Mueller Matrix Spectroscopic Ellipsometry Research Articles

Diffractive order Mueller matrix ellipsometry for the design and manufacture of polarization beam splitting metasurfaces.

Optical metasurface technology promises an important potential for replacing bulky traditional optical components, in addition to enabling new compact and lightweight metasurface-based devices. Since even subtle imperfections in metasurface design or manufacture strongly affect their performance, there is an urgent need to develop proper and accurate protocols for their characterization, allowing for efficient control of the fabrication. We present non-destructive spectroscopic Mueller matrix ellipsometry in an uncommon off-specular configuration as a powerful tool for the characterization of orthogonal polarization beam-splitters based on a-Si:H nanopillars. Through Mueller matrix analysis, the spectroscopic polarimetric performance of the ±1 diffraction orders is experimentally demonstrated. This reveals a wavelength shift in the maximum efficiency caused by fabrication-induced conical pillars while still maintaining a polarimetric response close to ideal non-depolarizing Mueller matrices. We highlight the advantage of the spectroscopic Mueller matrix approach, which not only allows for monitoring and control of the fabrication process itself, but also verifies the initial design and produces feedback into the computational design.

Geometric analysis algorithm based on a neural network with localized simulation data for nano-grating structure using Mueller matrix spectroscopic ellipsometry.

Mueller matrix spectroscopic ellipsometry (MMSE) is a nondestructive tool for nanostructure analysis, and recently the enhanced computational power, combining neural networks and simulation data, enhance its analysis ability on more complex geometries. This study introduces a deep learning method to realize fast and accurate analysis; predicting nanostructure parameters by pairing Mueller matrices with relatively limited library data and then applying neural network algorithm. Thus, it was realized to predict the width and height of 1D grating structure with an accuracy of MAE below 0.1 nm through the proposed two-step prediction algorithm. Finally, experimental validation on SiO2 grating of 38 nm width and 100 nm height showed a good agreement in the dimensions with reasonable range compared to those measured by scanning electron microscopy.

Quantitatively Exploring Giant Optical Anisotropy of Quasi-One-Dimensional Ta2NiS5.

Optical anisotropy offers a heightened degree of flexibility in shaping optical properties and designing cutting-edge devices. Quasi-one-dimensional Ta2NiS5, with giant optical anisotropy, has been used in the development of new lasers and sensors. In this research endeavor, we successfully acquired the complete dielectric tensor of Ta2NiS5, utilizing the advanced technique of Mueller matrix spectroscopic ellipsometry, enabling a rigorous quantitative assessment of its optical anisotropy. The results indicate that Ta2NiS5 demonstrates giant birefringence and dichroism, with Δnmax = 1.54 and Δkmax = 1.80. This pursuit also delves into the fundamental underpinnings of this optical anisotropy, drawing upon a fusion of first-principles calculations and critical points analysis. The anisotropy of Ta2NiS5 arises from differences in optical transitions in different directions and is shown to be due to van Hove singularities without exciton effects. Its giant optical anisotropy is expected to be useful in the design of novel optical devices, and the revelation of the physical mechanism facilitates the modulation of its optical properties.

Plasticizer-Induced Enhancement of Mesoscale Dissymmetry in Thin Films of Chiral Polymers with Variable Chain Length.

Conjugated polymers with chiral side chains are of interest in areas including chiral photonics, optoelectronics, and chemical and biological sensing. However, the low dissymmetry factors of most neat polymer thin films have limited their practical application. Here, a robust method to increase the absorption dissymmetry factor in a poly-fluorene-thiophene (PF8TS series) system is demonstrated by varying molecular weight and introducing an achiral plasticizer, polyethylene mono alcohol (PEM-OH). Extending chain length within the optimal range and adding this long-chain alcohol significantly enhance the chiroptical properties of spin-coated and annealed thin films. Mueller matrix spectroscopic ellipsometry (MMSE) analysis shows good agreement with the steady-state transmission measurements confirming a strong chiral response (circular dichroism (CD)and circular birefringence (CB)), ruling out linear dichroism, birefringence, and specific reflection effects. Solid-state NMR studies of annealed hybrid chiral polymer systems show enhancement of signals associated with aromatic π-stacked backbone and the ordered side-chain conformations. Further studies using Raman spectroscopy, X-ray diffraction (XRD), differential scanning calorimetry (DSC), atomic force microscopy (AFM), and polarized optical microscopy (POM) indicate that PEM-OH facilitates mesoscopic crystal domain ordering upon annealing. This provides new insights into routes for tuning optical activity in conjugated polymers.

Optimizing the Design of the Vapor‐Deposited CsPbCl3‐Based Optoelectronic Devices via Simulations and Experiments

AbstractWide‐bandgap CsPbCl3 perovskite has fueled studies on applications in a variety of newly developing optoelectronic devices, including solar cells, lasers, light‐emitting diodes, and photodetectors. Most of them are now focused on film fabrication and device performance optimization, technology transfer of these proof‐of‐concept devices to the market will necessitate optimization of the device structure to minimize the optical loss and fabrication cost. While device model‐based electro‐optics simulations are considered a powerful method to attain the purpose, during which accurate optical constants are preconditions. Herein, for the first time, the optical constants of CsPbCl3 film through Mueller matrix spectroscopic ellipsometry (SE) are reported. Taking optoelectronic devices in vertical structure as a demonstration, simulations on the distributions of 2D electromagnetic field and photo‐generated electron field are arranged, successfully demonstrating the profile of the photons and electrons inside the devices. The evolution trend of device performance in the experiments matched with the simulations, for device performance is closely related to the photons and photo‐generated electrons. Benefitting from the simulations and experiments, general design criteria of the CsPbCl3‐based optoelectronic and photonic devices are posed, inevitably accelerating their development and commercialization.

Pseudo-dielectric functions, band-to-band transitions, and dielectric-related factors in a single-crystal LiTi2O4 thin film

This article is devoted to studying the optical properties of a novel single-crystal LiTi2O4 thin film. A high-quality (011)-oriented LiTi2O4 single-crystal thin film was prepared on a MgAl2O4 (011) substrate by pulsed laser deposition. The weak in-plane optical anisotropy is discovered by Mueller-matrix spectroscopic ellipsometry, which can be attributed to the cooperative Jahn-Teller distortion in the Ti–O octahedrons. The pseudo-dielectric functions were determined in the photon energy of 1.24–5.06 eV using the ellipsometric spectra. The optical conductivity, plasma frequency, effective mass, scattering time and other dielectric-related factors are also discussed. The critical points obtained in the pseudo-dielectric functions are originated from the charge-transfer transitions of the Ti related pairs. The results demonstrate that the enhanced effective mass is responsible for the high optical transparency of LiTi2O4 rather than the large high frequency dielectric constant ε∞.

Nondestructive monitoring of annealing and chemical–mechanical planarization behavior using ellipsometry and deep learning

The Cu-filling process in through-silicon via (TSV-Cu) is a key technology for chip stacking and three-dimensional vertical packaging. During this process, defects resulting from chemical–mechanical planarization (CMP) and annealing severely affect the reliability of the chips. Traditional methods of defect characterization are destructive and cumbersome. In this study, a new defect inspection method was developed using Mueller matrix spectroscopic ellipsometry. TSV-Cu with a 3-μm-diameter and 8-μm-deep Cu filling showed three typical types of characteristics: overdishing (defect-OD), protrusion (defect-P), and defect-free. The process dimension for each defect was 13 nm. First, the three typical defects caused by CMP and annealing were investigated. With single-channel deep learning and a Mueller matrix element (MME), the TSV-Cu defect types could be distinguished with an accuracy rate of 99.94%. Next, seven effective MMEs were used as independent channels in the artificial neural network to quantify the height variation in the Cu filling in the z-direction. The accuracy rate was 98.92% after training, and the recognition accuracy reached 1 nm. The proposed approach rapidly and nondestructively evaluates the annealing bonding performance of CMP processes, which can improve the reliability of high-density integration.

Broadband Mueller ellipsometer as an all-in-one tool for spectral and temporal analysis of mutarotation kinetics.

Spectroscopic Mueller matrix ellipsometry is becoming increasingly routine across physical branches of science, even outside optics. The highly sensitive tracking of the polarization-related physical properties offers a reliable and non-destructive analysis of virtually any sample at hand. If coupled with a physical model, it is impeccable in performance and irreplaceable in versatility. Nonetheless, this method is rarely adopted interdisciplinarily, and when it is, it often plays a supporting role, which does not take benefit of its full potential. To bridge this gap, we present Mueller matrix ellipsometry in the context of chiroptical spectroscopy. In this work, we utilize a commercial broadband Mueller ellipsometer to analyze the optical activity of a saccharides solution. We verify the correctness of the method in the first place by studying the well-known rotatory power of glucose, fructose, and sucrose. By employing a physically meaningful dispersion model, we obtain 2π-unwrapped absolute specific rotations. Besides that, we demonstrate the capability of tracing the glucose mutarotation kinetics from just one set of measurements. Coupling the Mueller matrix ellipsometry with the proposed dispersion model ultimately leads to the precisely determined mutarotation rate constants and spectrally and temporally resolved gyration tensor of individual glucose anomers. In this view, Mueller matrix ellipsometry may stand as an offbeat yet equal technique to those considered classical chiroptical spectroscopy techniques, which may help open new opportunities for broader polarimetric applications in biomedicine and chemistry.

Characterization of amorphous carbon films from 5 nm to 200 nm on single-side polished a-plane sapphire substrates by spectroscopic ellipsometry

In this work, a series of amorphous carbon films were deposited on a-plane sapphire substrates by magnetron sputtering with deposition time from 15 min to 8 h, in order to investigate the thickness and optical properties in the process of growth in a non-destructive way. They were characterized by using Mueller matrix spectroscopic ellipsometry together with topography profilometry and Raman spectroscopy. Two models of a Bruggeman effective medium approximation model and a single Cody-Lorentz oscillator model have been proposed to fit films thickness and optical constants from Ultraviolet (UV) to visible (210 nm–800 nm), and Transmission Electron Microscope (TEM) has been used to verify the proposed model for thickness fitting results. The optical constants of the amorphous carbon film have been determined by fitting together all measurements in samples deposited for 2 h or more, with the film thickness being the only sample-independent parameter. The results show that the thickness from 5 nm to 200 nm can be characterized in a nondestructive way although there is a relatively large thickness error compared with the Transmission Electron Microscope results for thin films (d < 20 nm) when the deposition time is less than 2 h because of the nonuniform deposition in the beginning. The relative error between the TEM and Spectroscopic Ellipsometry results can be reduced to 1% after 4 h sample. That means spectroscopic ellipsometry can still provide an indicator for the trend of thickness growth.

Structural and Optical Characteristics of Flexible Optically Rewritable Electronic Paper

A comprehensive theory of light-reflective characteristics and experimental technique of liquid crystal layer thickness control for flexible optically rewritable electronic paper is presented. Cylindrical pillars were used to control the gap between flexible substrates. The introduced prototype of optically rewritable electronic paper has shown very promising performance. In this regard, we report theoretical results of structural photosensitive alignment of nematic liquid crystals on flexible substrate. The focus of theoretical study is on understanding the self-assembled complex structure, governed by the interplay between surface anchoring and liquid crystal elasticity. Mueller matrix spectroscopic ellipsometry was used to study light-reflecting characteristics and polarization properties of the twisted nematic film.

Anisotropic dielectric function, direction dependent bandgap energy, band order, and indirect to direct gap crossover in α-(AlxGa1−x)2O3 (≤x≤1)

Mueller matrix spectroscopic ellipsometry is applied to determine anisotropic optical properties for a set of single-crystal rhombohedral structure α-(AlxGa1−x)2O3 thin films (0 ≤ x ≤ 1). Samples are grown by plasma-assisted molecular beam epitaxy on m-plane sapphire. A critical-point model is used to render a spectroscopic model dielectric function tensor and to determine direct electronic band-to-band transition parameters, including the direction dependent two lowest-photon energy band-to-band transitions associated with the anisotropic bandgap. We obtain the composition dependence of the direction dependent two lowest band-to-band transitions with separate bandgap bowing parameters associated with the perpendicular (bEg,⊥ = 1.31 eV) and parallel (bEg,|| = 1.61 eV) electric field polarization to the lattice c direction. Our density functional theory calculations indicate a transition from indirect to direct characteristics between α-Ga2O3 and α-Al2O3, respectively, and we identify a switch in band order where the lowest band-to-band transition occurs with polarization perpendicular to c in α-Ga2O3 whereas for α-Al2O3 the lowest transition occurs with polarization parallel to c. We estimate that the change in band order occurs at approximately 40% Al content. Additionally, the characteristic of the lowest energy critical point transition for polarization parallel to c changes from M1 type in α-Ga2O3 to M0 type van Hove singularity in α-Al2O3.

Mueller matrix spectroscopic ellipsometry

Abstract The Mueller matrix is a mathematical description of how light is altered by an optical element or a sample under study. It describes both intensity (irradiance) and polarization changes, including a reduction of the total polarization. Mueller matrix spectroscopic ellipsometry has gained recent popularity in the optics and semiconductor communities as an effective means to characterize complex sample structures and anisotropic materials. While this method is not new, its recent expansion to new fields has left many users with only a pedestrian understanding of the data they collect. This tutorial provides an overview of Mueller matrix spectroscopic ellipsometry with focus on practical aspects for those new to the technique.

Anisotropic optical properties of indium tin oxide thin films prepared by ion beam sputtering under oblique angle deposition

Unraveling the anisotropic optical properties of nanometer-scale structured thin films is of great interest for both fundamental and applicative perspectives, but can be challenging and is therefore generally overlooked, especially for transparent and conducting materials. In this paper, porous slanted columnar thin films of indium tin oxide are prepared under Oblique Angle Deposition (OAD) by Ion Beam Sputtering (IBS) using argon and xenon as process ions. Their anisotropic optical properties are investigated both in the Visible–NIR range (400nm to 1.7μm) and the Infrared range (1.7 to 30μm) by means of Mueller Matrix Spectroscopic Ellipsometry. The optical models and their results are confronted to and confirmed by High Resolution Transmission Electron Microscopy (HRTEM) studies. In the Visible–NIR range, the resulting picture is that of a ripple-like structure with greater optical index in the direction perpendicular to the slanting plane. This configuration is quite original for OAD films, for which the optical index is usually greater in the direction parallel to the columns, and appears to be a specific footprint of IBS due to the enhanced diffusion of the species during deposition. In the Infrared range, the strong optical anisotropy observed for the Xe-deposited films is explained by the anisotropic free-carrier scattering inside the nanoscopic sub-columnar structure evidenced by HRTEM, yielding to a biaxial Drude model. This mechanism is highly original for OAD films, and may be of a great help to elucidate the anisotropic optical properties of other OAD metallic systems, for which such a sub-columnar structure appears to be a general trend. More generally, this work proposes an original and thorough method combining advanced optical modeling and transmission electron microscopy studies to unravel the anisotropic optical properties of nanostructured thin films.

Mueller Matrix Ellipsometric Characterization of Nanoscale Subsurface Damage of 4H-SiC Wafers: From Grinding to CMP

Subsurface damage of 4H-silicon carbide (SiC) wafers, which is detrimental to the performance and lifetime of SiC-based photoelectric devices, is easily induced during surface machining process due to their particular mechanical and physical properties. A nondestructive and effective characterization technique is essential for high quality products in the wafer manufacturing process. A method based on the Mueller Matrix Spectroscopic Ellipsometry (MMSE) is proposed to detect the nanoscale subsurface damage of 4H-SiC wafers induced by grinding and polishing. The Mueller matrix elements which are sensitive to the damage information have been identified through both simulation and experiment. The damage layer and its roughness are considered in optical modeling at different processing stages. The results show that both the surface texture and the damage layer contribute to the Mueller matrix values. The fitting thickness of the damage layer is consistent with the value from transmission electron microscope (TEM); the refractive index of the damage layer matches the surface elements analysis result from X-ray photoelectron spectroscopy (XPS). The results suggest that the MMSE-based method could offer a promising nondestructive method to detect global wafer subsurface damage and its evolution during grinding and polishing, which eventually could benefit process optimization in the whole wafer manufacturing process.

Dispersion of resonant modes in patch antenna lattices.

Spectroscopic polar angle resolved Mueller matrix ellipsometry at multiple azimuthal incidences, together with a full-field model, reveal new details in the interplay between localized gap surface plasmon resonances and propagating surface plasmon polaritons (SPPs) in a rectangular array of metal-insulator-metal patches. A plane-wave expansion of the field in the insulator shows that the fundamental localized resonances are composed of oppositely propagating modes. Sharp dispersive resonances observed in p-polarization, excited near the opening of diffracted orders, are shown to be grating coupled SPPs. The SPPs show strong coupling with localized modes of similar symmetry, while they appear suppressed by modes of dissimilar symmetry.

Analysis of non-idealities in rhomb compensators.

In-line rotatable rhombs that are only weakly chromatic are desired as compensators for a wide variety of applications in spectroscopic polarimetry and Mueller matrix spectroscopic ellipsometry. These devices employ multiple total internal reflections to generate differences in the phase shifts upon reflection for orthogonal fast and slow axis optical electric field components. A framework has been developed for characterization of non-idealities in the performance of rhombs due to dissipation and associated dichroism upon each reflection as well as stress-induced birefringence along each beam path. External oblique reflection measurements by spectroscopic ellipsometry for the internally reflecting interface structures has enabled characterization of the dichroic effects and retardance generated by the reflections. The framework for analysis of the effects of stress relies on simulations demonstrating that the contributions to polarization modification from each beam path depend only on the accumulated stress-induced retardance and average azimuthal angle of the fast principal stress axis along the given path. The overall approach has been applied to straight-through Mueller matrix measurements of a three-reflection rhomb in its operational configuration to establish the set of stress parameters for each of the four beam paths needed to fit the measurements. Thus, device geometry and optical structure, including layer thicknesses and component media optical properties, as well as stress-induced retardances and average stress azimuthal angles, which are all deduced in the analysis, enable a complete description of the polarization modifying properties of the rhomb when serving as a compensator.

High-frequency and below bandgap anisotropic dielectric constants in α-(AlxGa1−x)2O3 (≤x≤1)

A Mueller matrix spectroscopic ellipsometry approach was used to investigate the anisotropic dielectric constants of corundum α-(AlxGa1−x)2O3 thin films in their below bandgap spectral regions. The sample set was epitaxially grown using plasma-assisted molecular beam epitaxy on m-plane sapphire. The spectroscopic ellipsometry measurements were performed at multiple azimuthal angles to resolve the uniaxial dielectric properties. A Cauchy dispersion model was applied, and high-frequency dielectric constants are determined for polarization perpendicular (ε∞,⊥) and parallel (ε∞,∥) to the thin film c-axis. The optical birefringence is negative throughout the composition range, and the overall index of refraction substantially decreases upon incorporation of Al. We find small bowing parameters of the high-frequency dielectric constants with b⊥=0.386 and b∥=0.307.

Spectroscopic Mueller matrix ellipsometry of a gap surface plasmon array at conical incidences

Spectroscopic Mueller matrix ellipsometry is used to study an array of rectangular Au patches on a S i O 2 film backed by optically thick Au. The array supports resonances related to gap surface plasmons and Rayleigh anomalies, and these are mapped out by full rotation of the azimuthal angle of incidence. The finite element method is used to model the system, and it is found that the Ti adhesion layers at S i O 2 / A u interfaces used in the manufacture process must be included in the model for accurate results. We show how oxidation of the Ti layer beneath the Au patch causes the optical response to drift in time, and we demonstrate an extreme sensitivity of the Mueller matrix to the dimensions of the patch.

Effective medium approximation based interpretation for Mueller matrix spectra of polydimethylsiloxane gratings

Dielectric corrugated gratings are of considerable interest due to their applications in acousto-optics, quantum electronics, integrated optics, spectroscopy, and holography integrated optics. Rigorous coupled-wave analysis has been widely used for the analysis of dielectric gratings. However, this approach is not only time-consuming and computer intensive but it also does not really promote the physical understanding of the origin of the observed optical behavior. Here, we use Mueller matrix (MM) spectroscopic ellipsometry to systematically study the sinusoidal polydimethylsiloxane grating. We correlate the observed polarization mixing in the Mueller matrix to the underlying physical origin using the physics-based approach. The calculated MM contour plots obtained from a biaxial Bruggemann effective medium approximation model are completed by the presence of Rayleigh-Woods anomalies. The roles of optical interference, geometric anisotropy, and diffraction orders are respectively identified by their different dispersion behavior, with their interactions and couplings highlighted. Such a straightforward procedure provides a new method for analyzing dielectric gratings, which requires considerably less computer power and is directly linked to the physical interpretations.

Double-sided and single-sided polished 6H-SiC wafers with subsurface damage layer studied by Mueller matrix ellipsometry

The complex optical constants and the subsurface damage layer of uniaxial doped 6H-SiC wafers are measured using Mueller matrix spectroscopic ellipsometry. A comparison is made between measurements on a single-sided polished wafer that can be treated as a semi-infinite substrate and on a double-sided polished wafer that is studied with the partial-wave theory. The refractive indices and extinction coefficients for ordinary and extraordinary directions are determined below the bandgap after point-by-point fitting of experimental Mueller matrices. The thickness of the subsurface damage layer caused by mechanical polishing and chemical mechanical polishing determined by ellipsometry is consistent with the result of transmission electron microscope. The ellipsometry results show that the analysis based on a double-sided polished wafer is more informative about the optical properties of 6H-SiC than that of the single-sided polished wafer as it renders information properties about the bulk properties of the material, for example, allowing the determination of the very weak absorption coefficient (k≈10−4) due to doping.