Optical studies of AlN and GaO based nanostructures using Mueller matrix spectroscopic ellipsometry

......................................................................................................... iii Svensk sammanfattning av avhandlingen ........................................................... v Preface ........................................................................................................... vii Acknowledgements .......................................................................................... ix List of publications .......................................................................................... x


II.
Growth and polarizing properties of GLAD deposited InAlN chiral sculptured thin films.

Introduction
In the vast spectrum of the natural world, interaction between light and matter manifests itself in the form of color. This color represents a particular wavelength of light that can arise as a result of two primary mechanisms [1]: either from the absorption of selective wavelengths of light -as seen in pigments, dyes, and metals where the color is generated as a consequence of relaxation of excited electrons within the material (such as in Fig. 1a); or as a result of scattering of selective wavelengths of light -where the color is observed after a physical interaction such as reflection, interference or diffraction of the incident light with the spatial features of the structure (shown in Fig. 1b).

Brief history
Historically, the fascination with optical phenomena dates back several centuries. Ancient Greek philosophers Pythagoras, Democritus, Empedocles and others (569 -400 BCE) are credited with developing the first theories of light, while explanations of laws related to propagation of light are credited to Euclid (300 BCE), Hero of Alexandria (60 CE) and Abu Sa`d al-`Ala' Ibn Sahl (984 CE) [2,3]. The first scientific description of structural interactions of light and matter came much later in Hooke's work Micrographia (1665), which explained the vibrant feathers of peacocks and ducks, suggesting a crucial role played by alternate layers in reflecting light [1,4]. One such interaction integral to the development of the science of optics is Polarization. It is a primary property that refers to the orientation of the electric field's vibrations as the light wave travels through space, ranging from linear polarization (where the electric field vibrates along a single direction, while its propagation occurs along the perpendicular axis) to circular polarization (where the tip of the electric field traces a helical path as the light propagates). In 1669, Erasmus Bartholin first observed the phenomenon of polarized light when he witnessed double refraction in Iceland spar (calcite), labelling the rays produced from the anisotropic crystal as ordinary and extraordinary. Christiaan Huygens built upon Bartholin's observations by introducing the wave theory of light in 1678, effectively explaining the double refraction seen in calcite. These early works were aimed to understand the generation of polarized light in anisotropic media [5]. The manner of absorption and re-emission of light from matter was explained much later -after resolution of the "ultraviolet catastrophe" [6] and discovery of the photoelectric effect [7] by Max Planck and Albert Einstein, respectively -in the form of Quantum Mechanics. Planck hypothesized the release of energy carried by electromagnetic waves in packets (1900), which was advanced by Einstein (1905) in the photoelectric effect explaining the emission of electrons when light hits a material, and later successfully proven by Neils Bohr (1913) in his hydrogen atom model [2]. With progress in technology, the study of optics has witnessed a transition from the pursuit of not only understanding these optical interactions but also engineering materials to harness or manipulate these properties. This led to the advent of advanced optical elements for perception of light, such as engineered thin films and optical coatings, which have become central to modern optics.

Thin film optics
Thin film coatings can be used to enhance the functionality of surfaces, from improving wear resistance and optical properties to altering electrical and thermal characteristics. The properties of these films are majorly influenced by the deposition process used to create them, meaning the same material can yield different results depending on the chosen process. The early history of modern thinfilm optics can be traced back to the discovery of "Newton's rings" by Robert Hooke (1665) and Sir Isaac Newton (1666) which was later explained as interference of light in a thin film by Thomas Young (1801). For a perfect interface, the amplitude of reflected light is described by Fresnel's reflection coefficients and is determined by the complex refractive indices of the two media. For steep angles of incidence this also includes a possible phase shift of rad if the light is incoming from a medium of lower refractive index than the adjacent. When light is reflected in a thin film it is split into multiple reflected wave fronts (illustrated in Fig. 2) which can interfere constructively or destructively depending on the film thickness, the film refractive index, and relative phase shifts in the two interfaces. A common use of these optical results is antireflection coatings, which are made to cancel out certain bands of wavelengths of reflected light. Conversely, high reflectance coatings can be made using stacks of several high-and low-index films, often having quarter wavelength optical thickness to reflect a range of wavelengths with a higher intensity. Such designs serve as building blocks for various types of thin-film filters, like long-pass filters, short-pass filters, and band-pass filters, which can transmit light over long, short or narrow bands of wavelengths, respectively [8]. In essence, thin films can be tailored to precisely control how they interact with light, serving as key components in diverse optical applications. This can be achieved by incorporating high-quality materials or advanced structures such as multilayered superlattices and sculptured thin films using advanced fabrication techniques such as metal organic chemical vapor deposition, atomic layer deposition, glancing angle physical vapor deposition, high power pulse magnetron sputtering, etc [9].

Objective
For the works presented in this thesis, the structure and composition of AlN-and GaO-based thin films were tailored to induce and study optical properties related to circular polarization and band transitions, respectively. In papers I, II and III, sculptured thin films of AlN, InAlN and HfAlN were grown by tailoring their morphology and crystal structure to study their structural and optical properties related to chirality and polarization selective reflectance. In papers IV and V, single crystalline ZnGaO and ZnAlGaO thin films were investigated to study their structural and bandgap characteristics. Chapters 2 and 3 provide a conceptual background relevant to the papers, about how light interacts with different materials and how samples can be fabricated to exhibit such optical response. Chapters 4 and 5 present the different experimental methods used and a summary of the results obtained. Lastly, the main research results are presented in the form of appended articles and manuscripts.

Light -matter interaction
This chapter provides a comprehensive background about the different kinds of optical properties that decide light-matter interactions. Polarization properties from sculptured thin films and properties related to band transitions from homogeneous thin films are emphasized pertaining to the main scope of this thesis. Finally, some methodologies that can be implemented to quantify these properties are discussed.

Basic optical relations
The interaction between light and matter is a foundational aspect in optics, resulting from distinctive material properties that have both fundamental significance and practical applications. These properties govern how materials interact with light, spanning from reflection and transmission to absorption and scattering [2]. A convenient descriptor of these properties is the complex refractive index, . It combines the real-valued refractive index of the material, which dictates the phase velocity of light within the material, and its extinction coefficient , which conveys how the irradiance of light decays as it propagates through the material. Mathematically, for an isotropic material is expressed as: Alternatively, optical response from materials can also be expressed using the complex dielectric function, ε = 2 as: Where, the real and imaginary parts 1 and 2 , respectively, together embody both the dispersive and absorptive characteristics of the material, offering comprehensive understanding of a material's interaction with electromagnetic radiation. Fig. 3 shows for a typical Si wafer.

Fig. 3: Complex dielectric function of Si
The absorptive properties can also be described by the absorption coefficient , determining the exponential decay of the irradiance. This can be calculated from the Bouguer-Lambert law: where 0 and are the initial and transmitted irradiances, respectively, and is the path length for light propagating through the medium. In the context of the complex refractive index, the absorption coefficient is directly related to its imaginary part through the equation: Where, is the wavelength of the light in free space. In this way, the complex refractive index encapsulates both the phase-changing and absorptive behaviors of light and material, providing a comprehensive framework to understand the optical properties. As light interacts with materials, its behavior is influenced by atomic and molecular structures, electronic transitions, and even external stimuli like temperature or applied fields. Properties such as polarization, arising due to the geometrical arrangement of atomic constituents, or bandgap characteristics stemming from electronic transitions, are investigated in this thesis. Some of the other optical responses include scattering from inhomogeneities and interfaces, non-linear properties, radiative recombination-related phenomena such as photoluminescence and electroluminescence, photoconductivity, opto-acoustic and thermo-optic effects, surface plasmon resonance, etc.

Properties related to polarization
Optical polarization is a fundamental property of light that describes the orientation of its oscillations in the electric field vector of an electromagnetic wave. Mathematically, if a plane wave is propagating in the -direction, it can be represented as the vector sum of superimposed orthogonal electric field components, and . This can be represented as: ( , ) = ( , ) + ( , ) = 0 (ω − )̂+ 0 (ω − + Δϕ)̂(5) Where Δϕ = ϕ − ϕ (or ϕ − ϕ ) defines the phase difference between and directions, ω is the angular frequency, is the angular wave number. The parameters , and Δϕ will determine the polarization state of the wave with the two special cases: linearly polarized (Δϕ a multiple of radians) and circularly polarized (Δϕ a multiple of 2 and = ). These are illustrated in Fig. 4. The general case when Δϕ is constant is the elliptically polarized state. If and are partly correlated, the plane wave is said to be partly polarized, and if they are totally uncorrelated the plane wave is said to be unpolarized. Historically, the concept of polarization played a crucial role in the development of the wave theory of light. It was the double refraction observed in calcite crystals by Erasmus Bartholin in 1669 that first hinted at the existence of polarization. Later, in the early 19th century, Etienne-Louis Malus discovered that light reflected at a certain angle from a glass surface becomes linearly polarized, which was eventually explained by Sir David Brewster. This observation, combined with the subsequent experiments and theoretical formulations by other pioneers like Augustin-Jean Fresnel and François Arago, firmly established the wave nature of light. The study of polarization not only advanced our fundamental understanding of light but also opened doors to a host of applications in modern optics -from polarized sunglasses that reduce glare to advanced imaging techniques that leverage polarization properties to reveal hidden details -the significance of polarization in both foundational science and applied optics is profound.
When light encounters matter, it interacts primarily with the atomic and molecular structures within that material. At the heart of this interaction lies the electric field component of the light wave, which can perturb the electron cloud surrounding an atom or molecule. As light impinges on a material, its oscillating electric field can cause the bound electrons to oscillate in response. This oscillation is, in essence, a driven harmonic motion, represented by: Where is the electron mass, is its displacement, κ is the effective spring constant (or binding strength) of the electron, is the electron charge, and ( ) is the electric field of the incoming light. The result of this interaction is an electrical polarization within the material, which is the net dipole moment per unit volume induced by the applied electric field. For linear and homogenous materials, assuming a low dipole density (such that the local and applied ( ) are the same), the relationship between the induced polarization and the applied electric field is given by: Where ε 0 is the permittivity of free space and χ is the electric susceptibility of the material. That is, polarization is proportional to the electric field and this induced polarization affects the original state of the impinging light, depending on the molecular and atomic arrangement within the material. This arrangement or ordering is critical in determining the interaction between light and the material, particularly concerning the polarization state of transmitted or reflected light. These ordered materials that affect polarization are broadly classified as crystals, where atoms and molecules are arranged in a repeating lattice; nanostructures, which are structures of varying shapes engineered at the nanoscale exhibiting subwavelength properties; polymers and liquid crystals, which can retain molecular order in liquid states; and natural materials, such as biological tissues and fibers that exhibit ordering and can affect the properties of incident light.
Linear Birefringence. Birefringence, often termed as double refraction, is an optical property exhibited by certain materials where they possess two distinct refractive indices. This results in an incident unpolarized light beam splitting into two orthogonally polarized beams that travel at different velocities within the birefringent material. Linear birefringence is quantified by the difference between the refractive indices for the two polarizations, typically denoted as o (refractive index in the ordinary direction) and e (refractive index in the extraordinary direction). The birefringence Δ of a material is then defined as: Note that here e can be higher or lower than o , and therefore Δ can have a positive or negative value. The physical basis for birefringence lies in the material's anisotropic nature, which means its optical properties differ along different axes. When light enters such a material, its electric field interacts differently with the atomic or molecular arrangement aligned along these distinct axes, giving rise to the phenomenon. The structure of a material is crucial in determining its birefringent nature. The atomic or molecular arrangement in crystals, for example, dictates the spatial orientation of its optical axes. Crystals such as calcite or quartz, which lack center symmetry, often exhibit birefringence due to their anisotropic lattice arrangement. In other materials like glasses or polymers, external stresses can lead to a non-uniform distribution of molecules, causing anisotropy and resulting in birefringence. Furthermore, in specific polymers or liquid crystal phases, the alignment of molecules or chains in a particular direction can also introduce birefringence.
Birefringent materials are widely used in optics due to their unique properties. For instance, optical compensators, often crafted from birefringent materials, are designed to introduce a specific phase delay between the ordinary and extraordinary rays, compensating for undesired phase discrepancies in optical systems. Another application is in wave plates or retarders, these devices introduce a targeted phase shift between the two orthogonal polarization components of light. Quarter-wave and half-wave plates are prevalent examples of this; they can transform linearly polarized light into circularly polarized light and vice versa or alter the polarization axis. Furthermore, the characteristic of birefringence is also utilized in polarizing microscopes, enabling detailed study of the anisotropic nature of samples, thus offering valuable insights into their internal structures or stresses.
Similarly, birefringent materials exhibit different extinction coefficients in different directions ( o , e ) in the non-transparent wavelength regions. This difference is defined as linear dichroism (Δ ): Circular and Elliptical Birefringence. While linear birefringence involves the possibility of dividing light into two linearly polarized parts with different velocities, circular and elliptical birefringence focusses on the transformation of light into circularly or elliptically polarized light with different handedness. This type of birefringence fundamentally originates from chiral or optically active materials, structures that lack mirror symmetry. In such materials, the molecules themselves exist in non-superimposable mirror-image forms, which leads to a differential interaction of the material with left and right circularly polarized light. Mathematically, this can be described as the difference in refractive indices between the right ( R ) and the left ( L ) handed components of circularly polarized light: Similarly, difference in extinction coefficients between the right ( R ) and left ( L ) handed components of circularly polarized light is defined as circular or elliptical dichroism (Δ ):

Fig. 5: Chrysina victorina beetle as seen through (a) left handed and (b) right handed circular polarizer.
Natural and synthetic materials are known to exhibit such unique optical properties. Biological molecules, such as sugars and amino acids, are chiral, displaying optical activity. Similarly, insects like jewel scarab beetles (Chrysina victorina) also showcase circular birefringence (shown in Fig. 5). Chiral liquids, like solutions of molecules such as camphor or limonene, manifest circular birefringence when dissolved in an appropriate solvent. On the synthetic side, certain materials, including chiral photonic crystals and chiral plasmonic nanostructures, are intentionally designed with a chiral geometry, granting them properties of circular and elliptical birefringence. Moreover, optically active metamaterials can be crafted to display extreme optical activity and circular dichroism.
Polarization from engineered nanostructures. Nanostructures offer opportunities to manipulate light in ways unattainable by bulk materials. A good example of this is the ability to engineer and control the polarization state of light by means of chiral sculptured thin films (CSTF) [10]. A characteristic feature of CSTFs is their intrinsic helical morphology, typically achieved through oblique angle deposition during substrate rotation. This deposition process results in a periodic structure with a helical morphology, where the pitch (one complete rotation of the structure) and thickness of the helices can be finely controlled. Light propagation through such a film exhibits circularly polarizing properties atypical of isotropic materials, requiring descriptions with 4 × 4 matrix or dyadic formalisms due to the interaction of light with its helical arrangement. These effects were first reported by Young and Kowal in 1959 for MgF 2 films [11] deposited with slow substrate rotation which exhibited optical activity. When a light wave passes through a CSTF, the difference in propagation velocities for its circularly polarized components (left and right) leads to a phase difference and subsequently a change in the overall polarization state. This phenomenon is called circular birefringence, as discussed above, and enables CSTFs to serve as versatile optical elements in polarization optics, such as circular polarizers or analyzers.
Comprehensive details about solutions to propagation of light through CSTFs can be found elsewhere [12]. In the scope of this thesis, this section discusses the most examined effect in helical CSTFs -the circular Bragg phenomena.
The circular Bragg phenomenon corresponds to the Bragg resonances occuring when light interacts with periodic multilayer structures and refers to the almost complete reflection of circularly polarized light of a particular handedness-either left or right-by a structurally chiral material, and the transmission of the other handedness in a defined spectral range [13]. An example of handedness selective reflection of circluarly polarized light is shown in Fig. 6 for optical data measured from a CSTF sample used in this thesis. The spectral zone where this reflection occurs is termed the circular Bragg regime. Structurally chiral substances, such as cholesteric liquid crystals (CLCs) and chiral sculptured thin films (CSTFs) are prime examples which demonstrate this phenomenon due to their helical molecular orientation and structure, respectively. The wavelength at which the circular Bragg resonance condition is fulfilled is called the circular Bragg wavelength, λ Br and can be shown to occur at [14]: Also, the Full Width at Half Maximum (FWHM) of the circular Bragg resonance band is calculated as: In the equations, avg is the average refractive index of the material, ∆ avg is the linear birefringence and Ω is the dielectric pitch (or dielectric period) of the material. This phenomenon is rooted in the intrinsic chirality of the material, where helical structures selectively reflect light of the same handedness. For instance, a left-handed helix will selectively reflect left circularly polarized (LCP) light, while a right-handed helix reflects right circularly polarized (RCP) light [12]. Engineering CSTFs to achieve circular Bragg resonance at specific wavelengths requires careful manipulation of the intrinsic helical microstructure. Some of the following key parameters can be tailored to obtain the desired optical behavior. Dielectric Pitch dictates the location of the circular Bragg resonance in the optical spectrum. It is set by controlling the substrate's rotation in relation to the vertical growth rate during the GLAD process and the circular Bragg wavelength can be shifted according to Eq.12. Twist Angle ( ) gives the orientation difference between consecutive deposited layers making up the segments in a CSTF. The direction of rotation decides the handedness of the CSTF, enabling selective Bragg reflection of either right circularly polarized or left circularly polarized light, and steering the optical rotation direction. For small (≈ 1°) the rotation can be seen as continuous, while for larger (> 10°) a polygonal helix is obtained. In the latter case the Bragg condition will also be fulfilled for other periods in the structure [Paper III] offering additional tailoring capabilities. Linear Birefringence depends on the material and deposition conditions such as temperature and affects the spectral width of the circular Bragg resonance according to Eq.13. The magnitude of the circular Bragg resonances is proportional to the number of helical periods in the CSTF structure. Comparable to periodic multilayers in traditional Bragg reflectors, this can be adjusted to enhance the intensity of the circular Bragg resonance. However, unlike traditional Bragg reflectors, longer deposition times can introduce growth instabilities, degrade the helical structure, and affect the circular Bragg resonance negatively. Aside from the structural parameters, the inherent optical properties of the material used to fabricate CSTFs, such as refractive index, absorption coefficient, and intrinsic chirality, selecting the right material is crucial for tuning the circular Bragg resonance as desired and contributes to their performance. Postdeposition treatments like annealing can further refine the CSTFs' optical properties. These treatments can change the crystallinity, density, and refractive indices, thus providing another layer of control over the circular Bragg resonance. Lastly, employing advanced GLAD techniques like phisweep [10] and serial bideposition [15] and optimizing process variables (e.g., temperature, pressure, and flux collimation) can mitigate broadening effects and other instabilities in longer time depositions, thereby preserving the desired circular Bragg characteristics. Beyond CSTFs, various other classes of nanostructures demonstrate optical activity. Chiral metamolecules are engineered materials with unit cells smaller than the wavelength of light, and their inherent chiral nature leads to pronounced optical activity and circular dichroism. Their interaction with light can be interpreted using effective medium theories, where the effective refractive index becomes a tensor influenced by the structure's geometry and orientation. Nanospirals are nanostructures with different helical diameters that can selectively reflect specific circularly polarized light owing to their geometric chirality and exhibit optical rotation near their plasmonic resonance. Nanorods are not naturally chiral, but when fabricated with intrinsic chirality, they can display notable optical activity [16]. Their elongated structure supports plasmonic resonances, facilitating augmented light-matter interactions. Key applications of CSTFs encompass a variety of vital areas. Polarizationsensitive sensors are adept at detecting subtle shifts in environmental parameters, such as the presence of specific molecules, by observing alterations in transmitted or reflected polarized signals. Optical isolators and circulators are devices integral to optical communications, ensuring light travels exclusively in one direction and thereby averting back reflections. Furthermore, the realm of security and anticounterfeiting employs polarization-sensitive nano-patterns in critical items like currency notes and passports, preventing replication through conventional methods.
Formalisms for polarizing properties of materials. When light interacts with a material, its polarization state changes due to the polarizing properties of the material. Discussing this change in terms of amplitudes and phases is feasible but can become challenging when light encounters multiple optical elements or matter with complex structures and anisotropic features. In such scenarios, matrix formalisms offer a better approach of systematic representation and prediction of the polarization state of light and polarizing properties of the material. Some of the important formalisms are discussed in brief as follows.
Jones Matrices: In conjunction with Jones vectors which are used to express the polarization state of light, Jones matrices are mathematical tools that provide a linear transformation framework to describe how an optical element modifies the amplitude and phase of polarized components of light [17]. However, Jones matrices are only suitable for systems that maintain coherence and do not depolarize light. Using Eq.5, if the Jones vector for light in and directions is introduced as = 0 exp( ϕ ) and = 0 exp( ϕ ), then the Jones matrix is expressed as = , or: [ ] = [ 11 12 21 22 ] [ ] (14) where, and represent the outgoing and incoming light beams, respectively.
Mueller Matrices: For more general optical systems, especially those that depolarize light, Mueller matrices serve as a beneficial framework. The Mueller matrix comprises of 16 elements and provides a comprehensive description of how light's polarization state gets transformed upon interaction with an optical element, by means of Stokes parameters (often represented as [ , , , ] ) [18]. A modern evolution of traditional ellipsometry, Mueller matrix spectroscopic ellipsometry (MMSE) combines the robustness of Mueller matrices and the sensitivity of ellipsometry. By measuring the full 4 × 4 Mueller matrix as a function of wavelength, MMSE allows one to extract rich information about a sample's polarization properties across the spectrum. Given a measured Mueller matrix of a reflection measurement from an ellisometer,  Applications of polarizing materials. After a detailed examination of the properties and measurement techniques of polarization, the focus transitions to its practical applications in prevalent technologies. Despite its abstract treatment in academic discussions, polarization plays an important role in various technological advancements.
Polarization in Modern Imaging Techniques: Modern imaging techniques, whether they be in the realm of medical diagnostics or advanced microscopy, have often harnessed the power of polarization. Polarized light microscopy, for example, takes advantage of the birefringence properties of certain materials-built on the principles detailed earlier-to accentuate contrasts and reveal structural details otherwise obscured under normal illumination. In medical imaging, polarizationsensitive optical coherence tomography provides deeper insights into biological tissues, enabling more accurate diagnostics.
Role in Communication Systems, Sensors, and Other Optical Devices: The field of communication has experienced a significant boon with the advent of optical technology. Polarization division multiplexing is a technique that allows multiple data streams to be sent simultaneously over optical fibers, enhancing the capacity of data transfer. By using different polarization states (as categorized by Stokes parameters and Jones matrices) to carry different data streams, it's possible to double the data capacity of a single optical channel. Sensors, especially those designed for remote sensing and environmental monitoring, employ polarization to discern properties of targets. For instance, by analyzing the polarization state of reflected light, sensors can identify surface characteristics, atmospheric aerosols, or even underwater features.
Future Perspectives: Potential Breakthroughs and Innovations in Polarization Control and Manipulation: With our current understanding of nanostructures, like chiral sculptured thin films, and their effects on polarization, the horizon looks promising for further innovations. As we dive deeper into nanoscale engineering, there's potential to create materials with custom polarization responses, which can be tailored for specific applications. For e.g., displays with enhanced color quality due to better polarization control or communication systems that can handle even more data as they exploit more intricate polarization states. The evolution of materials such as chiral metamolecules, nanospirals, and nanorods could pave the way for advanced devices that not only manipulate the amplitude and phase of light but also its polarization state in unprecedented ways.
To summarize, polarization is no longer far from being just an esoteric concept but is intricately woven into the fabric of our technological landscape. Its principles underline numerous applications, and its future promises even more revolutionary breakthroughs, enabled by our deepening understanding and ability to engineer structures at the smallest scales.

Properties related to band structure
At the atomic level, electrons reside in specific energy states known as atomic orbitals. Each of these orbitals can be thought of as a region in space around a nucleus where there is a high probability of finding an electron. The electron energies associated with these orbitals are quantized, meaning they can take on only certain discrete values. For single atoms, electrons reside in orbitals characterized by quantum numbers: (principal), (azimuthal), (magnetic), and (spin). The energy of these electrons is dictated by the principal quantum number . As atoms bond to form molecules, atomic orbitals combine, leading to molecular orbitals which have their own distinct energy levels. The simplest example is the molecular orbital of the hydrogen molecule H 2 , where atomic 1s orbitals combine to form bonding ( ) and anti-bonding ( * ) molecular orbitals [20].
Energy Bands in Solids. When we consider a crystal lattice, composed of a vast number of atoms, these discrete atomic orbitals merge to form continuous bands of energy due to the periodic potential of the lattice [21]. The most significant energy bands are the valence and conduction band, as illustrated in Fig. 7. The Valence band is the highest energy band that might be occupied by electrons at absolute zero temperature, which can be considered as originating from the outer shell atomic orbitals of the constituent atoms. The Conduction band is situated above the valence band, where the electrons transition to conduct electric current. It is typically empty for insulators at absolute zero temperature. The energy difference between the top of the valence band and the bottom of the conduction band is termed bandgap or energy gap g . For a photon to be absorbed by an electron in a solid, its energy should at least be equal to the bandgap energy, i.e., ph ≥ g . Here, ph = ℏω, where ℏ is the reduced Planck constant and ω is the angular frequency. This energy is then utilized to promote an electron from the valence band to the conduction band, as a result of optical absorption. In essence, the process of electronic transition in solids is governed by the movement of electrons between these energy bands. The nature of these bands and the bandgap, in turn, govern many of the optical properties observed in materials.

Fig. 7: Energy banding in crystalline semiconductors
The size and nature of a material's bandgap are influenced by several factors. Firstly, the material composition plays a pivotal role; the type of atoms and their arrangement can determine a material's bandgap, given that elements in the periodic table possess inherent energy levels which reconfigure upon bonding, establishing the bandgap of the resultant compound. Secondly, the crystal structure or the spatial arrangement of atoms in a material can lead to variations in the bandgap. For instance, silicon has various crystal structures or allotropes, each with its distinct bandgap. Transitioning from structures like graphene to graphite or diamond results in a substantial bandgap shift due to atomic arrangement discrepancies. Lastly, quantum effects become dominant when structures approximate the de Broglie wavelength of electrons. Notably in nanostructures such as quantum dots, the bandgap can be adjusted by the dot's size. As these structures become smaller, the bandgap widens due to the spatial confinement of electron wavefunctions, leading to a blue shift in the emission wavelength.
A note on nomenclature. While the term "bandgap" in solid-state physics represents the energy range where no electronic states are allowed to exist, its implications can vary in different fields of research. Whether discussing the electronic transitions in solids or the behavior of photons in specialized materials, understanding bandgaps is important as they provide insights into material properties, ranging from optical characteristics to electrical conductivity. In the context of this thesis, bandgap or g refers to "Optical bandgap", which is the minimum energy required for the absorption of a photon [22][23][24] by a material to propel an electron from the valence band to the conduction band. However, this does not always coincide with the energy needed for the most basic electronic transitions in a solid [25]. That minimum energy is termed the electronic bandgap. It's crucial to note that while the optical bandgap can serve as an indicator of the electronic bandgap, they might not always match. The difference between these two is often attributed to various factors, such as exciton absorptions, phonon interactions, and bandgap renormalization due to reasons including doping and impurities. In organic semiconductors, the HOMO-LUMO gap is the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) [26]. HOMO-LUMO gap generally tends to be smaller than a semiconductor's intrinsic or fundamental bandgap due to the molecular nature of the materials involved. In photonics, photonic bandgaps are specific frequency ranges where photons cannot propagate through a material due to their structure [27]. Such materials are called photonic structures. The distinction between optical and photonic bandgap becomes clearer when considering the nature of the interaction -while the former revolves around absorption of photons leading to electron excitation, the latter pertains to the structural prevention of photon transmission.
In materials with a direct bandgap, the maximum of the valence band and the minimum of the conduction band occur at the same crystal momentum of lattice electrons (denoted by wavevector such that crystal = ℏ ). When an electron transitions between these bands, it can directly emit or absorb a photon without requiring a significant change in its momentum, as illustrated in Fig. 8a. Materials with a direct bandgap, such as Gallium Arsenide (GaAs), are efficient light emitters, making them suitable for optoelectronic devices like LEDs and laser diodes. Mathematically, this transition can be denoted as: ph = CB − VB , where CB is the energy of the bottom of the conduction band, and VB is the energy at the top of the valence band. In materials with an indirect bandgap, the maximum of the valence band and the minimum of the conduction band occur at different . This means that an electron transitioning between these bands requires a change in momentum, typically facilitated by a phonon (quantized vibrational energy). This is illustrated in Fig. 8b which shows two possible pathways for electron transition from the valence to conduction band, with * indicating intermediate states for the phonon assisted transition. Silicon (Si) is a notable example of an indirect bandgap material. Such materials are typically inefficient light emitters due to the additional requirement of momentum change in electronic transitions. Understanding how to tune the bandgap for desired optical properties is key for the development of tailored optoelectronic devices and materials and has broad-ranging implications, from creating efficient solar cells to designing advanced optical communication systems [28][29][30][31]. This can be achieved via quantum confinement, doping, alloying, or by applying external stimuli such as pressure, temperature and external fields [32,33]. Various formalisms and techniques have been developed over the years to accurately determine the bandgap of materials. Among these, absorption-based linear extrapolation techniques stand out for their simplicity and directness [21]. They provide a comprehensive insight into electronic transitions through the analysis of transmitted or reflected radiation, quantified using the absorption coefficient, . Ellipsometry is a powerful non-invasive optical technique that measures the change in polarization state of light after it reflects off or transmits through a material (discussed in section 4.3). These measurements can offer vital insights into the dielectric function of a material, which in turn can be related to .
g of the material can be derived by plotting 2 against photon energy , and then performing a linear fit to the onset of the absorption edge [25]. A widely adopted formalism to extract g (originally developed for amorphous semiconducting materials) is the Tauc plot [34], which has now become a standard tool for determining g of different materials. For direct transitions, the Tauc relation is expressed as: α = ( − g ) 1/2 (16) whereas, for indirect transitions, it is expressed as: Here, is a constant and g can be determined by extrapolating the linear portion of these curves to the axis. However, this formalism has a few inherent limitations [35,36]. Firstly, it doesn't always produce a unique slope, making identification of an appropriate linear region within the experimental data challenging due to the noticeable energy-dependent slope variations. Materials with high absorbance below g can yield distorted results when analyzed with the Tauc method, possibly producing an incorrect bandgap value. Often, the Tauc method underestimates g , leading to potential misconceptions about the semiconductor's photosensitization or the reduction of g . Lastly, additional intra-band defect states might appear in materials with defects, dopants, or surface alterations. These manifest in the absorption spectrum as an Urbach tail-a broad absorption bandwhich can distort the Tauc plot. Utilizing the Tauc formalism without adjustments in these situations can result in incorrect bandgap estimations.
Given these limitations, researchers have sought alternative methods to improve bandgap estimations [35,[37][38][39]. One such method adopted in this thesis for determination of g of crystalline and poly-crystalline materials is the modified Cody formalism [40,41]. It is expressed as: Where, is chosen as 1⁄2 or 2 for direct or indirect bandgap semiconductors, respectively, is the photon energy, is the absorption coefficient, is a constant and is the refractive index of the material. In comparison to other formalisms, modulating the linear functional dependence of the Cody formalism by incorporating refractive index provided the best linear curve around the band edge [42]. Besides linear extrapolations, examples of other techniques to calculate bandgaps include photoluminescence spectroscopy, reflectance and transmission measurements, electro-reflectance, ultraviolet photoelectron spectroscopy and theoretical techniques such as density functional theory. Different formalisms that can be employed to calculate bandgaps are presented and compared in Paper IV [42].

Applications of bandgap engineering.
Exploring materials with engineered wider and narrower bandgaps opens the door to advanced applications. Wide bandgap materials, such as GaO, are suitable for high-power and high-temperature electronics. On the other hand, narrow bandgap materials, like InSb, are ideal for infrared detection. As materials science advances, exploring the extremities of bandgap energies becomes crucial in driving next-generation optoelectronic innovations. Light-Emitting Diodes (LEDs) are semiconductor devices that produce light through electroluminescence. The efficiency of an LED is intrinsically linked to its bandgap where specific color (or wavelength) of light emitted by an LED is directly determined by the energy difference between the conduction and valence bands. Optimal recombination rates and reduced non-radiative losses contribute to high LED efficiency. Photodetectors are devices that sense light by converting photons into electric current. The spectral sensitivity of a photodetector, or the range of wavelengths it can detect, is determined by its material bandgap. Only photons with energies greater than or equal to the bandgap can be absorbed and contribute to the photocurrent. Hence, by tuning the bandgap, photodetectors can be tailored for specific spectral ranges, such as UV, visible, or infrared. Solar Cells work by absorbing sunlight and converting it into electricity. The efficiency of a solar cell is maximized when its bandgap is optimized for the solar spectrum. A material with a bandgap that matches the photon energy peak of the solar spectrum will absorb more photons and generate a higher voltage: oc ∝ ( g − loss ), where oc is the open-circuit voltage and loss represents energy losses in the cell. Multijunction solar cells use multiple materials with different bandgaps to better harness the broad spectrum of the sun.

Chapter 3 Thin film growth
Thin films play an important role in optics and photonics in the regulation and manipulation of light. Their inherent ability to influence optical properties stems from factors including material composition, morphology and inhomogeneities in those properties. With thicknesses spanning nanometer-scale layers to a few micrometers, thin films have the distinct capability of modifying the surface characteristics without significantly altering the bulk properties of the substrate. This duality, between preserving the essence of the substrate and imposing unique optical properties to it, is a consequence of the growth techniques and material choices employed for their fabrication. For instance, homogeneous thin films maintain uniform properties throughout their volume. Such films are crucial in applications demanding high purity and uniform behavior, such as in semiconductor devices and photovoltaics. Their homogeneity ensures consistent optical responses, making them integral to many technological applications. Conversely, sculptured thin films are usually of an anisotropic nature. These are fabricated to possess columnar or layered morphologies and can exhibit varied optical properties in different directions within their structure. This allows tailored properties used in polarization filters, spectral selective optical elements, gas sensing, data storage, biomedical implants, etc [43]. An example of a sculptured InAlN thin film deposited on Si is shown in Fig. 9.  (AlN, InAlN,  HfAlN), thereby enabling investigation of polarization related optical phenomena arising due to the film structure.

Physical vapor deposition
Physical Vapor Deposition (PVD) is a versatile technique for producing thin films of metals, alloys and compounds dating all the way back to 1857 when Faraday exploded metal wires in a vacuum to 1888 when Kundt measured refractive indices of Joule heated thin films. PVD is generally classified into three processesevaporation, ion-plating and sputtering -involving the evaporation of a source material in a vacuum environment. The evaporated "vapor-phase" material consisting of ions or plasma reacts with gases to form compounds and condenses onto a substrate to form a thin film. This process takes place under controlled conditions to yield films of precise thickness, structure, and composition. Some advantages of PVD processes are as follows. They offer versatility in the selection and composition of materials and enable the fabrication of films with tailored crystallographic alterations. Moreover, PVD can produce films with self-supported morphologies, and the method provides extensive variability in processing parameters, including working temperature and pressure.

Direct Current (DC) Magnetron
Sputtering is a widely adopted PVD technique that employs a magnetically enhanced glow discharge plasma to eject atoms (sputter) from a conductive material (target) by bombarding it with energetic ions, to be deposited onto a substrate. The fundamental setup comprises a vacuum chamber, substrate holder, sputtering target of the material to be deposited and magnetron assembly. In operation, the chamber is first evacuated to base pressures of the order 1 × 10 −4 Pa and then filled with an inert sputtering gas, typically argon. When a DC voltage (≈ 2 kV) is applied between the target (cathode) and the chamber wall (anode), it ignites the plasma. The electrons from the plasma collide with the gas atoms, leading to the release of positive ions. These ions are attracted to the negatively biased target, causing target atoms to be ejected due to the momentum transfer. The sputter yield of this ejected species depends upon the energy and mass of the flux of ions and fast neutrals bombarding the target. Applying a magnetic field increases electron retention in the glow discharge, enabling the production of more ions for the same electron density. This reduces the glow discharge pressure and enhances ion velocity towards the cathode. In this way sputtered atoms experience fewer collisions when reaching the substrate, resulting in higher deposition rates compared to standard diode glow discharge methods. These ejected atoms then condense onto the substrate, thereby forming a thin film [9].
Glancing angle deposition (GLAD) is a sophisticated thin-film deposition process integrating both top-down and bottom-up nanofabrication techniques. Unlike standard deposition where vapor-phase atoms arrive at the substrate at close to perpendicular angles, in GLAD the substrate is tilted to an oblique angle almost parallel to the direction of incoming flux, establishing a unique deposition geometry. As these atoms arrive and settle on the substrate, they form tiny nuclei. Due to ballistic shadowing, the incoming vapor is deterred from condensing behind these nuclei, leading to the formation of nanoscale columns leaning towards the vapor source and resulting in oriented columnar nanostructures [44]. Furthermore, the substrate can be rotated, allowing the possibility to steer the columnar growth at an azimuthal angle with respect to the incoming vapor direction. This synergy between substrate motion and arriving vapor flux enables the growth of different morphologies. Manipulation of the substrate is delineated by two angles: the deposition angle α, which describes the angle between the substrate normal and the incoming vapor flux; and the azimuthal angle or step angle ξ, which denotes the substrate's azimuthal rotation. These angles provide spatial flexibility to dictate the orientation of incoming flux and "sculpts" the resulting thin films [13]. The deposition setup for GLAD and some of the fabricated nanostructures are shown in Fig. 10.

Fig. 10: GLAD (a) sputter configuration, and GLAD deposited thin films showing (b) inclined, (c) spiral and (d) chevron STFs
Some important considerations for the growth of sculptured thin films using GLAD are mentioned as follows, with details discussed in Paper I. Incident Vapor Collimation: Collimation of incoming vapor flux is important for GLAD processes to ensure atomic shadowing which is essential for sculptured growth. This can be achieved either by decreasing the distance between the vapor source and the substrate, reducing the working pressure or through physical screens that select certain parts of an uncollimated vapor plume [13]. Film Nucleation and Column Growth: GLAD thin film growth is largely influenced by the nucleation of the film under oblique deposition. α accentuates any surface topology due to ballistic shadowing, resulting in an inherent roughening of the substrate by means of Volmer-Weber growth [9]. Over time, the arriving vapor flux forms nuclei that grow into columns with shadows. Some of these columns suppress the growth of their neighboring nuclei through their shadowing effect. This phenomenon, known as column extinction, persists throughout GLAD film growth. Essential to the process is that the surface mobility of adatoms remains low, leading to the creation of isolated columns. This process is majorly seen in Zone I of Movchan and Demchishin's structure zone model [10]. As growth continues, only the top parts of these nuclei continue to grow, evolving into columns that tilt towards the vapor source, by an angle β. Column Tilt: The column tilt is affected by the incidence angle of vapor flux. The tilt angle of GLAD deposited columns are almost never equal due to thermal and kinetic considerations of the arriving flux. Various relationships, such as the tangent rule (tan α = 2 tan β) and Tait's rule (β = α − arcsin ( 1−cos α 2 )) have been formulated to describe this behavior [45], however, the actual behavior can deviate from these rules due to several factors such as temperature changes, deposition rates, chamber pressure, and the specific materials being used. Microstructural control via substrate rotation: By manipulating substrate movements at the macroscale, control over the nanoscale growth environment can be achieved by using parameters α and ξ, which dictate the local atomic shadowing conditions pivotal for film growth. This methodology facilitates the production of various sculptured thin film morphologies: tilted columns arise from deposition with consistent α and ξ values; zigzag (chevron) columns are crafted by holding α steady and implementing discrete 180° rotations of ξ; vertical columns materialize by depositing with a static α amidst rapid, continuous ξ rotation; and helical columns are realized by depositing at a constant α while either continuously or stepwise rotating ξ. However, these mentioned nanostructures represent only a small portion of the capabilities of GLAD. Through intricate substrate movement designs, GLAD can be employed to generate unique structures with varied morphologies.

Chemical vapor deposition
Chemical Vapor Deposition (CVD) is a technique where a solid material is deposited from a vapor through a chemical reaction near a heated substrate surface. The resultant material can manifest as a thin film, powder, or single crystal. By manipulating factors such as substrate temperature, material, and gas mixture composition, diverse materials with a broad spectrum of properties can be produced. Two notable features of CVD are its "throwing power", which ensures coatings of uniform thickness even on intricately shaped substrates, and its ability for selective deposition on patterned substrates. CVD is integral for creating dielectrics, conductors, passivation layers, oxidation barriers, and other specialized coatings. It's utilized in areas like microelectronics, high-temperature materials production, solar cells, and even in the fabrication of innovations like carbon nanotubes and high critical-temperature superconductors. Due to its chemical reaction-driven process, CVD is renowned for producing high-purity and highperformance thin films, often devoid of the imperfections present in other deposition methods, making it an optimal choice for applications demanding high quality and purity. Some advantages of CVD processes are as follows. They enable the achievement of uniform film thicknesses across extensive areas, result in the production of films with high purity and crystal quality, and permit tailoring of film properties through a versatile choice of precursors [9]. (MOCVD) is a subtype of the CVD process, specialized for the deposition of compound semiconductors and metal films. The distinctiveness of MOCVD lies in the precursors it uses; as the name suggests, it employs metal-organic compounds. These metal-organic precursors decompose on the substrate, yielding a film of the desired material and releasing organic by-products. Contrary to standard CVD, which can use a variety of gaseous precursors (including metal halides and hydrides), MOCVD specifically uses metal-organic sources, offering unique advantages, such as relatively lower deposition temperatures and a broader range of compound materials.

Metal-Organic Chemical Vapor Deposition
While selecting an "ideal" MOCVD precursor, considerations include the precursor's synthesis being cost-effective, based on readily available chemicals, and its decomposition being clean to ensure minimal contamination. Recent advances have been made in designing precursors to optimize their physical properties and performance. But, achieving a balance among all desired properties remains a complex task, emphasizing the importance of continued research and innovation in precursor chemistry for MOCVD. The precursor should exhibit adequate volatility to ensure optimal growth rates at moderate evaporation temperatures; however, some metal oxide precursors necessitate elevated evaporation temperatures due to their low vapor pressures, thereby posing challenges like premature thermal decomposition. Liquid injection MOCVD offers a solution by dissolving the precursor in an inert solvent, maintaining it at room temperature until its deployment. Additionally, there should be a considerable temperature margin between the evaporation point of the precursor and its thermal decomposition onset. The decomposition process should be clean, leaving no residual contaminants that might compromise the deposited film's quality. Compatibility with co-precursors is paramount, especially in liquid injection MOCVD scenarios where they might coexist in the same solution. Furthermore, these precursors should demonstrate stability at room temperature and have extended shelf-lives. Lastly, from both an economic and safety perspective, the ideal precursor would be cost-effective, available in high yields, and pose minimal hazards [46,47].

Sculptured and homogeneous thin films
For studies presented in papers I, II and III, AlN-based sculptured thin films were selected as the focal point for investigating optical properties and polarization behavior. AlN and its binary counterparts, GaN and InN, stand as critical constituents in the semiconductor landscape, thanks to their superior optical and electronic characteristics. Under ambient conditions, they exist in thermodynamically stable wurtzite crystal structure, with (0 0 0 1) c-, (1 1 2 0) a-, and (1 1 0 0) m-planes being the most important from a growth standpoint. Also, AlN based ternary alloys have been successfully grown into nanostructures, with InAlN nanospirals being the first (to our knowledge) sputter deposited crystalline ternary nitride CSTFs [48]. AlN has drawn significant interest in optoelectronic devices due to its capability to form AlGaN alloys with GaN. These alloys are instrumental in fabricating AlGaN/GaN and AlGaN/InGaN-based optical devices, which are operative across a range from green to ultraviolet wavelengths. Additionally, AlN in the nitride-based AlInGaN quaternary allows for the independent tuning of bandgaps while preserving lattice-matched conditions with the underlying epitaxial structure. From an optical standpoint, AlN exhibits an absorption band edge slightly above 6 eV at low temperatures in high-quality samples, making it suitable for transparent optical elements. This is complemented by a refractive index ( ) range of 1.99 -2.25, wherein it exhibits minimal variation in the vicinity of visible wavelengths 400 -600 nm, providing a near-constant for polarization studies. These properties could be further extended by complementing with refractory metals resulting in compounds such as HfAlN, to impart properties like thermal stability, corrosion resistance and hardness. From an optical standpoint, they form stable hexagonal crystals like AlN, and can be fabricated into thicker CSTFs (longer nanostructures) without distorting their morphology thereby aiding the exhibition of optical properties which require uniform repetitive structure (such as circular Bragg phenomena in section 2.2). The polarization-dependent optical properties of AlN therefore offer an additional layer of complexity and utility, making it an ideal candidate for comprehensive optoelectronic investigations. All samples in papers I, II and III were prepared on Si (with native oxide) as the substrate. AlN samples in paper I were prepared at room temperature (25 °C) under varying working pressures (1.5 mTorr to 10 mTorr) using normal ( = 0°) and GLAD ( = 85°) deposition configurations. HfAlN and InAlN samples in papers II and III were prepared at 300 °C and 3 mTorr working pressure in GLAD deposition configuration, but with differing substrate rotation schemes for growth of different morphologies.
For studies presented in papers IV and V, we focused on GaO-based homogeneous thin films such as ZnGa 2 O 4 (ZGO) to explore their optical properties, particularly in relation to band transitions. ZGO possesses a spinel crystal structure, with Zn 2 + occupying the tetrahedral sites and Ga 4 + ions filling the octahedral sites. This unique arrangement enables ZGO to exhibit both direct and indirect band transitions, with an ultra-wide direct bandgap of ≈ 5.0 eV and indirect bandgap of ≈ 4.7 eV, exhibiting a range of emissions from blue to red when doped with varying elements like Cr and Mn. This wide bandgap structure is conducive for applications in photoelectronic and optical domains, including reflective optical coatings in aerospace applications and transparent conducting oxides. Notably, the Baliga's Figure of Merit and the breakdown voltage for Ga 2 O 3 are considerably higher than those of SiC and GaN, suggesting superior performance in power devices. Furthermore, ZGO exhibits excellent thermal and chemical stability, a feature that stands in stark contrast to sulfide phosphors that are susceptible to corrosive gas emission under electron bombardment. While alternatives like SiC are relevant for similar applications, they present manufacturing challenges such as slow growth rate and high working pressures. In contrast, Ga 2 O 3 based materials can be synthesized using standard melt growth methods, making it advantageous for mass production. In addition to being touted as a next-generation semiconducting material, it is possible to mass produce very high quality ZGO, thereby making it an interesting choice of material for the studies presented in this thesis. All samples in papers IV and V were prepared at 655.3 K and 3.3 Pa with Sapphire as substrates. Samples with varying thicknesses were used in paper IV while samples in paper V were annealed at varying temperatures to study the optical properties.

Chapter 4 Characterization techniques
This chapter gives a conceptual overview of the characterization techniques used in studying the thin films described in this work. The morphology and crystal structure of the thin films were studied using electron microscopy and X-ray diffraction techniques, while the optical properties of the thin films were studied using Muller matrix spectroscopic ellipsometry.

Electron microscopy
Electron Microscopy encompasses a variety of techniques that investigate the microstructure, morphology, and chemistry of materials by deploying an accelerated, focused electron beam onto a specimen. At the core of these techniques is the generation of an electron beam, achieved through thermal or field emission. Subsequent application of voltage accelerates these electrons, which are then focused into a beam using electromagnetic lenses. Once generated, this focused electron beam serves as a probe, scanning across the surface of the sample. Depending on the technique, the electron beam interaction with the surface can cause several responses, such as backscattering, secondary electron emission, or transmission through the material. These responses are then detected, interpreted, and used to form detailed images of the specimen at varying scales, offering insight into the surface, cross section, and planar morphology. The two most prevalent techniques in electron microscopy are Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM).

Fig. 11: Interactions of high energy electrons with matter
Scanning electron microscopy (SEM) is a versatile, non-destructive imaging technique widely employed due to its easy operation, and ability to provide high resolution images of specimen surfaces. It operates by directing a focused beam of accelerated electrons onto the surface of a sample, with the accelerating voltage ranging from 0.5 kV to 30 kV controlling the spatial resolution, which typically lies between 1 and 10 nm. The superior resolution of SEM compared to optical microscopes arises from its use of accelerated electrons instead of photons, with electrons having much shorter wavelengths thereby reducing the diffraction limit. This superior resolution, coupled with its three-dimensional imaging capabilities, allows SEM to provide a more detailed understanding of the surface structure of a sample. When the electron beam interacts with the sample, multiple types of electron emissions can occur, including Secondary Electrons (SE) and Back-Scattered Electrons (BSE), illustrated in Fig. 11. The former is most commonly used for SEM imaging, as it provides better details of specimen topography, with the number of SE determining the brightness of each pixel in SEM images. Conversely, BSE is recommended for materials containing phases with different atomic mass densities. SEM operates by scanning the sample line by line in a raster pattern, with each interaction of the beam with the sample generating signals, detected by specific detectors, which include SE, BSE, and characteristic X-rays. The SE and BSE are utilized for imaging surface and cross-section morphology, while the characteristic X-rays provide chemical information about the sample. In applications such as the imaging of thin films, the cross-sectional and plan-view morphologies are obtained using SE. In this thesis, SEM was used to study the morphological details of the samples, such as film thickness, shape, size, and tilts of the nanostructures. It was also used to analyze the top and cross-section morphologies of the films to understand the growth process.

Fig. 12: Schematic illustration of a TEM column
Transmission electron microscopy (TEM) is a powerful, high-resolution microscopy technique that operates by transmitting a beam of electrons through an ultrathin specimen, typically less than 100 nm thick, or through a suspension on a grid. The TEM column comprises of an illumination system with an electron gun, accelerator, and condensing lenses, and an imaging system that includes the objective lens, projection lenses, and detectors, illustrated in Fig. 12. Like SEM, accelerated electrons are used to probe the samples, but using much higher voltages between 100 -300 kV. The interaction between the electron beam and the sample forms an image, which is subsequently magnified and focused onto an imaging device, such as a fluorescent screen, photographic film, or a charge-coupled device. In contrast to techniques like XRD, TEM provides local information about the sample area being investigated, reaching resolutions even higher than SEM. But the sample preparation process can be challenging and time consuming. In this thesis, TEM was used to gain detailed local information about the samples, such as imaging the lattice planes, determining the crystal quality, and elemental mapping capability of the TEM to view material anisotropy between the binary phases of the samples.

X-ray diffraction
X-ray diffraction (XRD) is a nondestructive method utilized to obtain an array of crystallographic information including crystal structure, phase content, preferred crystal orientations (texture), average grain size, crystallinity, strain, and crystal defects. In XRD, x-rays possessing a wavelength comparable to the interatomic spacing (0.5 -10 Å) in a lattice elastically interacts with atoms by means of Thomson scattering. The first investigations of x-ray diffraction from crystals were done more than 100 years ago. One of the basic expressions predicting diffraction wavelengths is the Bragg law. When this expression is fulfilled, the in-phase scattered x-rays undergo constructive interference. Bragg's law is defined by: n = 2d (19) where the integer n is the order of reflection, is the wavelength of x-rays, d is the characteristic spacing between the specimen crystal planes (hkl), and 2 is the angle between the incident and diffracted beams (shown in Fig. 13). The allowed reflections must also obey the structure factor relationship determined by the crystal structure. Consequently, a diffraction pattern emerges as a result of such a scattering interaction. Some of the XRD measurement techniques employed in this thesis are discussed below.
− symmetric scans are a common measurement technique used in X-ray diffraction (XRD) studies to elucidate the crystallographic structure of a material. These scans adhere to a specific geometry in which the incident angle, is always half of the diffracted angle, 2 . Consequently, the scattering vector remains perpendicular to the surface under investigation, allowing only crystal planes parallel to this surface to contribute to the Bragg diffraction. This results in a diffraction pattern characteristic to a specific crystal orientation, making − 2 scans particularly informative when examining single-crystal samples. This diffraction pattern comprises of sets of peaks at different 2 angles with corresponding intensities. The peak position (2 ) provides information on the size of the unit cell, while the peak intensity can be indicative of the unit cell's contents. Furthermore, the broadening of peaks can provide insights into the crystallite size and strain within the sample. These diffraction peaks appear when lattice planes satisfy the criteria for Bragg's Law and are typically unique for a particular material phase with uniformly distributed crystal orientations. Although factors like the atomic number of the atoms within the structure and the crystal structure influence the intensity pattern of the peaks, they do not affect the peak positions. Databases containing these distinct patterns for known phases aid in identifying the phases present within a sample through comparison.

Fig. 13: Schematic illustration of Bragg's law
A common geometric configuration employed for these scans is the Bragg-Brentano geometry, which utilizes a parafocusing setup allowing divergent x-rays to interact with the sample and be refocused onto a detector. This arrangement, where the diffraction vector remains normal to the sample surface, provides a favorable combination of peak shape and angular resolution for a wide variety of samples. − 2 scans and -scans, otherwise known as rocking-curve measurements, are two main types of measurements conducted within the Bragg-Brentano geometry. While − 2 scans shed light on the positions, shapes, and intensities of diffraction peaks, rocking-curve measurements involve fixing the detector to the centroid position of the Bragg reflection under investigation while the sample is tilted. This provides data about substrate curvature and residual stress and/or insights into the sample crystal quality by elucidating how well the crystallites of a certain orientation are aligned. In this study, the − 2 symmetric scans were utilized to determine the different phases of materials present in the samples, and rocking curve measurements were utilized to provide insights into the crystal quality of the samples.
Pole figure x-ray diffraction measurements are a key tool used for discerning the crystallographic orientations of lattice planes being investigated in a given sample.
In this method, the diffractometer's sample holder is moved, rather than the x-ray source and detector, and measurements are performed with the incoming and reflected beam angles fixed to the 2 value of the selected crystal planes. This measurement process consists of tilting the surface normal of the sample towards the diffraction plane in steps denoted by the angle , followed by the sample's rotation around the surface normal by the angle, recording a -scan at each step (illustrated in Fig. 14). By systematically repeating this process, a series of scans map a hemisphere centered at the sample surface normal. This measurement technique enables the identification of sample orientations that give rise to reflections from the chosen planes. A pole figure is a stereographic projection that represents the likelihood of finding a specific hkl plane as a function of the sample orientation. By scanning the sample reference frame through varying and angles at a fixed 2 angle, information about the crystal texture properties can be inferred from the intensity distribution of the poles in the pole figure. For example, randomly oriented crystallites will exhibit a similar intensity distributed uniformly across the entire hemisphere, whereas textured crystallites with one plane oriented diversely across all crystallites would result in a distinct ring pattern on the hemisphere. In comparison to a conventional − 2 diffractogram, where only a subset of grains contributing to the Bragg reflection are monitored, pole figure measurements evaluate reflections from all grains in the sample. For visualization, circular representations of the ( , ) plane are generally used, requiring restrictions on the angle values: 0 ≤ < 360° and 0 ≤ ≤ 90°. This process encapsulates the complete angular relationship between the scattering vector and the sample normal, offering valuable insights into the crystallographic orientations and texture of the sample.

Spectroscopic Ellipsometry
Spectroscopic Ellipsometry is an optical technique primarily used to determine thickness and optical properties of thin films. By employing polarized light as a probe, these properties can be obtained across various wavelengths of light, including ultraviolet, visible, and infrared spectral ranges. The process involves analyzing the change of polarization state of a light beam as it reflects (or transmits) from a surface or coating interface. Measurement of the frequency-dependent shift in this polarization state after interaction with the sample provides quantitative data about the layered sample constituents. It's noteworthy that this technique measures ratios between intensities of different polarization states, rather than absolute intensities. This feature reduces the sensitivity to imperfections such as background radiation and source power fluctuations, thereby increasing data reliability.
The basic quantity measured via standard ellipsometry is then expressed as a ratio between the complex reflection coefficients where, ψ and Δ are the ellipsometric parameters (or ellipsometric angles) representing the angle determined from amplitude ratio and phase difference between reflected p-and s-polarizations, respectively.
Mueller Matrix ellipsometry is used when samples exhibit optical anisotropy or depolarization, leading to conversion of p-polarized light into s-polarized light and vice versa upon reflection or transmission. For such situations, the two parameters ψ and Δ are insufficient to describe the sample's optical response and the description of the outgoing and incoming electric fields for reflection (transmission) are then represented by the following equations: , = + ( , = + ) (24) In these equations, pp , ps , sp , ss , ( , ps , sp , ss ) are four complex reflection (transmission) coefficients that elucidate the interaction of light with the sample.
A Stokes vector, comprising of four real valued Stokes parameters is used to represent the polarization state of light: Where, , , +45 and −45 are irradiances of linearly polarized light along , , +45° and −45° directions and R and L are irradiances of right-and left-handed circular polarizations, respectively, in a -Cartesian coordinate system with as the direction of propagation.
The transformation of polarization state between incident and reflected light due to the sample is expressed using the Mueller matrix, (comprising ] [ ] (26) Here, the description is restricted to normalized Mueller matrices ( = 11 w.r.t. Eq. 14). For unpolarized incident light, the degree of polarization and the degree of circular polarization c of the reflected light can be expressed as: = √ 21 + 31 + 41 (27) and, c = 41 (28) A schematic of the Mueller matrix spectroscopic ellipsometer used for analyzing samples used in this thesis is shown in Fig. 15.

Analysis.
Ellipsometry is an indirect technique and in most cases, direct interpretation of the properties of samples being analyzed is not feasible. Consequently, an optical model fitting is employed, relying on regression analysis. An example of such a model description and parameter considerations depending on sample type is described in Paper IV [42]. This method involves comparing the response predicted by a given model with actual data measured using an ellipsometer. The aim is to adjust the model's fit parameters to minimize the discrepancy between the model's predictions and the observed data, as depicted in Fig. 16. The optimal parameter values determined from this process are then used as the outcome of the analysis. However, it's worth noting that some initial model assumptions may not yield satisfactory fits. In such cases, refining the model might be necessary, such as by introducing elements like a roughness layer, anisotropy, or graded optical properties. To measure the accuracy of the fit, an error function is employed. Typically, this function is based on the mean squared error between the model's predictions and the experimental data. While introducing more fitting parameters can enhance the fit, it can also introduce correlations among parameters, which can in turn reduce the reliability of their values. As such, it is essential to evaluate the quality of a fit post-analysis. There are multiple model types available for analyzing various samples, and a deeper exploration into these models can be found elsewhere [41].

Summary and contribution
This chapter summarizes the works presented in the thesis and discusses the contribution of its results to the field of thin film optics.

AlN-based sculptured thin films
In Paper I, the focus was on AlN thin films grown on 111-oriented Si substrates using DC reactive magnetron sputtering in both GLAD and normal deposition configurations. The growth behavior of AlN nanocolumns was observed to be critically dependent on working pressures, ranging from 1.5 to 10 mTorr, and the direction of the incoming flux. In the GLAD configuration, working pressure inversely affected the growth angle of nanocolumns, which varied between 2° and 38° relative to the substrate normal. Regardless of pressure or morphology of the resulting nanocolumn, the c-axis orientation remained nearly constant, inclined toward the source at an angle of approximately 55°. At higher pressures, a biaxial texture evolution and longer column lengths were observed. In contrast, in the normal deposition setup, the c-axis tilt abruptly shifted from 0° to around 60° when the working pressure increased from 3 to 5 mTorr. This was attributed to increased scattering and lower energy of the incoming flux, leading to preferential growth in the direction requiring lower energy. These morphological orientation variations were supported by a kinetic energy dominated growth process model and using SiMTRA simulations. These results underscore the importance of lower working pressures for directing high-energy incident flux, setting the stage for the growth of more complex nanostructures.
In Paper II, the research focuses on finding optimal parameters for fabrication of InAlN STFs using reactive magnetron sputtering and GLAD configuration. The study evaluates the influence of various synthesis parameters such as partial pressure, temperature, and composition of binary constituents on the crystal structure and morphology of the resulting STFs. Different morphologies like nanocolumns and spirals were successfully grown by manipulating substrate rotation. Specifically, a 2:1 ratio of Ar:N partial pressure, about 70% Al composition, and 300 °C deposition temperature were found to be critical for an optimal spiral morphology in the resulting CSTFs. In terms of optical properties, the CSTFs displayed a high degree of circular polarization, although with under-developed resonance features at the calculated circular Bragg wavelengths. This was attributed to the reduced number of periods compared to the typical 20 -40 needed for a strong circular Bragg resonance. Overall, the research identified optimal fabrication parameters for InAlN CSTFs and highlighted their potential implications in circular polarization and circular Bragg resonance phenomena.
In Paper III, we reported the fabrication and optical properties of HfAlN CSTFs through reactive magnetron sputtering using the GLAD configuration. MMSE was employed to analyze the CSTFs, which revealed circular interference resonances at specific wavelengths. These resonances were achieved by manipulating the growth of the chiral films to result in desired pitches, ranging from 87.1 nm to 260.9 nm. A noteworthy observation was that the actual spectral positions of the circular interferences were almost twice the values calculated from the circular Bragg regime. This discrepancy was attributed to the c-axis tilt of about 45° from the substrate normal. Consequently, the dielectric pitch of these CSTFs was the same as the rotational pitch, in contrast to traditional CSTFs where the dielectric pitch is half of the rotational pitch. Crystallographic and microstructure characterizations using X-ray diffraction and transmission electron microscopy, confirmed this tilt in the crystal lattice. Furthermore, MMSE measurements revealed that these samples exhibited a non-reciprocal behavior and reflected incident unpolarized light as lefthanded elliptically polarized light with a high degree of circular polarization. Simulations using a conceptual optical model based on the Cauchy dispersion formalism were used to demonstrate a strong correlation between the morphological parameters of the CSTF and its optical properties. This work showcases the polarization selective reflection properties by manipulating the dielectric pitch without affecting the morphology of CSTFs.

GaO-based homogeneous thin films
In Paper IV, epitaxial thin films of ZnGa 2 O 4 (ZGO) were successfully synthesized on c-plane sapphire substrates utilizing MOCVD. The resultant film thickness, surface roughness, and optical properties were evaluated using SE and the MSA approach, and it was determined that the optical characteristics of ion-etched samples, spanning 1 -4 minutes, were identical to those of the unetched samples. A comprehensive analysis of the absorption coefficient dispersion showed that ZGO demonstrated both direct and indirect interband transitions. Their optical bandgaps (calculated using the modified Cody formalism) were determined to be 5.07 ± 0.015 eV (direct) and 4.72 ± 0.015 eV (indirect). These outcomes were subsequently corroborated with results from other prevalent bandgap extrapolation techniques, showcasing the stability of optical properties, and hence the material, for high power semiconductor device applications.
In Paper V, the thermal stability of ZGO epifilms on sapphire substrates and the development of a quaternary Zn(AlGa) 2 O 4 (ZAGO) epilayer were examined using insitu annealing XRD and XRC measurements between 600 to 1100 °C. The ZGO films maintained their crystal quality up to 750 °C, as evidenced by a narrow XRC peak with an FWHM value of 0.1°. However, we observed a degradation in quality and incorporation of Al into the ZGO film, as temperature increased beyond 850 °C. This resulted in the formation of an epitaxial ZAGO layer, with an intermediate epitaxial -AGO layer between ZAGO and the sapphire substrate, which was confirmed through various characterization techniques. It was observed that increasing the annealing temperatures led to a greater incorporation of Al into the ZGO layer as a consequence of the interdiffusion between the ZGO film and the sapphire substrate. This theory was corroborated using DFT evaluations and substitution energy costs related to ZGO, ZAGO and Sapphire. Optical bandgaps for both ZGO and ZAGO were determined using the modified Cody formalism, revealing a shift to higher energies for ZAGO due to the incorporation of Al. These findings suggest a simple and efficient pathway to engineer high quality, thermally stable semiconducting material with an ultrawide bandgap for advanced electronic device applications.

Contribution to the field
The goal of this thesis has been to study the interaction of light with matter in terms of optical properties related to polarization and band transitions. This required the fabrication of thin films exhibiting necessary optical properties, to be investigated using advanced analytical techniques. Paper I laid the challenging foundation of setting up the deposition framework and exploration of growth parameters that would enable fabrication of crystalline STFs to study optical properties arising from morphology and structure. Paper II broadened the knowledge on CSTF optics and their dependence on synthesis parameters, offering insights into circular resonance features observable from CSTFs with a low number of periods. Paper III pioneered the fabrication process resulting in the first report of CSTFs using HfAlN. These samples exhibited non-reciprocal optical activity and capability to reflect handedness-selective elliptically polarized light from an unpolarized source. More importantly, this work presented a novel approach of manipulating the dielectric pitch by tilting the basal crystal lattice -offering a possibility to obtain circular resonances at longer wavelengths without affecting the rotational pitch in the CSTFs. This approach shortens the deposition time required for fabrication of CSTFs and adds yet another degree of freedom (in addition to pitch and refractive index) to tailor CSTFs for specific optical attributes. Paper IV contributed to the understanding of optical properties and interband transitions in ZGO -a material gaining attention for its wide bandgap and thermal stability -while also elucidating an efficient yet precise methodology to determine optical bandgaps in semiconductors. Paper V presented a simple pathway to engineer bandgaps in ZGO by means of Al incorporation via thermal annealing. It also shed light on interband transitions in ZGO and emergent ZAGO, advancing the knowledge about their thermal stability and optical characteristics.
In summary, this thesis -with the invaluable input of co-authors -provides critical insights into optical properties of various thin films, encompassing both nitride and oxide materials. It systematically correlates growth behaviors, morphological and structural features, and post-deposition processing with specific optical phenomena. The research presents novel and efficient methodologies for fabrication of complex nanostructures and determination of interband transitions and thoroughly explores phenomena pertinent to optical coatings such as circular Bragg resonance, selective reflectance, bandgap characteristics and thermal interdiffusion. Altogether, this thesis highlights the versatile applications of Mueller matrix spectroscopic ellipsometry and expands the understanding and possibilities within the field of thin film optics.