reduce the size of the NSs faster and at lower temperature which will enable to avoid the increase the disorder of the structure, but may damage and deform the NSs. Using an isotropic method may favor disordering the NSs, but it will maintain their original shape.

In order to compare these two approaches and their impact we tested two different types of etching machines: a plasma cleaner machine (Diener Nano) and CCP-RIE machine (Nextral-NE 100). For simplicity we shall refer to the plasma cleaner as "PC" and the CCP-RIE as "RIE".

One technique that is used to minimize the disorder caused by the isotropic etching method is to cool the cathode [1,5]. Unfortunately, this was not possible in our PC machine so, to minimize the heating inside our plasma chamber, the etching was done by steps. Between two steps the sample was removed, and the machine was left at atmospheric pressure for 15 minutes or more to cool the substrate holder and the plasma chamber back to room temperature.

We should note that the RIE machine has a cathode temperature control. It was set to 16 o C for all processes.

In Table 4.1 and Table 4.2 we have the results of calibration test for the two machines. As expected, the RIE etching method causes more deformation to the shape of NSs and damages its surface. The NSs after this etching method are flattened and their surface is rough (Figure 4.5, left).

The PC method does not deform the NSs but induces an increase in the disorder of the NSs, as expected from the results from previous works [4] (Figure 4.5, right). The NSs maintain their spherical shape but form a deformed hexagonal structure. We identified two main reasons for this difference:

 the first one is temperature. An increase in temperature inside the machine means the gas molecules have more kinetic energy: they can more easily transfer some energy to the NSs and displace them, increasing the disorder of the structure. The cooldown steps used in the process with the PC were able to reduce the induced disorder, but the effect was still significant.

 the second one is the flattening of the PS NSs in the RIE etching. This makes them unable to move, while the PC etching maintains the spherical shape which allows the NSs to move.

Another difference between the methods is the etching times. The RIE method has a much higher etch rate, reducing the NSs to half of their initial size in less than 2 minutes, while the PC method takes nearly 9 minutes of etching time and more than 45 minutes when considering the cooldown steps required.

These results also show that the disorder caused by the isotropic etching (PC cleaner method in our case) does not happen for small size reductions since the NSs do not have space to move (etching PC.C and PC.D in Table 4.2). This is in accordance with previous works [4]. From these results RIE appears as the best candidate for PS NSs size reduction as it is faster and does not increase disorder.

Stamp fabrication by PDMS direct etching

We used a novel technique for stamp fabrication by directly etching the PDMS, decorrelating the minimum dimensions attainable from the initial viscosity.

We present the etching step for the PDMS using a PS NSs mask and we compare two different methods: one low-pressure high power and one high-pressure low power.

Furthermore, we detail the cleaning procedure to remove the remaining PS after etching.

PDMS etching

By dry etching the PDMS using a mask, the dimensions which can obtained are limited by the dimension of the mask pattern, which in this work is the PS NSs deposited and resized on to the substrate, and the quality of our etching process.

We tested two different kinds of etching processes: the first low-pressure process (10mTorr (13 µbar), 50 sccm O2, 200 sccm CF4, 150 W). The calibrated etch speed was 1.2 µm/min for a flat unmasked layer of PDMS.

The second process was a high-pressure process (100mTorr (133 µbar), 20 sccm O2, 40 sccm CF4, 50 W) which was done by Frédéric Pommereau at III-V Lab. The calibrated etch speed was 200 nm/min for a flat unmasked layer of PDMS.

By analyzing the etching results in Table 4.3 and Table 4.4 the first thing we can note is that the height transferred using the lowpressure method is higher than with high-pressure, when using the same mask (except for the mask obtained with RIE.C but due to very small dimensions this difference could be caused by a measurement error). This is explained by the isotropic nature of the high-pressure process which will etch away the PS mask in all directions, reducing it faster resulting in worst selectivity between the mask and the substrate and consequently, a lower transferred height.

Furthermore, it will etch laterally the walls of the pattern being formed in the PDMS, resulting in thinner shapes, as can be observed on the images on the left of The low-pressure process, on the other hand, is highly anisotropic. This means the diameter of NSs composing the mask will not be reduced as fast, since the etch direction will be mostly downwards. Furthermore, the sidewalls of the pattern will not be etched laterally. This will increase the transferred height and the width of the cones that make up the pattern as can be observed on the images on the right of If we now compare the performance of the mask obtained with different methods, the first thing we can note is that PS NSs perform differently depending on their side reduction. Under a certain size the mask is either too small or too deteriorated and the height transferred to the structure is very small. This is the case for masks with NS diameters of 125nm (method RIE.C) and 95nm (method PC.B). Nevertheless, we can also see that even though the mask using the isotropic PC etching method has smaller diameters it can transfer more height to the PDMS (22nm compared to 11nm and 4nm for the RIE method). This is most likely due the NSs being less damaged during the size reduction process and having more volume due to their spherical shape (the NSs with RIE size reduction have a flattened shape) which results in a better masking of the PDMS.

If we now look at the height transferred for masking structures for NSs with larger diameters, the opposite becomes true. Indeed, from Table 4.4 the height transferred with a mask reduced using RIE.D, which corresponds to a NS diameter of 150nm, is 55nm compared to 48nm for the mask reduced using method PC.D which corresponds to a structure with NS diameters of more than 190nm. Our hypothesis here is that the flattening of the NSs in the RIE process improves the masking since the plasma cannot flow under it. For both methods, the masks without NS reduction are the ones that transfer the most height to the PDMS, not only in absolute terms (as would be expected), but also in relative terms, with more than 1/3 of the dimensions of the mask being transferred with the highpressure method and close to 0.9 for the low-pressure method.

One reason for this improvement is the fact the PS NSs that compose the mask have not been damaged with the size reduction process resulting in a better etch mask.

Another possible reason is the bridge connections that form between the NSs after deposition [5]. These connections have two effects that can improve the masking: the first one is that they will maintain the NSs in place during the PDMS etching (particularly at the start of process) meaning the PDMS under each NS will be better masked. The second is that these connections will reduce the total surface of the NS that is exposed to the plasma reducing lateral etching.

Considering that the high-pressure process is more isotropic (meaning higher lateral etching), we should expect a higher improvement with the unetched mask than for the low-pressure process which already has very low lateral etching by nature. This is confirmed with an improvement on the etched height from a mask obtained with PC.D to an unetched mask of 65% for the high-pressure method compared to 44% for the low-pressure method.

We should note that the low-pressure etching method damaged the PDMS creating long fissures (Figure 4.9). This could be due to the highly physical nature of the etching or a quick expansion and contraction of the PDMS due to heating. This effect could also be seen in samples etched using the high-pressure process but to a lesser degree.

These results allow us to conclude that the low-pressure method performs better as a PDMS etching method when using PS NSs as mask since it can transfer more than double the height to the PDMS than the high-pressure with the same mask.

In terms of masks, unetched PS NSs monolayer clearly perform the best but if size control is required, they may not be a viable option. If this is necessary, the masks obtained with RIE NSs reduction method has better performances. Furthermore, it does not seem possible to maintain a good masking performance for NS reduced to more than 75% of their initial size, using these methods.

PS cleaning

Before using the stamps in a NIL process the remaining PS from the etch mask must be removed (PS increases adhesion of the stamp to the resist). In the case of high-pressure etched stamps, a 5-minute acetone bath was sufficient to completely remove the PS layer.

In the case of low-pressure etched mask this was proved to be insufficient, so we cleaned these samples with a 10-minutes 100W O2 plasma followed by 10-minutes acetone ultrasound bath.

The disadvantage of this procedure was that the PDMS stamp was damaged after the cleaning, resulting, in some cases, in inhomogeneous pattern transfer as shown in Figure 4.10.

One thing to note is the lack of repeatability of this procedure. Some stamps did not present adhesion to the resist after the cleaning but, this was not true for all stamps fabricated with the exact same parameters introducing a level of uncertainty in the process using lowpressure etched stamps.

PDMS etching process comparison

We presented two different processes for PDMS etching: a high-pressure and low-pressure processes.

These two techniques have differences in the characteristic of the stamps obtained and in the resulting usage of the stamps for the fabrication of metasurfaces.

The first clear difference is the height and shape of the pattern obtained on the PDMS stamp.

The low-pressure method can transfer patterns with higher height and larger width from the mask to the PDMS, with the transferred dimensions being almost one to one to those of the mask (for an unetched mask). The high-pressure method is only capable of transferring around one third of the dimensions in height of the mask to the PDMS (again for an unetched mask).

This also means the low-pressure method allows for a better control of the final NP diameter.

Since it performs better at transferring the pattern from the mask to the substrate there is more room to reduce the diameter of NSs, allowing us to control the dimensions of the final structure, and still obtain a good stamp. In the case of the high-pressure method a reduction of the mask would result in a pattern with a height too small to obtain a good transfer onto the resist.

Another important factor where the two methods show a difference is the difficulty to remove the PS mask after etching (and subsequent adhesion in the NIL process). As discussed in the previous section the adhesion of the stamp can damage the transferred pattern or even the stamp itself rendering it unusable.

The stamps obtained with the high-pressure etching method presented no adhesion to the resist layer after a simple acetone cleaning and an anti-sticking process.

The stamps obtained with the low-pressure etching method presented significant adhesion and required further cleaning ( § 4.4.2). Furthermore, this cleaning step combined with the anti-sticking treatment was able to solve the adhesion problem only for certain stamps.

Unexpectedly, even when fabricated with the same parameters for all processes the stamps presented different adhesion behaviors. Their characteristics were unpredictable and in consequence, processes using these stamps were non-reproducible. Furthermore, even in the case where the stamp did not adhere to the resist these were damaged and had local variations in height.

Both methods were capable of transferring near the totality of the area of the mask to the PDMS stamp. Considering the differences between the stamps obtained with each method the highpressure method was given preference due its reliability in terms of adhesion and better height homogeneity.

Soft UV-NIL description

The process we used during the fabrication of large area metasurfaces is composed of six main steps: Lift-off

Anti-sticking

Before the imprint an anti-sticking process is done on the stamp to ensure the stamp does not stick to the resist so we can remove it easily and without damaging the pattern transferred on to the resist nor the stamp itself. This process was particularly important for our stamps since, even after cleaning, it was possible for some PS NSs from the mask to be present on the stamp which increased the adhesion to the imprint resist.

For this purpose we use 1H,1H,2H,2H-perfluorooctyltriethoxysilane (POTS) which is commonly used as an anti-sticking layer [6]. The chemical vapor deposition we use was an adapted version of the one used in Wang et al. [7].

The PDMS stamp is put in a glass box with approximately 10 drops of POTS (Figure 4.11). We then place the box on a heating plate at 135 o C for 1 h with a lid over it in order to create a POTS saturated atmosphere. The glass box is then removed from the heating plate and the lid is taken out. Finally, the box is placed again on the heating plate at 165 o C to remove unreacted POTS molecules.

Bilayer deposition

The first step of the process is to clean the substrate in an acetone bath with ultrasounds for 5 minutes and then dehydrated in a heating plate at 90ºC for 10 minutes.

The imprint resist used is AMONIL MMS4, a UV-curable resist from AMO-GmbH, but due to its inorganic nature we cannot do a lift-off with solvent. For this reason, we first deposit a PMMA sacrificial layer. This resist can be lifted off, its low viscosity allows us to spin thin layers and it can be etched with an O2 plasma meaning we have high etching selectivity between PMMA and AMONIL, since the later can only be etched with fluorinated gases. The PMMA is spun at 3000 rpm followed by a bake at 180ºC for 10 minutes to obtain a 80 nm layer.

We then spin the AMONIL on the PMMA. We used 8000rpm, to obtain an 111nm layer (Figure 4.12).

After imprint there is a layer of the imprint at the bottom of the pattern called the residual layer (more details in the following section). For samples used to calibrate this residual layer we spin a layer of AMOPRIME, instead of PMMA (PMMA resist makes measuring the residual layer more difficult) to improve the adhesion between AMONIL and the Si substrate. The AMOPRIME is spun at 3000rpm. The layer thickness is negligible (<10 nm).

PDMS Mold in POTS atmosphere Anti-sticking layer We use gravitational NIL, meaning only the weight of the stamp ensures the imprint pressure.

This technique is not very widely used because of the thicker residual layer obtained. But since it can be done by hand, not requiring any machine (except a UV lamp) it is very simple to put in place with very little material which further demonstrate the potential of our process as a low-cost method.

The PDMS stamp is placed on top of the AMONIL/PMMA layer. The sample is then exposed to UV light at 365nm (Hamamatsu LC8, 200mW/cm 2 ) for 2 minutes to cure the AMONIL resist.

Lastly the stamp is removed from the substrate.

Bilayer etching

Once the pattern is transferred onto the resist, we need to transfer the pattern to the substrate. To do this we must first remove the residual layer. Indeed, after the imprint a thin residual layer of imprint resist is present at the bottom of the pattern (Figure 4.14, left).

We first etch the residual layer of the imprint resist to reach the sacrificial PMMA layer followed by an etch of this second layer to transfer the pattern down to the substrate. A schematic of the etching process is presented in Figure 4.14.

The first, the residual layer of the AMONIL is removed with a RIE etch (2sccm O2, 20 sccm CHF3, a power of 25W and 7mTorr). The duration of this etching process depends on the thickness of the residual layer. The calibrated etching speed for a flat, non-structured AMONIL layer was 40nm/s but this is not valid for the etching of the residual layer at bottom of the pattern holes. This is due to RIE lag effect caused by the transportation limit of the gases, which slows down etch rate for small openings [8][9][10], meaning our actual etching rate of the residual layer will be much slower than the one measured for an non-structured layer. Furthermore, since we have cone shaped holes, this means we will have a gradient etching rate that decreases the further we go down each of the patterned holes.

This effect, coupled with lateral etching, will result in a lateral increase of the size of the patterned holes (the pattern becomes larger), as can be seen in Figure 4.15. This will result in an increase of the dimensions of the NPs composing the final metasurface.

Furthermore, this increase of the patterned holes will in turn reduce the lag effect meaning the etch rate will increase the further we etch our pattern (but staying below the 40nm/s calibrated). This makes the actual etch speed very difficult to calibrate since it will depend on the form factor of the pattern holes (thinner holes meaning a slower etching speed) and evolution of their shape during the etching. For this reason, the AMONIL etching step must be calibrated for each stamp with different pattern heights and widths.

The 80nm layer of PMMA is etched away with 2 minutes RIE etching (10sccm O2, 15W and 4.7mTorr).

Metal deposition

The Ag deposition is done by electron-beam physical vapor deposition machine.

To improve adhesion of the metallic layer the sample undergoes an Ar ionic etching followed by the deposition of a Ge interface layer.

Furthermore, the speed of the deposition of the final 30nm thick Ag layer, initially set at 1nm/s proved to be too fast, resulting in highly deformed NP (

Lift-off

The solvent used for the lift-off is butanone. The samples are left in the solution over night to ensure the PMMA is completely dissolved. The butanone solution with the sample is then put in an ultra-sound bath for 5 minutes to ensure the metallic layer is completely removed. Lastly the sample is washed with acetone, to remove any possible metallic redepositions, and dried.

Comparison with standard stamp fabrication by molding

The main method for PDMS stamp fabrication is the molding of the liquid PDMS on a, usually Si, master mold.

In annex 1 we present our method for fabricating large surface Si master mold based on PS NSs self-assembly and the subsequent PDMS stamp fabrication from those stamps and metasurface fabrication using the stamps obtained with this method.

The first clear difference between the stamps obtained by molding and by dry etching was the height of the pattern obtained.

Indeed, since the smallest feature PDMS can fill is directly linked to its viscosity, the molding technique resulted in lower pattern height.

An attempt to improve upon this was to use diluted PDMS, but if the dilution was too high the pattern would laterally collapse rendering the stamp unusable. Lower dilutions would result in low pattern height (see Figures in Annex).

The option of using Hard-PDMS was also investigated. The pattern height was improved compared to standard PDMS with low dilution (17nm to 46nm) and it presented no collapse of the structure. Unfortunately, the height of the pattern was too low for a use in a gravitational NIL process (section 4.5.3).

By slightly increasing the dilution of standard PDMS to 3wt/% hexane we were able to obtain a usable stamp which was successfully used in the fabrication of a metasurface. Nonetheless, the fabrication of this metasurface required the use of a resist with lower viscosity (AMONIL MMS10, opposed to MMS4 used for directly etched stamps), to obtain a thinner resist layer.

This was necessary due to the low height of the pattern in the stamp.

Stamps fabricated by direct PDMS etching had a clear advantage in term of the height obtained, reaching over 100 nm without presenting any collapse of the structure. This is due to the higher Young's modulus of the undiluted PDMS. The stamps presented good homogeneity in term of height and size of the pattern across the whole surface and work well in a gravitational NIL process using resists with a higher viscosity (AMONIL MMS4).

Furthermore, the fabrication of the stamps required only five steps: PS NS deposition, PS NS reduction, PDMS etching and stamp cleaning. In some cases, only four were necessary since the PS NS size reduction was not done (when using unetched masks). In the case of stamps by molding eight steps were required: PS NS deposition, PS NS reduction, metallic layer deposition, PS NS lift-off, Si etching, Si master anti-sticking process, PDMS molding and reticulation, PDMS stamp extraction.

This shows the potential of the direct PDMS etching as a low-cost technique that does not sacrifice performance in terms of dimensions.

Propositions for process improvements

We have shown in this section that direct PDMS etching can be used to fabricate PDMS stamps for NIL. The results are encouraging especially since we know that improvements can be made to optimize the process.

Stamps fabricated with low-pressure process were discarded due to them becoming highly damaged after the cleaning process required to solve the adhesion to the imprint resist layer, even though they presented higher pattern height ( § 4.4).

A first improvement would make the use of this stamps possible in one of two ways: by reducing the adhesion to the resist layer (without requiring such an aggressive cleaning) or by improving the cleaning method to not damage the stamps. Further work on the conditions of the surface of the PDMS after etching (i.e. surface energy variation) and the difference between the two methods is required to find a solution that could allow us to use the lowpressure etching process.

Among the stamps fabricated, the ones that presented the best characteristic used unetched PS NS masks, since the height dimensions transferred to the PDMS was maximized. The disadvantage of this technique is that we lose the possibility of controlling the width of the pattern we obtain in the PDMS and in consequence the size of the NPs in the fabricated metasurface.

The first option is to use reduced PS masks, which allows the control of the pattern width. As we saw in section 4.4.1, we obtained heights of 48nm and 133nm from a mask with 195nm PS NSs for the high-pressure and low-pressure processes respectively. The stamps obtained with the high-pressure process can be used in standard NIL processes using higher imprint pressure or even in a gravitational NIL process with an imprint resist with a lower viscosity.

The low-pressure stamps can be used in any of these two types of NIL processes but, as we just discussed, the adhesion problem must be solved first.

Another option is to use the shape of our pattern to do NP size control. Indeed, due to the conical shape of the holes transferred onto the AMONIL by controlling how far we etch the resist layer, we can effectively control the size of the NPs. We present a schematic of this in Figure 4.17. Short etching will only transfer the width at the bottom of the patterned hole, resulting in smaller NPs, while longer etching will transfer the width of the cone closer top resulting a larger NPs. We were unable to test this technique due to the isotropic nature of our resist etching which we discussed in section 4.5.4. This has the consequence of changing the patterned holes size and shape during the etching, making size control not possible.

To use this technique an etching machine and process with higher anisotropy is required to reduce lateral etching of the patterned holes.

Toward metasurface density control

The NP density is an important parameter which influences the reflectance and transmittance of a metasurface. By only using complete layers of self-assembled NS, the resulting metasurface may be too dense.

For this reason, a density reduction process was developed, which can be adapted to any "localization" process if the size of the remaining metasurface area is compatible with UV lithography.

After the imprint step ( § 4.5.3) and before the bilayer etching, we deposit an optical resist layer over the patterned AMONIL layer.

We then expose the resists using an optical mask where the final structure we want to obtain has been drawn (the mask pattern generation is detailed in section 6.4.2). The resist is then developed leaving exposed the areas on the patterned AMONIL that were drawn onto the mask. A schematic of the full process is shown in Figure 4.18.

We can then proceed with the rest of the fabrication process ( § 4.5.4 onward), obtaining a metasurface with NPs only in the regions selected with the mask, resulting in an effective density reduction of the structure.

This process was done with moderate success. In Figure 4.19 the pattern can still be observed in the AMONIL resists but we can also see the presence of rugosity of the AMONIL resist that was not present before. We hypothesize that this is due to leaking of the solvent from the optical resist towards the AMONIL resist resulting in an inhomogeneous swelling of the latter, which is maintained after development. If that obstacle is surpassed this process could potentially be used for multiple applications that require "localization" of structure due to its compatibility with most standard lithographic processes.

Conclusion

In this chapter we have proposed an original low-cost approach for large area metasurface fabrication based on Soft UV-NIL.

We have firstly presented the development of a novel fabrication method for Soft UV-NIL stamps based on direct etching of PDMS with a mask of self-assembled PS NSs. More precisely, two RIE processes were presented for the PDMS etching step: one low-pressure and one high-pressure. Even though the low-pressure process had more promising results, with patterns transferred with higher heights it was discarded since stamps presented significant adhesion to the resist layer, rendering them unusable.

Combined with gravitational Soft UV-NIL the full process is validated up to the metasurface silver NPs fabrication, at very low-cost:

 The self-assembly process of PS NSs allows us to obtain large areas in a very costeffective way.

 By patterning the PDMS stamp with RIE etching we were able to reach heights of nearly 200nm, dimensions lower than 100nm and a pitch of 220nm. These dimensions are in the ranges of the state of the art with the additional advantage to avoid dilution of the PDMS, use of lower viscosity materials like H-PDMS or complex processes.

This new approach was also compared with the standard process using molded PDMS stamps.

Lastly, we have proposed a process for density reduction of metasurfaces which can be easily adapted to different types of structures. The first results obtained with this method are promising but improvements are still required.

Introduction

Following the fabrication of the stamps using the method we developed, described in the previous chapter, these were used to fabricate large surface reflective metasurfaces composed of Ag disk-shaped NPs. As previously mentioned, we targeted NP diameter of 130nm with a NP center-to-center distance of 220nm for a resonance at approximately 550nm.

In this chapter we present the fabrication of two metasurfaces: one on a Si substrate and one on a fused silica substrate.

Both samples were fabricated using the same stamp to ease their comparison.

At the end of this chapter an analysis of the size dispersion of the two metasurfaces is done, using the program for NP diameter measurement ( § 3.4.2), followed by a comparison between the metasurfaces obtained for Si and silica substrate.

PDMS stamp

The stamp used for the fabrication of metasurfaces was obtained by deposition of 200 nm PS NPs onto a PDMS substrate previously cleaned in an ethanol bath and treated with a O2 plasma to become hydrophilic ( § 4.2). After deposition it was dried in a vertical position.

The stamp obtained (Figure 5.1) was fabricated as follows:

1. No PS NPs size reduction 2. High-pressure PDMS etching, 3 minutes 3. 5-minute acetone bath cleaning After this calibration step of the etching of the residual layer the full process was repeated on a sample with a bilayer deposition.

After bilayer etching the pattern is fully transferred to the substrate over a very large surface, leaving the substrate exposed on the areas corresponding to the NPs (Figure 5.4). Ge/Ag metallic deposition was done followed by a lift-off in butanone. In Figure 5.5 we have the final metasurface composed of Ag NP. We can validate the final structure presents an ordered hexagonal structure of Ag NPs. We can already visually verify that some NPs size dispersion is present as was expected due to the discontinuity of the imprint resist layer thickness. The metasurface has NP diameters close to targeted value of 130nm. The size dispersion is properly characterized and analyzed in section 5.5.

In Figure 5.6 we show a macroscopic photo of the metasurface fabricated with a total surface of 0.67cm 2 . The obtained shape corresponds to the shape of the PS NS monolayer deposited on the PDMS.

Fabrication on fused Silica substrate

Following the successful fabrication of a metasurface on Si, the process was repeated this time on a silica substrate (20x20x1.5mm 3 fused silica).

The parameters used were the same as for the Si substrate. The sample after bilayer etching is presented in Figure 5.7. The pattern was successfully transferred onto the substrate but some of the patterned holes in the AMONIL layer were not fully "opened" and presented micromasking (resist present in the openings). This has an impact on the metasurface fabricated. In Figure 5.8, on the right we have some NPs are broken into many smaller pieces due to this micromasking. We shall refer to this effect as NP breakage.

We also notice a shift to larger NP sizes compared to the metasurface on Si, with diameter oscillating between 140 and 180nm, above the target of 130nm. These two effects are discussed in more detail in section 5.6.

In Figure 5.9 we show a macroscopic photo of the metasurface fabricated on silica with a total surface, equal to that of the one on Si, of 0.67cm 2 .

Figure 5.9 -Macroscopic photo of the metasurface on silica.

Size dispersion analysis of the fabricated metasurfaces

To characterize the fabricated metasurface, we first did diameter measurement during SEM observations which allowed us to have a first idea of the size of the NPs: the metasurface on Silicon have radii around 130nm and the metasurface on silica around 170nm but with higher dispersion.

By considering the density of our structure of 22NP/µm 2 and the total area being 0.67cm 2 , we can estimate the total number of NPs in the structure is close to 1.5 billion. For this reason, measuring only a few tens of NPs does not give us a result that is in any way representative of the actual structure. Furthermore, we notice that depending on the observed area the average diameter measured and the dispersion were different. Following this conclusion, we developed a computer vision program ( § 3.4.2) to efficiently measure multiple NPs from images taken in different areas of the sample.

We used high-resolution SEM images with a pixel size of 3nm to minimize the error of our measurement. This means that, for our targeted NP size of 130nm, we have approximately 1475 pixels per NP. So, if we take equation 3.2 and plug in the values we obtain:

Considering the minimum resolution of SEM used is 1nm, we can conclude that we are not limited by the measurement resolution of the program.

In terms the error, we previously determined it to be 70% of the pixel size ( § 3.4, equation 3.8) which means that our absolute error will be 2.1 nm, independently of our NP size. For the targeted value of 130nm this represents a relative error of 1.6% which allows us to have strong confidence in our measurements.

Metasurface on Si substrate

For the metasurface on Si we used 10 SEM images. In total more than 49 000 NPs were measured, for a total surface of 2300 µm 2 .

One of the consequences of breakage was the creation of very small pieces of metal. For example, one 130 nm NP can create nine NPs with 40nm. The consequence is that the breakage of only a few NPs can have a disproportionate impact on the size dispersion, strongly shifting down the average NP size.

For this reason, we decided to set the program to remove NPs with less than 1/4 the area of the average NP (130 nm diameter) thus meaning any object with an area smaller than that of a circle with a 65nm diameter. This removes very small pieces of metal left due to breakage, but the reduction of the diameter of the NPs is still considered.

In Figure 5.10 we can understand that different areas present different types of structures.

𝑟 = 3nm

√𝜋 √1476 -√1475 = 0.022nm

(5.1)

Figure 5.10-a is the histogram of an "ideal" structure. There is a very clear maximum, the width of the peak is not very large, and the breakage is not significant (the percentage for small diameters is low). Figure 5.10-c is the histogram of an area with significant size dispersion. This is reflected in a lower peak maximum spread over many values and a larger peak. This can be due to an inhomogeneity in the transfer or very small breakage of large NP, reducing their diameter, but not forming measurable NPs. We should note that most areas of the metasurfaces on Si presented no or very low breakage.

The fact we can find different types of structures indicates that we not only need to measure a considerable number of NPs, but the images selected should also be from positions spread all over the sample. In consequence the images were taken 2mm away from each other. The approximate position of each area is indicated in Figure 5.11. In Figure 5.12 we plotted the size distribution for all of the 10 measured areas. The average NP size obtained from the measurement is 132.4 nm with a maximum at 136 nm with 3.6% b c a of the NPs. 50% of all NPs are in a 16nm interval from 128 to 144 nm. The average is shifted down relatively to the maxima due to the breakage of NPs which will always shift down the size of NPs or create multiple smaller NPs. This is clear if we compare the percentage for diameters above 150 nm to the percentage for those under 115 nm. The right side of the plot decreases faster and stays very close to 0 beyond 170 nm while the left side decreases slower and stabilizes around 0.15%. This tells us there is some breakage of the NP due to micromasking but it is not significant.

Metasurface on silica substrate

For the metasurface on silica substrate we used 12 SEM images. More than 55 000 NPs were measured, for a total surface of 2760 µm 2 .

Again, due to the breakage of NPs we set the program to remove any object with a total area smaller than one fourth that of estimated average value (circle with 170nm in diameter), meaning any object with an area smaller than that of a circle with 85nm diameter.

In Figure 5.13 we can clearly recognize the three different types of structures described in the previous section: an "ideal" structure, an area with breakage into multiple NPs and an inhomogeneous area (either due to the transfer or small breakage of the NPs). Breakage was more prevalent on the metasurface on silica compared to the one on Si.

We can identify two main differences: a shift towards bigger diameters, as anticipated by preliminary measurements and, most importantly, an increase in the percentage of smaller diameters (most clearly in Figure 5.13-b) meaning an increase in NP breakage.

Again, the images were taken 2mm away from each other. The approximate position of each area is indicated in Figure 5.14.

Metasurface substrate comparison

From the two previous sections it is clear that there is a difference between the metasurfaces obtained on a Si substrate and a silica substrate.

The first difference is the diameter of the NPs that compose each metasurface, with the metasurface on silica presenting larger NPs than the one on Si.

One possible explanation is the difference in thermal conductivity of the substrate materials.

It is well understood that the substrate temperature will affect the characteristics of RIE etching, with an increase in temperature increasing the isotropy of the etching [2][3][4]. Due to the difference in thermal conductivity between Si and silica (125 and 1.4 W/m.K) [5] of nearly two orders of magnitude the silica substrate experiences a high temperature increase, as it cannot evacuate the heat as fast to the cooled cathode, inducing an increase in the isotropy of the etching.

In the processes presented the cathode was cooled to 16 o C, but lower temperatures can be used to compensate for this effect.

The other difference was a higher presence of breakage of the NPs into smaller ones on the silica substrate due to micromasking of the openings in the resist ( § 5.4, Figure 5.8), inducing a much higher size dispersion. The metasurface on Si also presented some breakage but only for very few areas. This is most likely due to the non-conducting nature of the silica substrate.

Since charges are not evacuated properly to the cathode, positively charged areas can appear which will deflect ions creating unetched areas in the resist [6][7][8].

This may also contribute to the increase in the size of the opening in the resist observed in silica sample compared to the Si sample. The deflection of ions from the substrate surface will increase the lateral etching rate of the process which has the consequence of increasing the diameter of the openings in the resist.

Solutions to this have already been proposed such as the use of an intermediary metal layer [9] or conducting polymer [10] to evacuate the charges.

Conclusion

In this chapter we demonstrated the use of PDMS stamps in a Soft UV-NIL process for the fabrication of metasurfaces composed of Ag NPs on different types of substrates, namely Si and fused silica, with areas larger than 0.5cm 2 .

Analysis of the size of the NPs that composed each metasurface showed a difference between the metasurface on silica and Si, with the former having NPs with sizes larger than targeted and higher size dispersion (mostly due to breakage of the NPs). The metasurface on Si had sizes very close to the ones targeted. These differences are explained by the impact of the properties of the substrate on the etching step (charging of the substrate and temperature increase).

Lastly, we proposed improvements to the process, specifically for the metasurface on silica, in order to reduce the NPs size and dispersion (by reducing the breakage of the NPs).

Introduction

One of the objectives of this work is to analyze the diffusion and diffraction of structures with large areas, regardless of their level of order.

We can identify two types of analysis of our metasurfaces: one of the optical response related to the structure of the metasurface (by means of the OFT and the structure factor) and another which also takes into account the resonance of the plasmonic NPs (spectral measurements in transmittance).

In this chapter we first make use of the structure factor coupled with a computer vision program for identifying the position of large numbers of NPs to analyze the metasurfaces fabricated in the previous chapter. We establish the conditions that must be respected for a structure to be considered as non-diffracting and non-diffusing, we validate the method using OFT measurements ( § 3.5.1) and apply it to our structures.

Then, after presenting mask generation for the structure density reduction method proposed in section 4.7, we verify its impact on optical properties using the structure factor.

Lastly, we present the transmittance in the visible regime of the metasurface on silica and discuss its performance, for different structure densities.

Correlated disorder vs Subwavelength periodic structures

Considering our use case, two main characteristics are required (other than transmittance in the visible regime), to ensure the transparence of our device is not deteriorated:

1. Non-diffraction within the user observation conditions

Non-diffusion within the user observation conditions

The approach we chose to obtain structures which respect to these two conditions was using subwavelength periodic structures. Periodic structures are inherently ordered and so, do not present diffusion. With subwavelength periodicities they will present diffraction outside the visible regime. More precisely, based on equation 3.11, which we recall is:

𝜃 = arcsin 𝜆 𝑝 (6.1)
the largest wavelength that the structure will diffract is the same as its periodicity, meaning 220nm, which is well outside the visible regime at a grazing angle (90 o ).

User observation conditions

The structure factor is a very good tool to numerically analyze the optical response of various structures and can be used to identify whether a structure respects the two characteristics, non-diffusion, and non-diffraction, within the user observation conditions.

We must first define the values of the scattering vector which corresponds to our user observation conditions.

The wavelength interval will be that of the visible spectrum, meaning 400 to 800 nm.

For our application we consider that the user will not observe the device at angles wider than 60°. Thus, this is our maximum viewing angle.

Our minimum viewing angle was taken as being the angle whose area of angle opening was 10 times inferior to the area of angle opening of 60°. This is represented in Figure 6.1. We considered that light diffracted at this angle will be confused with the specular reflection. So, the minimum angle is:

(sin (𝜃 )) . 𝜋 = (sin(60°) This means that we do not want diffraction nor diffusion for values of the scattering vector between 𝑞 and 𝑞 .

Identification of diffraction and diffusion in the structure factor

When looking at the structure factor, diffraction will be represented by a significant increase for a small interval of the scattering vector. By using subwavelength structures, we are effectively "pushing" the diffraction peak to short wavelength and wide degrees, meaning large values of the diffraction vector. This means that the diffraction peak of our structure should appear at values of the diffraction vector larger than 𝑞 to be outside our user observation conditions.

In order word's, by using subwavelength structures we are placing our observation conditions "in front" of the first diffraction as is represented in Figure 6.2. The other optical phenomenon we want to avoid is diffusion. Since diffusion is the emission of light by a structure at multiple angles it will be represented by an increase in the structure factor over a large interval of the scattering vector. For example, the structure factor of a perfectly diffusive structure would be equal to 1 for all values of the scattering vector since it emits equally at all angles. Nevertheless, a structure with values lower than 1 may still be diffusive. To quantify at what value of the structure factor a structure becomes diffusive we can analyze structures we know to be diffusive and non-diffusive.

For this purpose, we show in Figure 6.3 the structure factor of a hexagonal structure and multiple correlated disorder structure zoomed on the area in front of the diffraction peak.

Since the structures have different dimensions the diffraction vector is normalized by multiplying it by the average first-neighbor distance (D) making them comparable to each other (see Figure 3.2). We have highlighted the structure factor of the hexagonal structure. Since this structure is perfectly ordered it is non-diffusing.

For generated correlated disorder structures we present two non-diffusing structures (full lines) and two diffusing structures (dashed lines). The non-diffusing structure are generated with 100 iterations which ensures a good level of order while the diffusing structures are generated with only 10 iterations resulting in higher disorder. For both cases we present one structure generated with 10k mesh points per particle and another with 5k mesh points per particle.

Unexpectedly we see that the structure factor of the hexagonal structure starts increasing earlier than the other non-diffusing structures (around 𝑞. 𝐷 = 2). This is due to the diffraction figure seen by the structure factor due to the rectangular shape of our image and not actual diffusion by the structure. This is clear if we look at the 2D version of the structure of the hexagonal structure presented in Figure 6.4. Correlated disorder structures are generated transform (OFT).

The OFT gives us an intensity in function of the diffracted wave-vector for a beam at normal incidence, a specific case of the structure factor where the incident wave-vector is set and only the diffracted wave-vector changes. By comparing the diffraction image obtained in the OFT bench and the 2D structure factor we can see whether there is an agreement between the experimental measurement and the simulated result.

This measurement set-up cannot be used directly on 220nm structures since they do not diffract in the visible regime. For this reason, the validation step was done using selfassembled 1µm PS NSs structures.

In Figure 6.5 we do a side-to-side comparison of the structure factor (left) and OFT (right) for two samples obtained by self-assembly of 1µm PS particles under the same conditions. Even though the self-assembled structure is hexagonal, due to imperfections in the structure and changes in the direction of the direction of the periodicity (multi-crystalline like structure) we obtain a ring shape which corresponds to the first-order diffraction. Higher orders are not presented since the angles corresponding to those orders cannot be collected by our optical system ( § 3.5.1). For each of the figures we present the measurement of the diameter of the diffraction ring in terms of the diffraction vector.

We can also see that there is some asymmetricity in the OFT (particularly on the figure on the upper right). This is likely due to asymmetricities in our optical bench such as non-perfect alignment of lenses or of the sample with the objective.

If we compare the two samples to each other there are certain elements that allows to conclude Sample 1 is more disordered than Sample 2:

Sample 2 presents spots of high emission (red areas) in the diffraction ring both in the Structure Factor and OFT, which are characteristic of structure with preferential directions in its periodicity. Sample 1 on the other hand presents a more homogeneous emission for all direction indicating a more isotropic structure, which, for a hexagonal-like structure (which we expect to obtain with self-assembly) means higher disorder.

Other elements that support this is the larger diameter of Sample 2. For structures resulting of the self-assembly of spherical particles, a perfectly ordered area will have first-neighbor distances equal to the diameter of the particles. If such a structure becomes disordered the first-neighbor distance can only increase since particles cannot get closer to each other than their diameter. The consequence is that the structure with higher disorder will have higher firstneighbor distance which means they will diffract at smaller angles which will result in diffraction at a lower value of the diffraction vector. We can then conclude that the larger diameter of the diffraction ring of Sample 2 means this structure is more ordered than Sample 1.

This means that both the structure factor and the OFT give similar indications in terms of the order of the structure.

If we now look at the measured diameter of the diffraction ring, we can see we have a difference between the structure factor and the OFT. The relative difference is 3.17% for We present the measurements of the diameter of the diffraction ring in term of the diffraction vector.

Sample 1 and 5.15% Sample 2. Multiple factors can explain this difference:

The first one is the previously mentioned non-perfect alignment of lenses or of the sample with the objective inducing a deformation of the OFT.

Another possible factor is a dispersion of the incident wave-vector, due to imaging for multiple wavelength (the filter width was 5nm for both OFTs) and non-perfectly collimated beam.

Lastly, we were not able to ensure the structure factor and the OFT were done on the same areas of the same structure. Local differences between the areas can explain differences between the figures obtained.

Nevertheless, the relative errors obtained are within values that allow us to have good confidence in the results obtained with the structure factor and validate its use to analyze the diffraction and diffusion of structures that cannot be characterized with an OFT.

Structure factor analysis

Fabricated metasurfaces

In this section we present the characterization of the fabricated metasurfaces, in terms of diffusion and diffraction using the structure factor.

As we saw in section 5.5 different areas of the metasurface present different size distributions due to breakage. This breakage also affects the level of order of the structure since NPs resulting from breakage will have non-periodic positions. This means areas with breakage will be more disordered and, in consequence, are expected to present higher levels of diffusion.

For this reason, we studied the metasurfaces on Si and silica for areas with low and high breakage which are indicated in Figure 6.6. In Figure 6.7 we present the structure factor for these 4 different types of areas. The red vertical lines in the plot represent 𝑞 and 𝑞 . In Figure 6.8 we have the structure factor for the same areas, calculated for a smaller range of the diffraction vector closer to the user observation conditions and with a higher resolution.

The first thing to note in Figure 6.7 is that the diffraction peak of all structures is well outside the user's observation conditions which allows us to conclude that diffraction will not affect the optical properties of the device for our application.

There is also a clear difference between the metasurface on Si and silica, with the diffraction peak for the Si structure appearing at lower values of the diffraction vector. This difference is most likely due to deformation of the image on silica due to charging of the substrate on the SEM which compresses the measured dimensions and not due to the structures on silica being more ordered.

Indeed, in Figure 6.8 the structure on silica consistently presents higher values (indicating higher diffusion) than the one on Si.

If we consider the average first neighbor distance for the four areas being analyzed (Table 6.1) the sample on silica presents a lower first neighbor distances. Considering that the two samples were fabricated using the same stamp, the first neighbor distance should be approximately the same, which makes us to conclude that this apparent difference is due to the measurement as previously stated. This error should be considered when doing measurements on samples on insolating substrate with SEM images and further work is required to properly quantify this error. If we now compare the areas with different levels of breakage on the same substrate, as expected, the areas with higher breakage are more disordered which is indicated by lower and wider diffraction peaks.

If we now interest ourselves in the diffusion by the structures in Figure 6.8, areas with higher breakage present higher level of diffusion than the areas with low breakage. The areas with high breakage do not respect our minimum requirement for non-diffusion of remaining under 0.1, while for the low breakage areas the stay below this value for most of the user observation conditions with the one on Si even staying below the ideal level of 0.05. The increase for low values of the diffraction vector is due to the diffraction figure seen by the structure factor due to the rectangular shape of our image and not diffusion by the structure as we mentioned previously. We can see this in 2D structure factor for the structure on Si substrate with low breakage in Figure 6.9.

We can conclude that the structures we obtain respect the non-diffraction and non-diffusion conditions as long as they do not have large amounts of breakage.

This result is qualitatively confirmed by the visual effect of metasurface on silica when observing an object behind. Indeed, in Figure 6.10, we can see the logo of our lab behind the metasurface clearly with the main optical impact being a blue coloration (which indicates lower filtering of short wavelengths). We can conclude that the transparency of the metasurface is sufficient for our application.

Metasurfaces with density reduction

One of the important parameters we need to control is the NP density due to its impact on the reflectance and transmittance of the metasurface.

The density of our structures is 22NPs/µm 2 . If we base ourselves on the results obtained by Bertin et al. [1] presented in Figure 2.6 ( § 2.6), we can expect an averaged transmittance of less than 60% for the whole visible spectrum which is not ideal for HUD applications (the measured average transmittance was ~35%, cf § 6.5).

This means that if we use subwavelength structure, we must then remove some of the NPs to reduce the overall density.

How we select the NPs to remove will have an impact on the optical response of the structure.

For example, Figure 6.11 on the left presents the structure factor for a structure with NPs removed periodically (here we used a square lattice of areas to remove). In these images we can see small red spots (circled in red) which represent diffraction peaks by this periodic removal of NPs.

If we remove the NPs randomly the consequence will be an increase in disorder and in consequence an increase of the diffusion. This is clear on the right of Figure 6.11 which represents the structure factor of a structure with NPs removed randomly. We can see that multiple points inside the user observation zone are higher than 1 and most are well above 0.1. To solve this problem, we decided to numerically create a mask for density reduction using correlated disorder.

Using the correlated disorder structure generation program presented in section 3.2, we generate a first structure, which defines the central positions of the areas. A second correlated disorder structure is generated whose points will be used to define the edge of the areas. The areas are defined by all the points of the second generated structure which are closer to the edge of a circle with the selected radius with its center being a point of the first generated structure. The radius is set depending on ratio of density reduction required. A schematic of the constructions of this mask is presented in Figure 6.12.

To study the optical impact of this density reduction, we numerically overlaid the mask on structures obtained, generating new structure with a reduced density by keeping the NPs that were inside or outside of the areas (see Figure 6.13). We chose an area on the Si sample with almost no breakage to ensure that the structure factor obtained was not affected by the increased disorder created by it. In Figure 6.14 we present the structure factor for two structures with reduced density, obtained from the same original structure, one where the NPs inside the mask areas were kept and the other where the NPs outside were kept. Both have a 0.5 density reduction factor so the final density is the same for both structures. The first thing to note is that keeping the NPs inside or outside the mask areas does not have a significant effect on the structure factor. The density reduction technique we decided to use was to keep the NPs inside the mask areas.

Furthermore, we can see two effects of the density reduction:

1. A widening of the basis and lowering of the original structure diffraction peak 2. The creation of a second diffraction peak due to the mask structure

The widening of the basis is due to the convolution of the diffraction figure of the shape of the areas used for density reduction with the diffraction of the original structure. This in turn reduces the diffraction by the original structure which reduces the height of the peak.

The appearance of a second peak is due to the diffraction by the correlated disorder structure used to determine the location of each area on the structure.

By plotting the structure factor for structures obtained with different distances between masking zones (keeping the 0.5 reduction ratio), we see that these two effects change with the variation of the distance (Figure 6. 15).

By looking at the image on the lower right, zoomed in on the diffraction peak, we can see the widening of the basis of the diffraction peak decreases with the increase of the distance between areas while the height of the peak has the tendency to increase. Indeed, as the distance between areas increases, for a constant density, the size of the areas must increase which in turn will reduce the width of the diffraction figure created by that area (increase in direct space is a decrease in the reciprocal space).

In the image on the lower left, we see that as the distance increases the diffraction peak associated with the structure is "pushed" towards lower values of the scattering vector (larger distance means diffraction at smaller angles) and, in consequence, out of the user's observation conditions. What both results indicate is that using higher distances between areas will eliminate any optical effect caused by the density reduction, within the user observation conditions.

If we now interest ourselves in the diffusion, we can see in Figure 6.16, that the larger the distance between areas the lower the value of the structure factor will be inside the observation conditions (due to the diffraction peak created by the structure moving toward lower values of the diffraction vector), which means the diffusion by the structure will be lower. The structure with 10 µm between areas stays below minimum level for non-diffusion of 0.1 for most of the user observation conditions. Nevertheless, we can see an increase of its structure factor for small values of the diffraction vector. From the 2D structure factor, with the observation conditions highlighted (space between the green areas), presented in Figure 6.17, we can conclude that this increase is not due to the diffraction figure seen by the structure factor due to the rectangular shape of our image (this rectangular shape is mostly eliminated by the density reduction) but is indeed due to an increase of the diffusion. We can then expect that even for distances of 10 µm between areas we will have some low-level diffusion for the shorter wavelengths. Due to limitations in computational capacity, we could not simulate larger distances between areas (which required larger images with more NPs). Based on these results, we can expect that diffusion will be eliminated for large distances while maintaining the non-diffraction condition. For this reason, we used a mask with distances between areas of 100 µm for the density reduction process presented in section 4.8.

Transmittance measurement

As we have established previously, the main objective of using plasmonic resonant structure for a reflective combiner plate is to have wavelength selective reflection, while keeping high transmittance on the whole visible range.

The selectivity of our metasurface, was measured using the ISOLASER bench presented in section 3.5.2. Here the transmittance of the sample was measured at normal incidence with linearly polarized light. Due to the isotropic nature of our structure and the circular shape of our NPs, we did not select a particular polarization.

Due to the large surface inhomogeneities identified in terms of disorder, dispersion and breakage, we characterized multiple positions in the sample which are indicated in Figure 6.18. The transmittance of each position and their average is presented in Figure 6.20. The first thing we can notice is that transmittance minimum, corresponding to the resonance of the NPs is red-shifted relatively to the one targeted (550nm), for all positions.

If we take the average transmittance, the minimum is around 700 nm. Based on the average NP size of 160nm we would expect to have a resonance at 590 nm (for Ag NP). Even if we take 170 nm NP, which is the NP size most present in our sample the resonant wavelength shifts to 600 nm giving a 100 nm off set from the 700 nm we obtain from the characterization. This means the error cannot be explained only by the NP size.

There are two factors that can contribute to this shift:

The first is a Ge adhesion layer thicker than the 1 nm targeted. From Figure 6.19 on the left, we observe that an increase in the thickness of the Ge will shift the resonance of the NPs to longer wavelength. This agrees with ellipsometry measurement performed which indicated a Ge layer of around 4 nm, revealing an error during the deposition step.

The second factor is an increased proximity of the NPs. In Figure 6.19 in the center and on the right, we have the transmittance in function of the distance between NPs for diameters of 160 nm and 80 nm respectively. For both cases we have a shift of the resonance to longer wavelengths which accelerates as the NPs get closer. In case of 80nm NP we can see that at very small distance they will resonate like a larger particle.

Due to the micro masking and resulting NP breakage that occurs during fabrication ( § 5.4),

NPs can split into many that very small distance. Even if the resonance of a single smaller NP is blue-shifted, their proximity induces a resonance red-shift. Additionally, the proximity of a small NP to larger NP will also induces a red-shift as well. All these phenomena can contribute to a shift of the minimum in the transmittance spectrum to longer wavelengths. The average transmittance is 30% (average of the transmittance at each wavelength), which is lower than the targeted value for reflective displays. This is partially explained by the high NPs density of our structure; but based on the results by Bertin et al. [1], we would have expected an average transmittance (integrated for both polarizations) closer to 50%. This lower average transmittance is most likely also due to the dispersion in the NP size. This means that multiple wavelengths will resonate with different NPs, increasing the overall reflectance over the whole visible spectrum and lowering it for the targeted wavelength.

This will also cause the metasurface to have less wavelength selectivity, meaning it will be less efficient for a single wavelength. Yet, this large resonance could be exploited for reflecting polychromatic images since multiple wavelengths can be reflected with higher intensities.

We should note that certain areas in the metasurface presented resonances with higher wavelength selectivity as is shown in Figure 6.21. For this area we have an average transmittance of 34.6% and a minimum transmittance of 14.6% at 590 nm and a much thinner resonance. This local improvement in the optical parameters targeted is likely due to a locally low size dispersion, which explains the thinner resonance, lower minimum transmittance and higher average transmittance, and low NP size, which explains the shift of the resonant wavelength (the smaller NP size will also have a small but non negligible impact on the width of the resonance since smaller NPs have thinner resonances). We should note this measurement was done without the optical filters used to remove second order diffraction modes to maximize the optical signal (due to low emission from the light source).

The resonance presented shows that, despite less than ideal optical parameters, structures fabricated with our method can have better performances with the necessary improvements in terms of NP size control, NP size dispersion and breakage (which would also lower NP size dispersion).

Overall optical performance

After analyzing the optical characteristics of the fabricated metasurface we can conclude that the fabrication process we developed has the potential to be used to fabricate plate combiners for AR systems, but further improvements are necessary.

In terms of transmission the performances obtained did not match the ones targeted as discussed in the previous section. Nevertheless, the sample can do color filtering due to an increased transmission for short wavelengths. We can understand this from Figure 6.22

where we observe that the sample has a blue color in transmission, but the image behind clearly visible. We can see we obtain enhanced reflection compared to standard glass. We circled in red areas outside the metasurface, which is itself circled with a white dashed line. We clearly have a lower reflected intensity outside the metasurface. The image on the metasurface is reflected with an intensity level that is readable by the user, while maintaining the capacity of seeing objects behind it. The structure with reduced density has smaller NPs for the same dosage (most likely due to proximity effects). This is consistent with the transmittance measurement (Figure 6.24) where the reduced density structures have a shorter resonant wavelength. We should note this measurement was done without the optical filters used to remove second order diffraction. We can evaluate this method for controlling the average transmittance of our sample:

we have extracted from the transmittance plots, the average transmittance of each structure, presented in Table 6.3. For a density reduction of half, we increase the average transmittance by approximately 1.7. In terms of the minimum transmittance (associated with the resonance of the NPs) we have a stronger attenuation of 3.6 for most of the structures fabricated, as shown in Table 6.4. Considering the structures fabricated have a 200 nm NP distance, for an hexagonal structure the NP density is 28.86 NP/µm 2 . This means that our density reduced structures have What we observe is that our structure has a higher average transmittance and lower 1 -𝑇 for 14.43 NP/µm 2 than would be expected from the other results presented. We can conclude that structures obtained with our density reduction method have optical properties equivalent to uniform structures (in this case square and correlated disorder lattice) with lower densities. For our structure the equivalent density is approximately 10 NP/µm 2 .

Nevertheless, we can conclude that this method can be used to obtain structures with optical effects of diffraction and diffusion of structures with subwavelengths NP distances while having transmittance and reflectance characteristics of structure with lower densities. The reflectance maxima (R peaks) and the average transmittance (Ttot) had been measured for square (Sq) or correlated disordered (Rd) lattices, and S and/or P polarization. The arrays density was uniform.

Chapter 7 :

Conclusion and future work

Introduction

We have proposed in this work two main developments which are required for optical metasurfaces use in macroscopic applications: large surface low-cost fabrication process and method for analyzing optical characteristics of metasurfaces due to their structure.

Large surface low-cost fabrication

Even though metasurfaces show great promise due to their unique optical characteristics and the possibility to tune very finely these, their fabrication is mostly limited to research laboratories since their cost is still too high for any industrial level application, especially when macroscopic areas are required. For these reasons, the first development is a new approach to fabricate large area metasurfaces.

We successfully demonstrated a fabrication technique for large surface PDMS stamps using a combination of PS NS self-assembly and PDMS plasma etching.

The use of self-assembly makes it possible to fabricate large areas, since surfaces with more than 1cm 2 can be obtained with a simple set-up. This maintains the cost of fabrication low compared to techniques such as electron-beam lithography, while being able to reach comparable and even higher dimensions.

PDMS etching decorrelates the minimum dimensions achievable from the viscosity of the polymer, without the need to change its chemical or physico-chemical properties [1,2](i.e.

PDMS dilution in solvents). Compared to other methods that allow to go beyond the limit imposed by the PDMS viscosity [3], PDMS etching presents itself as a simpler process that only requires usual micro-and nanofabrication facilities (standard RIE machine).

We showed further that these stamps can be used in gravitational NIL: this shows the ease of use of the fabricated stamps which do not require specific facilities such as NIL machine. This also lowers the barrier of entry for laboratories and research groups that want to experiment with NIL for their fabrication processes since the initial investment required is much lower.

This is an important step to help developing the use of NIL as a standard lithographic process.

More importantly, the global process proposed here includes much less (typically the half) technological steps than the usual process using molded stamps, and the most critical step (NS self-assembly) is the first one.

Finally, this process is able to compete with the NPs dimensions presented in the state of the art and, at the same time, to reach large areas.

Discussion on process improvements

Nevertheless, this process still requires improvements to become compatible with industry level fabrication. The main point that requires improvements is the control of NP size and its dispersion.

In terms of the size control, we have discussed possible solutions such as improving anisotropic PDMS etching processes to avoid the adhesion to the imprint resist, as proposed in section 4.6. This would allow us the use of reduced PS NS masks to tune the size of the final NPs obtained.

In section 4.6 as well, we discuss the possibility of doing NP size control, during the resist etching process thanks to the conical shape of patterned holes. Higher anisotropic resist layer etching is the main requirement to be able to use these techniques.

As far as the size dispersion is concerned, the first improvement that can be made is the use of lower viscosity imprint resist. This would enable the spinning of resist layers with the required thickness without needing high spinning speeds that created inhomogeneities in the resist layer thickness which create size dispersion in the final NPs ( § 5.2).

The second improvement required concerns specifically the fabrication on non-conducting substrate, which present high breakage on NP due to micromasking of the resist openings.

Indeed, as we discussed in section 5.4.2, the samples fabricated presents high size dispersion particularly in the case of the metasurface on silica.

Our hypothesis is that due to the insulating nature of silica there is accumulation of charges in certain areas of the surface which will deflect ions and "protect" the resist from etching. In section 5.5 we discussed the use of a metallic or conducting polymer layer to suppress surface charging. Considering our process, a conducting polymer such a PMMA Electra 92 seems more compatible (using metallic layer may require wet etching). This polymer layer could be placed before the PMMA A2 layer forming a resist trilayer (or could even replace the PMMA A2 layer). Since the Electra is also etchable with an O2 the rest of the process would remain unchanged.

calculation of larger surfaces with more NPs with a higher diffraction vector resolution.

Longer term perspectives

Resonance control

In this work we presented a novel fabrication process for PDMS stamps and NPs density reduction of metasurfaces. With some change to the process these could be adapted to obtain various interesting devices.

For example, the density reduction process could be adapted to obtain areas with different wavelengths of resonance, resulting in a polychromatic combiner plate. This can be done in three ways:

The first option is the optical lithography to mask certain areas and do a short etching of the resist layer in order to increase the size of the patterned holes in areas exposed without transferring the pattern. This can then be repeated masking a smaller set of areas. Lastly the rest of the process is be done. The areas that were exposed to more initial etching step will have larger size while the ones exposed to less etching will have smaller sizes (Figure 7.1)

resulting in different resonances. The second option is to first do the full etching of the bilayer followed by a first metallic deposition. Then, use the density reduction process to mask certain areas. Following that another metal deposition is done. We then increase the mask areas (with a second lithography) and repeat the metal deposition to obtain NP with different height which will sort of resonance most likely due to the isotropic nature of our structure (change of direction of the periodicity every few µm). Yet, a study that combines these two aspects is important to characterize at what degree of long range order this sort of resonances start to have an impact of the properties of the device.

Recently more research have taken interest to this question and have started to study the case of non-periodic structures using the structure factor as a tool to characterize the level of order. Hyperuniform structures have been an area of particular interest due to their nature being non-periodic and non-disordered at the same time [5,7,8] (correlated disorder is a subtype of hyperuniform structure). In this context our self-assembled structure is a new type of structure being both periodic and anisotropic which also has the characteristic of hyperuniformity. For Si substrates we use 2 inch wafer and squares of 2x2cm cut from 4 inch wafer. Following an O2 plasma, the substrate shows good hydrophilic behavior, due to the creating of silanol group on its surface. The monolayer adheres well during the removal from the solution.

Annexes

We could observe that the particles formed bridge-like connections between them (Figure 1). This effect is not uncommon and has been observed in other self-assembled PS NSs processes [1].

NS size reduction On Si substrate

For samples on Si we used the same RIE process described in section 4.2. The results for the 1 µm NSs are presented in Table 1. The calibration was then repeated for 200nm particles. The results are presented in Table 2. Due the flattened shape of the particles the lift-off process was not successful for thick Al layer or very small particles. To ensure the particles were lifted across most of the surface the Al layer cannot be thicker than 8nm. A lower thickness would not mask the Si properly. In terms of particle size, we were not able to lift-off NSs with diameters reduced to less than 70nm.

The following step is an Si etch performed with ICP-RIE machine to obtain the master mold (Figure 4) (15mTorr (20 µbar) with 160 sccm of SF6, 160 sccm of C4F8 ,20 W for the platen HF and 1000 W for the RF source). The etch rate is 600nm/min. To ensure the stamp does not stick to the mold after reticulation it goes through a silanization treatment followed by a TMCS antisticking process.

PDMS molding technique

The mold fabrication described in this section was performed by Frédéric Hamouda.

Due to the 100nm dimensions of the holes in the master the viscosity of the polymer used must be lower than standard PDMS for it to flow inside these patterned holes. For this reason, we test 2 different options: Hard-PDMS, and PDMS diluted in hexane. The results are presented in Table 4. likely they will adhere to each other 2. Form factor of the elements. Higher form factor elements have the tendency to collapse 3. Young's modulus of the substance. The lower the modulus the more likely to collapse

The stamps obtained using Hard-PDMS presented a height of more than 45nm and no collapsing. This is an improvement compared to the stamps obtained with standard PDMS, but the height is still within a range that is difficult to use for the gravitational NIL technique we used. Furthermore, the Hard-PDMS did not fill all the holes in master resulting in an incomplete pattern (Figure 7). We can observe that the pattern of the stamp obtained is incomplete.

2

  State of the art ___________________________________________________________ Introduction _____________________________________________________________________ Self-assembly of PS NSs and size reduction ____________________________________________ Self-assembled PS NSs structure as an etch mask _______________________________________ PDMS etching ____________________________________________________________________ Soft UV-NIL using PDMS stamp ______________________________________________________ 2.5.1 PDMS stamp for sub-micrometric structure fabrication _____________________________ 2.5.2 Fabrication of plasmonic metasurface by Soft UV-NIL _______________________________ Plasmonic metasurfaces for transparent displays _______________________________________ Objectives with respect to the state of the art__________________________________________ Bibliography _____________________________________________________________________ 3 Fundamental concepts and numerical tools ____________________________________ Introduction _____________________________________________________________________ Structure factor __________________________________________________________________ Numerical generation of correlated disordered structures ________________________________ 3substrate _______________________________________________ PS NSs size reduction on PDMS ______________________________________________________ Stamp fabrication by PDMS direct etching _____________________________________________ 4_____________________________________________________________________ Comparison with standard stamp fabrication by molding _________________________________ Propositions for process improvements _______________________________________________ Toward metasurface density control _________________________________________________ Conclusion ______________________________________________________________________ Bibliography __________________________________________________________________ 5 Fabrication of plasmonic metasurfaces ________________________________________ Introduction _____________________________________________________________________ PDMS stamp _____________________________________________________________________ Fabrication on Si substrate _________________________________________________________ Fabrication on fused Silica substrate _________________________________________________ Size dispersion analysis of the fabricated metasurfaces __________________________________ 5and diffusion in the structure factor _____________________ Validation of the structure factor ___________________________________________________ Structure factor analysis __________________________________________________________ 6.4.1 Fabricated metasurfaces _____________________________________________________ 6.4.2 Metasurfaces with density reduction ___________________________________________ Transmittance measurement ______________________________________________________ Overall optical performance _______________________________________________________ Transmission for metasurfaces with reduced density ___________________________________ Conclusion _____________________________________________________________________ Bibliography ____________________________________________________________________ 7 Conclusion and future work ________________________________________________ Introduction ____________________________________________________________________ Large surface low-cost fabrication __________________________________________________ 7.2.1 Discussion on process improvements ___________________________________________ 7.2.2 Integration of density control in the full process __________________________________ xxii Structure factor for structure analysis _______________________________________________ Longer term perspectives _________________________________________________________ 7interaction between the NPs resonance and structure order _____________ Bibliography ____________________________________________________________________ Annexes ____________________________________________________________________ ANNEX 1: Metasurface fabrication with PS NS self-assembly on Si substrate (using standard soft UV-NIL process) ______________________________________________________________ NS self-assembly onto Si substrate ____________________________________________________ NS size reduction On Si substrate ______________________________________________________ PDMS molding technique ____________________________________________________________ ANNEX 2: Deposition of 1 µm PS NSs self-assembled layer on PDMS ____________________ Bibliography _________________________________________________________________ ix Résumé en français: Développement de composants grande surface à nanostructures résonantes pour systèmes de réalité augmentée Contexte technologique Avec l'évolution de la technologie et son intégration dans notre vie quotidienne, la réalité augmentée (RA) découle de cette fusion entre la perception du réel et le numérique. Les dispositifs RA dits optiques sont basés sur un affichage transparent permettant à l'utilisateur d'observer directement le monde réel tout en y superposant un objet virtuel. Une façon d'y parvenir est d'utiliser un affichage réfléchissant. Ce type de dispositif comporte un afficheur lumineux et une lame (dite de combinaison) sur laquelle se reflète l'image de l'afficheur.

Figure 1 -

 1 Figure 1 -(gauche) Représentation schématique des propriétés optiques d'une plaque de combinaison réfléchissante classique et (à droite) exemples d'un HUD dans un avion de chasse. Une solution à ce problème est d'avoir une réflexion plus sélective en longueur d'onde. Si la réflexion de la lame de combinaison à la longueur d'onde de la source lumineuse est, par exemple, 60%, tout en laissant la lame essentiellement transmissive pour le reste du spectre visible, l'utilisateur pourra toujours voir l'extérieur et la puissance de la source lumineuse sera réduite de moitié.

Figure 3 -

 3 Figure 3 -Mesure AFM du timbre obtenu (gauche) en coupe et (droite) en 3D.

Figure 2 -

 2 Figure 2 -(gauche) Configuration du dépôt, (centre) formation de la monocouche et (droite) image MEB de la monocouche de PS NP n PDMS

Figure 4 - 1 )

 41 Figure 4 -1) Le tampon est placé sur le substrat recouvert d'une couche de PMMA et d'Amonil. L'échantillon est exposé aux UV pour réticuler la résine AMONIL 2) Le motif est transféré sur la résine après le retrait du tampon3) La couche résiduelle d'AMONIL est retirée par gravure 4) La couche de PMMA est retirée par gravure 5) Une couche d'Ag est déposée sur l'échantillon 6) La PMMA est retirée laissant seulement le substrat avec des NPs d'Ag (lift-off).

Figure 5 -

 5 Figure 5 -Images MEB et photo macroscopique des metasurfaces fabriquées sur (gauche) Si et (droite) Silice.En considérant que la densité de notre structure est de 22NP/µm² et que la surface totale est de 0,67cm 2 , nous pouvons estimer que le nombre total de NPs dans la structure est proche de 1,5 milliards. Pour cette raison, mesurer seulement quelques dizaines de NPs ne nous donne pas un

Figure 6 -

 6 Figure 6 -(gauche) Schéma des positions approximatives des images prises pour les mesures de tailles.(droite) Histogramme de la distribution de la taille de la métasurface sur le substrat Si.

Figure 7 -

 7 Figure 7 -(gauche) Schéma des positions approximatives des images prises pour les mesures de tailles.(droite) Histogramme de la distribution de la taille de la métasurface sur le substrat de silice.Ici 50% de toutes les NPs sont dans un intervalle de 18nm entre 161 et 179nm. La taille moyenne des NPs obtenue par la mesure est de 160,9nm avec un maximum à 172nm avec 3,2% des NPs. La moyenne est décalée vers le bas par rapport au maximum en raison de la rupture des NPs que nous avons pu observer en microscopie.

Figure 8 -

 8 Figure 8 -Transmittance mesurée pour (gauche) différentes zones de la métasurface et la moyenne des mesures et (droite) une zone spécifique de la métasurface qui a présenté une résonance plus fine à de courtes longueur d'onde. La transmittance moyenne était de 30 %, avec une transmittance minimale de 20 % à environ 700 nm. Certaines zones présentaient une résonance améliorée qui se traduisait par une transmittance moyenne de 34,6 % et une transmittance minimale de 14,6 % à 590 nm (Figure 8, à droite).

Figure 9 -

 9 Figure 9 -Description schématique des paramètres utilisés pour calculer le facteur de structure.

Figure 10 -

 10 Figure 10 -Facteur de structure des metasurfaces fabriquées pour les conditions d'observations de l'utilisateur.Le facteur de structure des métasurfaces reste inférieur à 0,1, la métasurface sur silice présentant une valeur légèrement supérieure. Néanmoins, nous pouvons conclure que les structures que nous obtenons respectent les conditions de non-diffraction et de non-diffusion.

Figure 11 -

 11 Figure 11 -Observation d'une image à l'arrière de la métasurface sur la silice.

Figure 12 -

 12 Figure 12 -Comparaison de notre metasurface (droite) avec celle fabriquée par Bertin et al. (gauche)

  of the work presented in this manuscript is concerned with the development of elements for AR systems based on plasmonic metasurfaces. AR systems, such as Head-Up Displays or Head-Mounted Displays are of particular interest to different domains including Mobility, Automotive and Defense. The present work has been co-founded by the Defense Innovation Agency to improve the fabrication and characterization of transparent combiner plates used in these systems.

Figure 1 . 1 -

 11 Figure 1.1 -The first augmented reality device known as "Sword of Damocles".

Figure 1 . 2 -

 12 Figure 1.2 -Example of (left) video blending, using a smartphone and (right) optical blending for AR.

Figure 1 . 3 -

 13 Figure 1.3 -(left) Google glasses are one example of a commercial application of reflective display for AR and (right) working principle of this device.

Plasmonics 1 . 3 . 1

 131 Definition and historyWhen talking about the modern history of plasmonics we must distinguish two types, which were studied as separate phenomena for a long time: surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs).

Figure 1 . 4 -

 14 Figure 1.4 -Schematic representation of the optical properties of a classic reflective combiner plate.

Figure 1 . 5 -

 15 Figure 1.5 -The Lycurgus cup in (left) reflection mode and (right) and transmission mode.

Figure 1 . 6 -

 16 Figure 1.6 -Schematic representation of a plasmonic resonance from Sun et al. [7]

Figure 1 . 7 -

 17 Figure 1.7 -Opaque glass, example of a translucent surface.

Figure 1 . 8 -

 18 Figure 1.8 -Schematic representation of opaque, translucent, and transparent objects.

  Introduction ....................................................................................................................................... Self-assembly of PS NSs and size reduction ....................................................................................... Self-assembled PS NSs structure as an etch mask ............................................................................. PDMS etching .................................................................................................................................... Soft UV-NIL using PDMS stamp ......................................................................................................... 2.5.1 PDMS stamp for sub-micrometric structure fabrication .......................................................... 2.5.2 Fabrication of plasmonic metasurface by Soft UV-NIL ............................................................ Plasmonic metasurfaces for transparent displays ............................................................................. Objectives with respect to the state of the art ................................................................................. Bibliography ....................................................................................................................................... Introduction One of the main objectives of this work is to propose solutions to fabricate a large area plasmonic metasurface at a low cost, which could be used for augmented reality in the visible spectral range (i.e. for transparent displays). This implies to control simultaneously:  Organization of the metallic nanostructures on a glass plate, with a sub-wavelength (periodic or not) pitch, or with a correlated disorder in case of sup-wavelength average first-neighbor distances  With nanostructures of ~100 nm typical dimensions to have plasmonic resonance in the visible range,  For several cm² surface fabrication,  With specific densities of nanostructures to reach relevant optical performance.

(Figure 2 . 1 . 4 )

 214 . This technique, proposed in 2007, allowed for the deposition of ordered structure with areas of 1cm 2 and was also the first reported deposition of self-assembled PS NSs onto polymer substrates. This technique was improved upon by Vogel et al. [18] (Figure 2.1.3) by adding sodium dodecyl sulfate (SDS) as surfactant which increases the water surface tension to obtain larger and more ordered monolayer structures, reaching depositions over an entire 2 inches Si wafer.

Figure 2 . 1 -

 21 Figure 2.1 -Results presented in the state of the art for PS NSs self-assembling 1) Full process by Haginoya et al. [11] to obtain nanohole patterned Si from self-assembly of PS NSs. 2) PS NSs after reduction by an isotropic RIE-ICP process by Plettl et al. [13] 3) (top) Schematic of the water-interface deposition method developed by Vogel et al. [18] and (bottom) deposition on a full 2-inch Si wafer. 4) Schematic of the water-interface deposition method developed by Weekes et al. [17] 5) Self-assembled PS particles on PDMS by Chen et al. [19].

Figure 2 . 2 -

 22 Figure 2.2 -Results presented in the state of the art for PS NSs as an etch mask 1) Process proposed by Ye et al. [26] for fabricating a subwavelength grating on fused silica using PS NSs and results using this process 2) Process proposed by Huang et al. [22] for the fabrication of Si nanowires by wet etching using PS NSs and results using this process 3) Pyramidal honeycomb structure fabricated by Chen et al. [23] 4) Structure fabricated by Weekes et al. [17].

Figure 2 . 3 -

 23 Figure 2.3 -Results presented in the state of the art for PDMS structuring 1) (top) PDMS etching process developed by Chen et al.[31] and (bottom) structures fabricated using this process. 2) Structures in PDMS fabricated by Hwang et al.[33] using a metallic mask for dry etching. 3) Hexagonal array of 6 µm diameter holes in PDMS etched using optical resist as mask by Hill et al.[30].

Figure 2 . 4 -

 24 Figure 2.4 -Results presented in the state of the art for PDMS stamps fabrication 1) Carbon nanotube master and transfer to resist with ~2 nm dimension by Hua et al. [9] 2) Pattern transfer by Cattoni et al.[START_REF] Cattoni | Soft UV-NIL at 20 nm scale using flexible bi-layer stamp casted on HSQ master mold[END_REF], onto AMONIL resist for NSs with 20 nm diameter and 60nm pitch. 3) (left) Pressure-assisted molding method developed by Koo et al.[START_REF] Koo | The fabrication of a flexible mold for high resolution soft ultraviolet nanoimprint lithography[END_REF] and (right) PDMS stamp fabricated with this method. 4) PDMS stamps fabricated by Koo et al.[START_REF] Koo | Improved mold fabrication for the definition of high quality nanopatterns by Soft UV-Nanoimprint lithography using diluted PDMS material[END_REF] for different percentages of PDMS dilution in toluene.

Figure 2 . 5 -

 25 Figure 2.5 -Images of metasurfaces fabricated by Soft UV-NIL with PDMS stamps by 1) Kontio et al. [54] 2) Barbillon et al. [49] 3) Cottat et al [51] 4) Bryche et al. [52] 5) Cattoni et al. [50] 6) Banville et al. [53].

Figure 2 . 6 -

 26 Figure 2.6 -Reflectance maxima in S polarization and averaged transmittance (for both polarizations on the whole visible spectrum) versus the array density by Bertin et al. [3].

Figure 2 . 7 -

 27 Figure 2.7 -Results presented in the state of the art for plasmonic metasurface for transparent displays 1) (left) Performance of the metasurface fabricated by Hsu et al. [1] and (right) demonstration of the transparent display 2) (top) Performance of the metasurface fabricated by Saito et al. [2] and (bottom) demonstration of the transparent display 3) (top) Optical performance of the metasurface, (center) demonstration of the transparent display and (bottom) image metasurface fabricated by Bertin et al. [3].

  To conclude, considering the state of the art, we have focused our technological work on the development of PDMS stamps combining (low-cost) NS self-assembly for the initial pattern ( § 4.2) and original short-cut fabrication of nanostructured PDMS stamps ( § 4.2 to 4.4), and we have proposed a method to control the nanostructures density ( § 4.8 and 6.4.2).

Introduction

  With metasurfaces being the focus of this work, the structures formed by ensembles of NPs is a point of particular interest, since the way the NPs (or meta-atoms) are arranged have an impact in optical effects, namely diffusion and diffraction.Due to the lack of tools currently present in literature for the analysis of these optical effects induced by the nanometric arrangement of structures, particularly for non-periodic structures, work was dedicated to adapting already existing methods (i.e. Optical Fourier Transform and Structure factor) to the analysis of these. With the fast development of the field of metasurfaces and the increased interest in correlated disorder structures[1][2][3][4] this sort of tools are necessary for the study of their optical behavior in a manner that allows for the comparison with fully ordered structures.

  3.1, Fig.3.2 left). The 1D structure factor can then be obtained by doing a radial average giving values for the function that are only dependent on the absolute value of 𝑞 (Figure 3.2, right).

Figure 3 . 1 -

 31 Figure 3.1 -Schematic description of the parameters used to calculate the structure factor. As shown in Figure 3.2 in the case of a hexagonal array, the structure factor is nearly identical to what we get by doing Fourier transform (i.e. without additional optical response of its elements, such as optical resonances).

Figure 3 . 2 -

 32 Figure 3.2 -2D structure factor (left) and 1D structure factor (right) for a hexagonal compact structure.The level of disorder of structures can be studied by plotting the structure factor as a function of the dimensionless unit qD, which is the multiplication of the scattering vector by the average first neighbor distance (Figure3.2). This allows us to compare the levels of order between structures with different scales of dimension.

Figure 3 . 3 -

 33 Figure 3.3 -1D structure factor of a self-assembled structure and a generated correlated disorder structure with average first-neighbors distances of 1 µm and 33nm respectively.



  Number of points in the meshNumber of iterations of the algorithm (repetition of steps 2 and 3)

Figure 3 . 4 -

 34 Figure 3.4 -Schematic description of the correlated disorder structure generation algorithm.

Figure 3 . 5 -

 35 Figure 3.5 -Structure factor for correlated disorder structure with different particles amounts.

Figure 3 . 6 -

 36 Figure 3.6 -Evolution of the 2D structure factor during the generation of a structure with 1000 particles and 10k mesh points per particle.

Figure 3 . 7 -

 37 Figure 3.7 -Comparison of structure factor of structure generated with different amount of mesh points at 10 iterations (left) and 100 iterations (right).

3. 4 . 1

 41 Particle position identificationTo apply the structure factor calculation to real systems, we developed a computer vision program in Python which was able to identify the particles positions on fabricated structures.In Figure3.8 we can see the application of this program (a) for self-assembled structures on glass composed of 1 µm PS particles and (b) for a metasurface on Si of Ag nanoparticles with a 220nm pitch, showing a good performance for different types of structures with different dimensions. The program operates as follows:

Figure 3 . 8 -

 38 Figure 3.8 -From left to right: original image, image binarized and cleaned-up, plot of particle positions detected for (top) Self-assembled structure of 1µm particles and (bottom) a fabricated metasurface.

3. 4 . 2

 42 NP diameter measurementIn case of PS NSs self-assembly, the diameters are quite well-known since we have mainly used low-dispersed NSs delivered by S. Ravaine from CRPP. Regarding the fabrication of plasmonic metasurfaces, the resulting nanostructures after several process steps may have different diameters.

Figure 3 . 10 -

 310 Figure 3.10 -Example of filling of all contiguous areas of white pixels.While the binarization and clean-up are quite efficient, some artifacts may occur. As illustrated in Figure3.11, objects resembling fused NPs and hollow NPs may appear even if they do not result from real NPs that fused together or that were made hollow during the fabrication. For example, in Figure3.11:

Figure 3 . 9 -

 39 Figure 3.9 -Diameter measurement of silver NPs. (left) Original image and (right) original image with circles with the measured diameter overlaid (yellow circles).

Figure 3 . 11 -

 311 Figure 3.11 -Binarization artifacts in the image processing program. (left) NP fusion due to high contrast between NPs and (right) hollow NPs due to low contrast inside the NPs.

Figure 3 . 12 -

 312 Figure 3.12 -Measurement resolution as a function of the pixel size and number of pixels in an object. The color scale is logarithmic.

Figure 3 . 13 -

 313 Figure 3.13 -The two possible types of errors when assimilating a circle to a sum of squares.

1

 1 Optical Fourier Transform (OFT) imaging set-upA part of the objective of this work is to characterize the spatial organization and optical response of different structures, particularly those obtained by self-assembly.

Figure 3 . 14 -

 314 Figure 3.14 -Schematic representation of the OFT bench.

Figure 3 . 15 -

 315 Figure 3.15 -Schematic representation of the (left) half-angular aperture used to define NA and of the (right) diffracted rays collected for a given NA depending on their angle.

Figure 3 . 16 -

 316 Figure 3.16 -Focusing of an incident plane wave onto a point.

( 3 . 17 )

 317 In consequence equation( 3.16) can be rewritten as:To obtain the diffraction vector for the OFT of the structure we must first convert the diffraction angle of the magnified structure into the diffraction angle of the real structure:

1 .

 1 Emission arm (left side of Figure 3.18) 2. Sample holder (center of Figure 3.18) 3. Reception arm (right side of Figure 3.18)

Figure 3 . 18 -

 318 Figure 3.18 -Schematic structure of the ISOLASER set-up (from S. Held PhD manuscript).

Figure 3 . 19 -

 319 Figure 3.19 -Schematic of the optical system.

Figure 3 . 20 -

 320 Figure 3.20 -Emission spectra of the 75W Xenon lamp for different light filters (from S. Held PhD manuscript).

Figure 3 . 21 -

 321 Figure 3.21 -Emission spectrum of the LSH-T250 light source with the different optical filters.

Figure 4 . 1 -

 41 Figure 4.1 -Full fabrication process. 1) NS deposition process 1.a) The PS NSs in a colloidal solution are deposited onto the blade 1.b) NSs go from the blade to the water surface 1.c) The NSs are deposited onto the PDMS film; 2) Stamp fabrication process 2.b) The PS NSs are reduced with an O2 plasma 2.c) The selfassembled pattern is transferred onto the PDMS with an O2 + CF4 RIE process 2d) After an acetone cleaning we obtain a PDMS stamp for NIL; 3) Soft UV-NIL process 3.a) The stamp is placed on the substrate covered by a layer of PMMA and Amonil. The sample is exposed to UV light to reticulate the AMONIL resist 3.b) The residual layer of AMONIL and the PMMA layer are etched away 3.c) An Ag layer is deposited onto the sample 3.d) The PMMA is removed leaving only the substrate with Ag NPs (lift-off).

Figure 4 . 2 -

 42 Figure 4.2 -Deposition set-up, monolayer formation, and monolayer extraction onto a substrate (from left to right).

Figure 4 . 3 -

 43 Figure 4.3 -Structure factor of samples dried in horizontal and vertical position.

  s

Figure 4 . 4 -

 44 Figure 4.4 -Deposited monolayers of PS NSs on PDMs substrate. We can observe that for similar amounts of time the NSs(left) fuse while (right) others remain separated.

Figure 4 . 5 -

 45 Figure 4.5 -Examples of PS NSs after etching with a RIE machine (left) and PC machine (right).

Figure 4 .

 4 8. A schematic description of the etching dynamic of the isotropic process is presented in Figure 4.6.

Figure 4 . 6 -

 46 Figure 4.6 -Schematic description of an isotropic etching (high-pressure process) and pattern obtained. The isotropic nature will reduce the mask faster and reduce the pattern during the etch.

  Figure 4.8. A schematic description of the etching dynamic of the isotropic process is presented in Figure 4.7.

Figure 4 . 7 -

 47 Figure 4.7 -Schematic description of an anisotropic etching (low-pressure process) and pattern obtained. Due to the directional nature of the etching the mask will not be reduced as fast, and the patterns will be etched deeper with less reduction of the side walls.

Figure 4 . 8 -

 48 Figure 4.8 -AFM measurements of stamps obtained with unetched PS NS masks. a-b)Profile plot and c-d)3D representation for a-c) high-pressure and b-d) low-pressure PDMS etching methods.

Figure 4 . 9 -

 49 Figure 4.9 -PDMS due fissuring due to etching.

Figure 4 .

 4 Figure 4.10 -SEM image of (left) pattern transfer onto a sample, after bilayer etching and (right) sample after lift-off. Both samples were fabricated with stamps fabricated with high-pressure PDMS etching and PS cleaning process. The pattern transfers obtained were highly inhomogeneous.

Figure 4 . 11 -

 411 Figure 4.11 -Schematic description of the anti-sticking.

Figure 4 . 12 -

 412 Figure 4.12 -Schematic representation of the sample after bilayer deposition 4.5.3 Imprint process

Figure 4 . 13 -

 413 Figure 4.13 -Schematic of the imprint process.

Figure 4 . 14 -

 414 Figure 4.14 -Schematic description of the bilayer etching process.

Figure 4 .

 4 Figure 4.15 -SEM images of a patterned AMONIL layer before (left) and after (right) the etching process. As we can observe the holes are increased in all directions after the etching process.

Figure 4 .

 4 16, left). By setting a lower deposition speed of 0.1nm/s the NPs obtained had a more circular shapes (Figure4.16, right).

Figure 4 .

 4 Figure 4.16 -Ag NP deposited at a rate of (left) 1nm/s and (right) 0,1nm/s.

Figure 4 . 17 -

 417 Figure 4.17 -Schematic of the NP diameter control by etching.

Figure 4 . 19 -

 419 Figure 4.19 -Sample with density reduction after optical resist development.

Figure 4 . 18 -

 418 Figure 4.18 -Schematic description of the sample density reduction process.

Figure 5 . 1 -

 51 Figure 5.1 -AFM measurements of the stamp used for the fabrication of metasurfaces.

Figure 5 . 3 -

 53 Figure 5.3 -SEM images of the residual layer measurements of residual layer etching calibration sample after a 2-minute AMONIL etch.

Figure 5 . 4 -

 54 Figure 5.4 -SEM images of the Si sample after bilayer etching.

Figure 5 . 5 -

 55 Figure 5.5 -SEM images of the fabricated metasurface on Si.

Figure 5 . 6 -

 56 Figure 5.6 -Macroscopic photos of the metasurface on Si substrate.

Figure 5 . 7 -

 57 Figure 5.7 -SEM images of the silica sample after bilayer etching.

Figure 5 . 8 -

 58 Figure 5.8 -SEM images of the fabricated metasurface on silica.

Figure 5 .

 5 Figure 5.10-b is the histogram of a structure with significant breakage. This is clear by the increase of the percentage of small diameters meaning NPs have been broken into two or more NPs due to micromasking ( § 5.4, Figure 5.7).

Figure 5 . 11 -

 511 Figure 5.11 -Schematic of the approximate positions of the images taken for measuremnet.

Figure 5 . 10 -

 510 Figure 5.10 -Size histogram with the percentage per nm, of three different areas of metasurface on Si substrate.

Figure 5 . 12 -

 512 Figure 5.12 -Histogram the size distribution (percent per nm) of the metasurface on Si substrate.

Figure 5 . 13 -

 513 Figure 5.13 -Size histogram with the percentage per nm, of three different areas of metasurface on silica.

Figure 5 . 14 -

 514 Figure 5.14 -Schematic of the approximate positions of the images taken for measuremnetIn Figure5.15 we plotted the size distribution for all of the 12 measured areas. The average NP size obtained from the measurement was 160.9 nm with a maximum at 172 nm with 3.2% of the NPs. 50% of all NPs are in an 18 nm interval from 161 to 179 nm. Here, again, we have a shift down from the maximum to the average. This is again explained by breakage of the NPs (which is more significant in this case). Looking at the histogram we can see it is asymmetric indicating the number of NPs with diameters smaller than the maximum is much more significant than the ones with bigger diameters.

Figure 5 . 15 -

 515 Figure 5.15 -Histogram of the size distribution (percent per nm) of the metasurface on silica substrate.

Figure 6 . 1 -

 61 Figure 6.1 -Geometrical description of the selection for the smaller viewing angles.

Figure 6 . 2 -

 62 Figure 6.2 -Schematic representation of the desired position of our user observation conditions relative to the structure factor of the metasurface. Here we plotted the structure factor a correlated disorder structure.

Figure 6 . 3 -

 63 Figure 6.3 -Structure factor of a hexagonal structure and multiple correlated disorder structure generated with different parameters. A smoothing of the plot was done to improve readability. The structure factor is zoomed on the area in front of the first diffraction peak.

Figure 6 . 5 -

 65 Figure 6.5 -(left) Structure factor and (right) OFT for 2 samples obtained by self-assembly of 1µm PS particles.We present the measurements of the diameter of the diffraction ring in term of the diffraction vector.

Figure 6 . 6 -

 66 Figure 6.6 -The structure factors presented in this section were calculated using images taken for the areas represented in each of the metasurfaces.

Figure 6 . 7 -

 67 Figure 6.7 -1D Structure factor for areas with different levels of breakage on the metasurface fabricated on Si and silica for a wide range of diffraction vector values.

Figure 6 . 8 -

 68 Figure6.8 -1D Structure factor for areas with different levels of breakage on the metasurface fabricated on Si substrate and fused silica substrate zoomed in on the user's observation conditions. This structure factor was calculated with a higher resolution in order to better visualize potential diffusion.

Figure 6 . 9 -

 69 Figure 6.9 -2D Structure factor for the structure on Si substrate with low breakage.

Figure 6 . 10 -

 610 Figure 6.10 -Observation of an image behind the metasurface on silica.

Figure 6 . 11 -

 611 Figure 6.11 -2D structure factor of structure density reduced using a (left) periodic method and (right) random method.

Figure 6 . 12 -

 612 Figure 6.12 -Schematic of density reduction mask generation.

Figure 6 . 13 -

 613 Figure 6.13 -Resulting structures after numerical density reduction of a structure obtained on Si.

Figure 6 . 14 -

 614 Figure 6.14 -1D structure factor for 2 structures obtained after density reduction: one keeping the NPs inside the areas and the other the NPs outside the areas. Both structures were obtained from the same original structure.

Figure 6 .

 6 Figure 6.15 -1D Structure factor of a fabricated metasurface with 0.5 density reduction for different distances between areas. We present zoomed areas to better visualize (lower left) the diffraction by the density reduction structure and (lower right) the widening of the diffraction peak by the original structure

Figure 6 .

 6 Figure 6.16 -1D structure factor of a fabricated, zoomed in on the user's observation conditions, metasurface with 0.5 density reduction for different distance between areas.

Figure 6 .

 6 Figure 6.17 -2D Structure factor of density reduced self-assembled structure with distance between areas of 10 µm.

Figure 6 . 18 -

 618 Figure 6.18 -Positions of the areas measured in transmission presented in Figure 6.20

Figure 6 . 19 -

 619 Figure 6.19 -Transmittance in the visible regime for an hexagonal array of Ag NP in function of (right and center) the center-to-center distance between NPs and (left) the thickness of the Ge layer. The Ge thickness for the distance sweep was set to 1nm, the NP distance for the Ge thickness sweep was set to 220nm an the Ag layer thickness was 30nm for all sweeps. The simulations were done using Lumerical's FDTD tool.

Figure 6 . 21 -

 621 Figure 6.21 -Transmittance for a specific area of the metasurface which presented a thinner resonance at shorter wavelengths.

Figure 6 . 20 -

 620 Figure 6.20 -Transmittance measured for different areas of the metasurface and average of the measurements.

Figure 6 . 22 -Figure 6 .

 6226 Figure 6.22 -Observation of an image behind the metasurface on silica. Furthermore, the metasurface on glass was qualitatively tested in the same HUD set-up as the one used by Bertin et al. [1], made available by PSA/Stellantis. The result is presented in Figure 6.23 with the image by Bertin et al. for comparison.

Figure 6 . 24 -

 624 Figure 6.24 -Transmittance measurements for (left) hexagonal structures and (right) hexagonal with reduced density structures fabricated by e-beam lithography.

14. 43 NP/µm 2 .

 432 We can place these values in the plot of the balance between the maximum reflectance and the average transmittance in function of the density, presented in the work by Bertin et al. [1]. Here we use 1 -𝑇 as an approximate estimation of the maximum reflectance (Figure 6.25).

Figure 6 . 25 -

 625 Figure 6.25 -Plot of the balance between the maximum reflectance and the average transmittance in function of the density presented in the work by Bertin et al. [1], with the average transmittance and 1 -𝑇 of Position 3 from the structures with reduced density.The reflectance maxima (R peaks) and the average transmittance (Ttot) had been measured for square(Sq) or correlated disordered (Rd) lattices, and S and/or P polarization. The arrays density was uniform.

Figure 7 . 1 -

 71 Figure 7.1 -Schematic of the size control of the NPS based on the density reduction process.

Figure 1 -

 1 Figure 1 -Link between 200nm particles after deposition onto Si substrate.

Figure 3 -

 3 Figure 3 -Example of samples with Al layer, (left) before and (right) after lift-off.

Figure 4 -

 4 Figure 4 -Examples of samples after Si etching.

Figure 7 -

 7 Figure 7 -AFM measurements of the stamp obtained with Hard-PDMS, molded into a Si master mold. (right)We can observe that the pattern of the stamp obtained is incomplete.

Table of contents

 of

	Introduction ______________________________________________________________________
	Augmented reality _________________________________________________________________
	1.2.1	Definition and history _________________________________________________________
	1.2.2	Display types ________________________________________________________________
	1.2.3	Reflective display combiners ____________________________________________________
	Plasmonics _______________________________________________________________________
	1.3.1	Definition and history _________________________________________________________
	1.3.2	Applications _________________________________________________________________
	Metamaterials and metasurfaces _____________________________________________________

  1.4.2 Transparence control by metasurfacesAn object is defined as transparent as soon as we can see what is behind it. If we cannot see behind an object, then we classify it as opaque.But we must also consider an intermediary case where light can pass through an object, but we cannot properly see what is behind it. This is called translucence. One example of this is what is often called opaque, or privacy glass presented in Figure1.7.

Table of contents

 of

Table 2 .

 2 1 -Summary of the state of the art of self-assembled PS NS structure

	First author Year	Deposition method	Substrate	NS size (min)	Surface (max)	Reduction method	Size after re-duction (min)
	Hulteen & Van Duyne [5]	1995	Spin coating	Mica, Silicon, Au, Glass, Cu	264nm	Not reported	Reduction not performed	Reduction not performed
	Haginoya et al. [11]	1997	Angled drop coating	Silicon	200nm	Not reported	RIE O2	83nm
	Weekes et al. [17]	2007	Water-inter-face	Polymer(20nm) on NiFe(30nm) on Silicon	120nm	1cm 2	RIE O2	120nm (from 390nm)
	Plettl et al. [13]	2009 Drop coating	Silicon	100nm	A few mm 2	Isotropic RIE-ICP O2	25nm
	Vogel et al. [18]	2011 Water-interface	Silicon	130nm 2' wafer	Plasma cleaner O2	50nm (from 250nm)
	Bauer et al. [16]	2013	Meniscus	Silicon	250nm	Not reported	Plasma cleaner O2	~50nm
	Chen et al. [12]	2019	Spin coating	Silicon	510nm	Not reported	Low-Pressure tem 40KHz O2 Plasma sys-	~70nm
	Shieh et al. [20]	2013	Dip coating	PDMS	258nm	Not reported	Reduction not performed	Reduction not performed
	Li et al. [21]	2017 Drop coating	PDMS	100nm	Not reported	Reduction not performed	Reduction not performed
	Chen et al. [19]	2019 Water-interface	PDMS	5µm	Not reported

Table 2 .

 2 2 -Summary of the state of the art for structures fabricated by etching with a self-assembled PS NSs mask

	Author	Year	Pattern dimension (min)	Pitch	Etched depth	Etched Material	PS NS reduction	Substrates etch method
	Weekes et al. [17]	2007	120nm	390nm	30nm (and 200nm)	NiFe (and polymer)	120nm	Ar ion plasma (and O2 RIE)
	Huang et al. [22]	2007	100nm	260nm	>3micron	Silicon	RIE O2	Wet etch with silver catalyst
	Chen et al. [23]	2007	>100nm	350nm	310nm	Silicon	RIE O2 (Cl2/SF6)	RIE Cl2/SF6 (O2)
	Li et al. [24]	2009	192nm	210mnm	236nm	Silicon	No size reduction	RIE Ar/CF4
	Tsai et al. [25]	2011	400nm	600nm	350nm	Silicon	No size reduction	RIE Cl2
	Ye et al. [26]	2016	180nm	260nm	227nm	Silica	RIE O2	RIE

Table 2 .

 2

	Author	Year	Patterning method	Masking	Structure dimension (min)	Structure etched
	Garra et al.[28]	2002	RIE CF4/O2	Copper or Aluminium	100micron	55micron
	Balakrisnan et al. [32]	2009 Wet and dry etching	Aluminium	30micron	10micron
	Hwang et al. [33] 2009	Microwave plasma	Nickel	10micron	50micron
	Chen et al. [31]	2012	RIE SF6/O2	Optical resist (AZ 9260)	2micron	20micron
	Li et al. [29]	2014	RIE SF6/O2	Optical resist (AZ 9260)	4micron	10micron
	Hill et al. [30]	2016	RIE SF6/O2	Optical resist (AZ 9260)	6micron	10micron

3 -Summary of the state of the art for PDMS dry etching

Table 2 .

 2 4 -Summary of the state of the art in PDMS stamp fabrication.

	Author	Year	Molding method and master mold	Stamp Substance	Pattern dimension	Pitch	Pattern height	Structure
	Schmid & Michel [41]	2000	Standard molding in Si master	Hard-PDMS	80nm (on stamp)	Not reported	100nm (on stamp)	Square lattice nanodots
	Hua et al. [9]	2004	Standard molding in Carbon nanotube on SiO2/Si	Hard-PDMS	~2nm (on stamp)	NA	1.7nm stamp) (on	Line
	Plachetka et al. [43]	2006	Standard molding Si master	Hard-PDMS PDMS	36nm 50nm	~850nm ~850nm	100nm 100nm	Square mesh Square mesh
	Koo et al. [38]	2007	Standard molding Si master	Diluted PDMS	43nm	150nm	70nm (on stamp)	Square lattice nanodots
	Koo et al. [46]	2008	Pressure-assisted molding in Si mas-ter	PDMS	52nm	150nm	75nm	Square lattice nanodots
	Zhou et al. [39]	2009	Standard molding Nanoporous alumina	Diluted PDMS	70nm	100nm	Not reported	Hexagonal-like lattice nanodots
	Cattoni et al. [42]	2010	Standard molding Si master	Hard-PDMS	20nm	60nm	Not reported	Square lattice nanodots
	Con & Cui [40]	2013	Molding on solvent wetted Si master	PDMS	150nm (in stamp)	Not reported	1µm (in stamp)	Dot square array

2.5.2 Fabrication of plasmonic metasurface by Soft UV-NIL

As we just discussed, sub-20 nm pattern transfer to a resist has been demonstrated. Limiting

Table 2 .

 2 5 -Summary of the state of the art for plasmonic metasurface fabrication.

	Auteurs	Année	Stamp substance	Dimensions	Pitch	Structure
	Kontio et al. [48]	2009	PDMS	130nm	300nm	Au nanocones in hexagonal lattice
	Barbillon et al. [49]	2010	Hard-PDMS	160nm	500nm	Au disk NP in square lattice
	Cattoni et al. [50]	2011	Hard-PDMS	235nm	400nm	Au square NP in square lattice
	Cottat et al. [51]	2014	Diluted PDMS (hexane)	220nm	400nm	Au disk NP in square lattice
	Bryche et al. [52]	2019	PDMS	200nm	400nm	Au disk NP in square lattice
	Banville et al. [53]	2019	Hard-PDMS	200nm	400nm	Au square NP in square lattice

Table 2 .

 2 6 -Summary of the state of the art for plasmonic metasurfaces for transparent displays.

			Peak at		Transmit-
	First author Year	resonant λ and	Resonant λ	tance for vis-	Fabrication	Structure
			optical effect		ible λ
	Hsu et al. [1]	2014	55% scattering (estimated from simulation)	458nm	60%	Chemical synthesis and deposition in polymer matrix	62nm Silica/Ag core/shell NPs (disordered)
							110nm Ag
	Saito et al. [2]	2015	15% back scattering	400nm (estimated)	>70% (estimated)	Chemical synthesis and drop coating	nanocubes on 110nm TiO2
							(disordered)
	Bertin et al. [3]	2018 75% reflectance	590nm	60%	E-beam lithography and metal deposi-tion	111x98nm Ag disk with 200nm distance (correlated disorder)
	Arslan et al. [4]	2022	70% scattering	1.38µm	>60% (estimated)	E-beam lithography and metal deposi-tion	468nm Ag disk with 800nm distance (per-turbed array)

Table 2

 2 .1 this is well within the dimensions achievable with this technique.Due to the subwavelength dimensions of the structure, necessary to avoid diffraction, we obtain NPs densities of 22 NP/µm 2 , which based on the results of Bertin et al.[3] presented in Figure2.6, would mean average transmittance of approximately 50%. To increase this value closer to 60%, we will present a method to reduce the particle density of the structure without affecting the diffusion and diffraction properties of the structure.

Table of contents

 of

	Introduction _____________________________________________________________________
	Structure factor __________________________________________________________________
	Numerical generation of correlated disordered structures ________________________________
	3.3.1	Main principle ______________________________________________________________
	3.3.2	Parameter influence _________________________________________________________

3.3.2.1 Numbers of particles ____________________________________________________ 3.3.2.2 Numbers of iterations ___________________________________________________ 3.3.2.3 Number of mesh points __________________________________________________

Table of contents

 of

	Introduction _____________________________________________________________________
	Polystyrene (PS) Nanosphere (NS) self-assembly ________________________________________
	4.2.1	Deposition step _____________________________________________________________
	4.2.2	Drying step _________________________________________________________________
	4.2.3	Deposition on to PDMS substrate _______________________________________________

PS NSs size reduction on PDMS ______________________________________________________ Stamp fabrication by PDMS direct etching _____________________________________________ 4.4.1 PDMS etching _______________________________________________________________

Table 4 .

 4 1 -Etch results for 200nm NSs on RIE machine.

Table 4 .

 4 2 -Etch result for 200nm PS NSs on a PC machine.

Table 4 .

 4 4 -PDMS etching results for the high-pressure process.

	PDMS etching		High-pressure process
	PS etching reference	No etching	PC.D (Ø = 195 nm)	RIE.D (Ø = 150 nm)	RIE.C (Ø = 125 nm)
	Pattern height (average)	79nm	48nm	55nm	11nm

Table 4 .

 4 5 -Summary of the comparison of the two etching methods.

	Method	Pattern	Diameter	Adhesion	Roughness	Transferred
		height	control		(post cleaning)	surface
	Low-pressure	+	+	-	-	+
	High-pressure	-	-	+	+	+

Table 6 .

 6 1 -Average first neighbor distance for the 4 areas represented in Figure6.6 and 6.7.

	Average first neighbor distance	High breakage	Low breakage
	Si substrate	218nm	218nm
	Silica substrate	204nm	205nm

Table 6 .

 6 2 -NP size of hexagonal structures and structure with reduced density for each of the positions of the sample fabrication.

	NP size (nm)	Position 1	Position 2	Position 3	Position 4
	Hexagonal	120	125	130	135
	Reduced density	107	110	113	115

Table 6 .

 6 3 -Average transmittance of hexagonal structures and structure with reduced density for each of the positions of the sample fabrication.

	Tave	Position 1	Position 2	Position 3	Position 4
	Hexagonal	48%	44%	40%	42%
	Reduced density	77%	74%	70%	74%
	Reduction ratio	1.6	1.68	1.75	1.76

Table 6 .

 6 4 -Minimum transmittance of hexagonal structures and structure with reduced density for each of the positions of the sample fabrication

	Tmin	Position 1	Position 2	Position 3	Position 4
	Hexagonal	15%	14%	11%	14%
	Reduced density	54%	51%	47%	51%
	Reduction ratio	3.6	3.64	4.2	3.64

Table of contents

 of

	Introduction ____________________________________________________________________
	Large surface low-cost fabrication __________________________________________________
	7.2.1	Discussion on process improvements ___________________________________________
	7.2.2	Integration of density control in the full process __________________________________
	Structure factor for structure analysis _______________________________________________
	Longer term perspectives _________________________________________________________
	7.4.1	Resonance control __________________________________________________________
	7.4.2	Non-planar substrates _______________________________________________________
	7.4.3	Structure control ___________________________________________________________

7.4.4

Study of the interaction between the NPs resonance and structure order _____________ Bibliography ____________________________________________________________________

Table of contents

 of ANNEX 1: Metasurface fabrication with PS NS self-assembly on Si substrate (using standard soft UV-NIL process) ______________________________________________________________ NS self-assembly onto Si substrate ____________________________________________________ NS size reduction On Si substrate ______________________________________________________ PDMS molding technique ____________________________________________________________ ANNEX 2: Deposition of 1 µm PS NSs self-assembled layer on PDMS _____________________ Bibliography _________________________________________________________________ ANNEX 1: Metasurface fabrication with PS NS selfassembly on Si substrate (using standard soft UV-NIL process) NS self-assembly onto Si substrate

Table 1 -

 1 Etch results for different parameters for 1 µm PS particles on a Si wafer.

		1 µm diameter particles
	Etching parameters	10W 100mTorr 10sccm O2
	Duration	5 minutes	2 minutes
	Radius	450nm	880nm
	NS displacement	No displacement	No displacement
	NS shape	Flattened	Spherical

Process development for large area plasmonic metasurfaces ______________________

Process development for large area plasmonic metasurfaces

Acknowledgements

For this reason, we decided to experimentally calibrate the effective Fourier plan distance, from the Fourier lens, with the camera placed at the position required for the formation of the OFT.

According to equation ( 3.18, we can obtain the effective Fourier plan distance (represented by 𝑓) from the periodicity of the structure and the wavelength used for imaging, by measuring the distance between peaks in the Fourier transform (represented by 𝑥).

We imaged the OFT of multiple calibrated gratings with known periodicities. The images are taken using the supercontinuum source or a 633nm laser to ensure our calculation are unrelated to errors from the light source.

We then measured the distance between the peaks of diffraction for each OFT and calculated the corresponding effective Fourier plan distance using equation 3.18. The results of this calibration are presented in Table 3.1.

In Figure 3.17 we have the OFT of a grating with 2µm periodicity. By measuring the distance between peaks, we obtain parameter 𝑥. The average of the effective Fourier plan distances calculated from the calibrated measurements is the value we use for the calculation of the diffraction vector for Nonetheless we were still able to successfully transfer the pattern to the substrate even though with a lot of height inhomogeneities, as shown in Figure 4.20. Even if the process was unsuccessful in producing a sample with a viable metasurface the results presented here indicate that this process has the potential to be used for density reduction for different types of structures if the swelling of the AMONIL resist is solved.

Based on our previous hypothesis the best way to improve this process would be to replace the optical resist used by one with a solvent that would not interact with the AMONIL resist eliminating the deformation of the imprinted layer. Considering that the resist used was AZ 5412, whose solvent is methoxy-propyl acetate (PGMEA) resists of the AZ MIR 701 and AZ Chapter 5 :

Fabrication of plasmonic metasurfaces

Fabrication on Si substrate

The NIL process was done using the standard process described in section 4.5. Before the actual fabrication we must first calibrate the residual layer thickness and its etching time ( § 4.5.4).

After imprint the sample was cleaved and observed in a SEM at 90 o angle, shown in Figure 5.2, to measure the residual layer. The height of the residual layer has some variation, oscillating between 25 and 40nm. Indeed, the high speed (8000 rpm) for the resist spinning allows us to obtain a thin layer required for the imprint process but this also causes the thickness of the layer to be discontinuous [1]. This also explains why thickness of the resist layer in the area observed was approximately 80nm, which is lower than the 111nm calibrated. The residual layer variation may induce an increase in the NP size dispersion of the fabricated metasurface. Lower viscosity resists should be used to obtain thinner resist layer without requiring elevated spinning speeds which cause discontinuities in the layer's thickness.

An AMONIL etching was performed with a duration of 2 minutes. The sample after etching is presented in Figure 5.3.

The residual layer has been completely etched away leaving the substrate exposed resulting in a good pattern transfer to the substrate.

Chapter 6 : with periodic boundaries which strongly attenuate this effect. Based on the results presented we have selected two target levels to respect the nondiffusion conditions: 0.1 is the minimum condition (represented with a blue line). Structures that stay below this value for most of the area considered may present some low-level disorder but will not have any visible diffusion. 0.05 is the ideal condition (represented with a green line). Structures that stay below this level can be considered to have virtually no disorder and will not present any diffusion.

Structure characterization

Validation of the structure factor

Before using the structure factor to characterize our sample we must experimentally validate the method. One experimental measurement that can allow us to do it is the Optical Fourier

We can conclude that our process is capable of fabricating sample with performances resembling those of the state of the art with a much lower fabrication time and cost. This performance can be improved if we remove the Ge adhesion layer. One option would be to use surface plasma treatment [2] to enhance the adhesion of the Ag layer to the glass.

The second improvement that can be done is the elimination of micromasking, which causes breakage. Solutions to this are proposed in section 5.6.

Eliminating breakage would also make our structure fully non-diffracting and non-diffusing, since, as we saw in section 6.4, diffusion was only present for areas that presented breakage of the NPs (all our structure were non-diffracting).

We should note that none of these improvements is related to the stamp fabrication process which demonstrates its reliability.

Transmission for metasurfaces with reduced density

To validate the method for density reduction and its impact on the transmittance, Navy Yam fabricated using e-beam lithography four metasurface with a standard hexagonal structure and four density reduced hexagonal structures. We reduced the density of the structures by half and used a distance of 10 µm between areas. We used a different dosage in the e-beam process for each position (positions with the same number used the same dosage) resulting in the sizes presented in Table 6.2.

Conclusion

This chapter was dedicated to the characterization of our fabricated metasurfaces.

We started by defining the conditions a structure needs to respect to be considered nondiffusing and non-diffracting. Then, after experimentally validating the structure factor calculation, we applied it to metasurfaces fabricated on Si and silica. We concluded that, the structure we obtained respected the non-diffraction and non-diffusion conditions as long as breakage remains low. Observation of the visual effect of the metasurface on silica confirms these results.

We then proposed a method for reducing the density of metasurfaces (to control the reflectance/transmittance rate). The impact on the properties of diffusion and diffraction was analyzed with the structure factor and we characterized its impact on transmittance by comparing metasurfaces with a hexagonal structure and density reduced hexagonal structures fabricated by e-beam lithography. These characterizations allowed us to validate it as a method that can control average transmittance (and reflectance) without significant impact on the diffraction and diffusion characteristics.

Lastly, we characterized the wavelengths selectivity of our metasurface in transmittance. The metasurface presented resonance at longer wavelengths than the ones targeted.

Nevertheless, it had good selectivity in transmission for wavelengths around 700nm. These characteristics added to the good transparency allowed us to consider the metasurface fabrication process as relevant for use as a plate combiner in a HUD set-up.

Integration of density control in the full process

The density control process was left unfinished due to time constraints, but a proposition was presented in section 4.7 which seems to validate the approach. The main obstacle was the swelling of the imprint resist, which we hypothesized was due to leaking of the solvent from the optical resist used for the 'localization' step. The most immediate solution would be to change the optical resist solvent.

Another option to get around this obstacle would be to eliminate the photolithography step on the imprint resist and do it directly on the PDMS substrate before PS NS deposition using the same mask. After revelation we can do a surface treatment of the PDMS with the same O2 used in our process to make the areas exposed hydrophilic. The PDMS film can then be used in the PS NS deposition process. The PS NSs would only be deposited in the hydrophilic areas [4]. The samples obtained can then be used in our PDMS stamp fabrication process resulting in a PDMS stamp with a reduced density.

Structure factor for structure analysis

The second area which we sought to develop was the method of analysis for the ensemble of NP particles. The main tool we proposed was the structure factor.

This was experimentally validated using OFT of 1 µm and showed a capability of analyzing various types of structures:

 Structure with different size dimensions, from 200 nm and 1 µm self-assembled areas  Structure with different levels of order such as perfectly ordered structure, ordered structure by areas (self-assembled) with variating degree of order and correlated disorder structures.

 Complex structures which combine different types of structures as in the case for the structure with density reduction.

The main limitation of the structure factor calculation is related to the calculation capacities of the machine used (for a structure composed of 10k particles the calculation time was approximately one week using our team's simulation desktop). With the constant increase of computational capacities observed today this will become less and less a limitation. In the more immediate term, the use of calculation servers can solve this problem and allow the also result in NPs with different resonances. Another option to control size is to do optical lithography directly on the PDMS. Again, using the density reduction process, we can reduce the size of the pattern present in each area of the stamp. The consequence would be a transfer of different pattern to the imprint resist.

After the full process the size of the NPs would reflect the size of the pattern in the stamp.

Non-planar substrates

One of the advantages of Soft UV-NIL is its adaptability to non-planar substrates.

The process could very well be adapted to be used on devices such as lenses, allowing for the integration of wavelength selective reflection. This could be used to control the distance at which the virtual image is formed or to add AR functionalities to classical vision glasses.

Structure control

In the current version of our process only hexagonal structure can be fabricated.

Other structures are achievable: for example, by functionalizing the NSs it is possible to directly obtain correlated disorder structures [5]. This process could be adapted to PDMS substrates and integrated in our stamp fabrication process to obtain PDMS stamps with correlated disorder structures.

Study of the interaction between the NPs resonance and structure order

In this work we studied separately the impact on the optical properties of the structure of the metasurface and of the NP. Nevertheless, interactions between the two exist as is the case, for example of Surface Lattice Resonances (SLR) [6]. In our structure we did not observe this The particles after etching can observed in

Si master mold fabrication

Before casting the PDMS, a master mold with the negative of the pattern intended must be fabricated. Most of the mold fabrication was performed by Frédéric Hamouda.

To fabricate this mold, we use the self-assembled PS monolayers as a mask. The particles are reduced to a diameter which corresponds to the width of the pattern we want to obtain. Then a layer of 8nm of Al is deposited by electron-beam metallic evaporation at a rate of 0.05nm/s (Figure 3, left).

The particles are lifted off in a dichloromethane bath, at 40 o for 30 min, leaving the areas where the particles were exposed (Figure 3, right).

Following the lift-off, a 5 minute O2 plasma cleaning is performed to remove any traces of PS. The PDMS dilution did not produce usable stamps. With a 2% dilution the height of the pattern obtained was too small to be able to be used in an imprint fabrication process (Figure 5). This indicates that adding 2% of hexane to our PDMS does not reduce the viscosity enough for it to enter holes in the range of 100nm. In the case of 5% the height of the pattern was as high as 100nm, but we also had a collapse of the structure and adhesion between the pillars that compose our pattern sticking together (Figure 6). In Table 5 we present the results for the two reduction processes tested: one with the PC and the other with the RIE. In Figure 8