Search

This work compares the reflection optical response of a homogeneous sample with natural optical activity with the Bragg reflection from an inhomogeneous system consisting of a periodic helicoidal structure. Examples of periodic helicoidal systems are cholesteric liquid crystals and the cuticle of some beetles. For transmitted light natural optical activity and Bragg reflection essentially lead to the same type of optical response, but there are fundamental differences on how they reflect circularly polarized light. The Mueller matrix symmetries for the two types of media are theoretically deduced and experimentally verified with ellipsometry measurements.

Ellipsometric scatterometry has gained wide industrial applications in semiconductor manufacturing after ten years of development. Among the various types of ellipsometers, Mueller matrix ellipsometer (MME) can provide all 16 elements of the 4 by 4 Mueller matrix, and consequently, MME-based scatterometry can acquire much more useful information about the sample and thereby can achieve better measurement sensitivity and accuracy. In this paper, the basic principles and instrumentation of MME are presented, and the data analysis in MME-based nanostructure metrology is revisited from the viewpoint of computational metrology. It is pointed out that MME-based nanometrology is essentially a computational metrology technique by modeling a complicated forward process followed by solving a nonlinear inverse problem. Several case studies are finally provided to demonstrate the potential of MME in nanostructure metrology.

The exoskeleton, also called the cuticle, of specimens of the scarab beetle Cetonia aurata is a narrow-band reflector which exhibits metallic shine. Most specimens of C. aurata have a reflectance maximum in the green part of the spectrum but variations from blue–green to red–green are also found. A few specimens are also more distinct blue or red. Furthermore, the reflected light is highly polarized and at near-normal incidence near-circular left-handed polarization is observed. The polarization and color phenomena are caused by a nanostructure in the cuticle. This nanostructure can be modeled as a multilayered twisted biaxial layer from which reflection properties can be calculated. Specifically we calculate the cuticle Mueller matrix which then is fitted to Mueller matrices determined by dual-rotating compensator ellipsometry in the spectral range 400–800nm at multiple angles of incidence. This non-linear regression analysis provides structural parameters like pitch of the chiral structure as well as layer refractive index data for the different layers in the cuticle. The objective here is to compare spectra measured on C. aurata with different colors and develop a generic structural model. Generally the degree of polarization is large in the spectral region corresponding to the color of the cuticle which for the blue specimen is 400–600nm whereas for the red specimen it is 530–730nm. In these spectral ranges, the Mueller-matrix element m41 is non-zero and negative, in particular for small angles of incidence, implicating that the reflected light becomes near-circularly polarized with an ellipticity angle in the range 20°–45°.

6th International Conference on Spectroscopic Ellipsometry (ICSE), Kyoto, JAPAN, MAY 26-31, 2013; International audience; We present a study on the optical properties of metamaterial layers containing U-shaped resonators. Using Finite Element Methods, we show that the description of the optical properties on one isolated resonator requires taking into account permittivity, permeability and magneto-electric tensors. The effect of weak spatial dispersion in arrays of resonators can be reproduced by adding two elements in the permittivity and magneto-electric coupling tensors. We show how the symmetries of the Mueller matrix of the sample can be used to discriminate the contributions of the different tensor elements. Generalized ellipsometry measurements made on a sample realized by e-beam lithography confirm the qualitative findings of the theoretical study. A quantitative determination of the different elements of permittivity, permeability and magneto-electric coupling is obtained by using oscillators with Lorentzian lineshape, to fit to the measurements. (C) 2013 Elsevier B. V. All rights reserved.

A partial in and out of incidence plane Mueller matrix scattering ellipsometry (MMSE) experiment is presented, where the Stokes vectors of the scattered light are detected in slightly more than a quarter hemisphere. The MMSE system is briefly reviewed. The Mueller scattering matrix obtained in reflection from as-cut rough solar grade mc-Si surfaces is reported. For the as-cut surface with an estimated correlation length of 4 μm and root mean square roughness of 550 nm, using an illumination wavelength of 532 nm, the degree of polarization is observed to be larger than 0.86, even far away from the incidence plane.

Metamaterials in the form of chiral nanostructures have shown great potential for applications such as chemical and biochemical sensors and broadband or wavelength tunable circular polarizers. Here we demonstrate a method to produce tailored transparent chiral nanostructures with the wide-bandgap semiconductor AlxIn1−xN. A series of anisotropic and transparent films of AlxIn1−xN were produced using curved-lattice epitaxial growth on metallic buffer layers. By controlling the sample orientation during dual magnetron sputter deposition, nanospirals with right-handed or left-handed chirality were produced. Using a dual rotating compensator ellipsometer in reflection mode, the full Mueller matrix was measured in the spectral range 245–1700nm at multiple angles of incidence. The samples were rotated one full turn around their normal during measurements to provide a complete description of the polarization properties in all directions. For certain wavelengths, unpolarized light reflected off these films becomes highly polarized with a polarization state close to circular. Nanostructured films with right- and left-handed chirality produce reflections with right- and left-handed near-circularly polarized light, respectively. A model with a biaxial layer in which the optical axes are rotated from bottom to top was fitted to the Mueller-matrix data. Hence we can perform non-destructive structural analysis of the complex thin layers and confirm the tailored structure. In addition, the refractive index, modeled with a biaxial Cauchy dispersion model, is obtained for the AlxIn1−xN films.

Recently, the Mueller matrix polarimeter (MMP) has been introduced for critical dimension and overlay metrology. In practice, the measurement process invariably has errors. These errors, which can be generally categorized into random and systematic errors, have great influences on the final precision and accuracy of the extracted structural parameters. In this paper, we present detailed formulations for the propagation and estimation of random and systematic errors in grating reconstruction using a dual-rotating compensator MMP (DRC-MMP). We derive a generalized first-order error propagating formula, which reveals the mechanism of error propagation in grating reconstruction using the DRC-MMP. According to this first-order error propagating formula and the measurement principle of the DRC-MMP, we then derive detailed formulations for the estimation of random and systematic errors that are propagated into the final extracted structural parameters. Simulations performed on silicon grating samples have demonstrated the validity of the present theoretical derivations.

The design of complete broadband polarimeters with high performance is challenging due to the wavelength dependence of optical components. An efficient genetic algorithm computer code was recently developed in order to design and re-optimize complete broadband Stokes polarimeters and Mueller matrix ellipsometers. Our results are improvements of previous patented designs based on two and three ferroelectric liquid crystals (FLCs). FLC based polarimeters are suited for broadband hyperspectral imaging, or multichannel spectroscopy applications. We have realized and implemented one design using two FLCs and compare the spectral range and precision with previous designs.

Producing surfaces textured with a homogeneous pattern of nanoscale structures is increasingly important for fabrication of semiconductor devices. Although techniques exist for imaging surface nanostructures on a local scale, these techniques are often impractical for use over large areas for finding average structural information. The nanostructured surface in this study consists of densely packed cones produced by sputtering a mono-crystalline GaSb substrate with a low-energy unfocused ion beam, yielding self-organized cones that are slightly tilted away from the sample normal. Here, we devise an all-optical non-destructive characterization scheme using Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) and Spectroscopic Mueller Matrix Ellipsometry (MME) for obtaining all main dimensions including average height, lateral spacing and packing motifs, and the cone top and bottom diameters. It is further shown that both MME and GISAXS are sensitive to small tilts of the nanocone axis from the surface normal.

In this work we derive the five patterns of symmetry of a Mueller matrix, a differential Mueller matrix and a Jones matrix that can appear in ellipsometry measurements. While a general nondepolarizing measurement depends on six parameters, we show that there are certain orientations of uniaxial, orthorhombic and monoclinic crystals that result in highly symmetric Muller matrices over all the spectral range, allowing a reduction of the number of independent parameters to less than six. The matrix symmetries for media with optical activity are also examined.

We report on the design and performance of a near infra-red Mueller matrix imaging ellipsometer, and apply the instrument to retardance imaging of strain in near infra-red transparent solids. Particularly, we show that the instrument can be used to investigate complex strain domains in multi-crystalline silicon wafers.

Mechanisms of molecular chirality induction are fundamental to many questions in chemistry. Interest in these mechanisms is shifting toward media of increasing complexity that simultaneously exhibit linear birefringence and dichroism and where the common assumption that optical activity is the only optical effect that affects light polarization is no longer valid. Light propagation through several of these anisotropic media can be appropriately studied with transmission Mueller matrix ellipsometry. The applications presented herein include the measurement of optical activity in stirred solutions of soft-matter nanophases and the determination of chiral domains in solid-state samples.

Current Mueller polarimeters, with either spectral or angular resolution, feature high enough precision and speed to be suitable for many demanding applications, with specific advantages over conventional spectroscopic ellipsometry (SE). Due to the simultaneous determination of depolarization, birefringence and diattenuation Mueller polarimetry (MP) can open new fields in surface and thin film characterization techniques with new and very powerful intrinsic analyses of roughness and/or anisotropy. For more conventional applications, such as scatterometry (i.e. the determination of the shape of periodic structures from optical measurements, mostly used in microelectronics), MP may overpass SE in terms of systematic errors and/or measurement spot size, as discussed from two examples. However, numerical simulations remain a key point to take full advantage of MP capabilities for the new challenges emerging in nanometrology.

Ellipsometry is well-suited for bioadsorption studies and numerous reports, mainly using null ellipsometry, are found on this subject whereas investigations addressing structural properties of thin biolayers are few. Here two examples based on the use of spectroscopic ellipsometry (SE) on the latter are briefly discussed. In the first example, time evolution of thickness, spectral refractive index and surface mass density of a fibrinogen matrix forming on a silicon substrate are investigated with SE and a structural model of the protein matrix is discussed. In the second example a model dielectric function concept for protein monolayers is presented. The model allows parameterization of the optical properties which facilitates monitoring of temperature induced degradation of a protein layer. More recently, photonic structures in beetles have been studied with SE. It is shown here that full Mueller-matrix SE can resolve very complex nanostructures in scarab beetles, more specifically chiral structures causing reflected light to become circularly polarized.

Two lithographic test masks, Stokes polarimeter mask and Mueller matrix polarimeter mask, are introduced. Both the masks comprise newly developed thin polarizers and wide-view-angle λ/4 plates. Photomasks are only 6.35 mm in thickness, and the illumination involves the oblique incidence of 20° at the most. Calcite plates thinned to less than 0.1 mm can perform as polarizers only at a wavelength of 193 nm. The combination of quartz and sapphire plates can mitigate the retardation change with angle of incidence. Stokes polarimeter and Mueller matrix polarimeter masks are used for the measurement of the illumination and the projecting optics, respectively.

We use azimuthally resolved spectroscopic Mueller matrix ellipsometry to study a periodic silicon line structure with and without artificially-generated line width roughness (LWR). We model the artificially perturbed grating using one- and two-dimensional rigorous coupled-wave methods in order to evaluate the sensitivity of the experimental spectrally resolved data, measured using a generalized ellipsometer, to the dimensional parameters of LWR. The sensitivity is investigated in the context of multiple conical mounting (azimuth angle) configurations, providing more information about the grating profile.

Rotatable retarders have been developed for applications in spectroscopic, full Mueller Matrix ellipsometry in the far-IR spectral range. Several materials, such as silicon, KRS-5, and a commercial polymer plastic (TOPAS) have been utilized to achieve a fully adjustable retardation between 0° and 90°. Experimental characteristics of the rotatable retarders that utilize three- and four-bounce designs are compared with calculations. We discuss the effect of light focusing on the performance of these rotatable retarders.

We synthesized polycrystalline Bi 2 + x Te 3 − x (− 0.2 x 2 Te 3 -like structure may be uniaxially anisotropic due to its rhombohedral crystallographic system, we investigated their optical behavior using ex and in situ Mueller matrix spectroscopic ellipsometry in the wavelength range of 470 to 830 nm (1.5–2.6 eV). We found that room-temperature electroplated polycrystalline appears optically isotropic and that no depolarization effect occurs from the first steps of growth until several micrometers thick films. Additional ex situ measurements permit to obtain their optical constants from far-ultraviolet to near-infrared (190–2100 nm).

Phase Modulated Spectroscopic Ellipsometry as well as Liquid Crystal Mueller Matrix Polarimetry in reflection and in transmission configurations were used to systematically study five types of anisotropic polymer sheets: polyethylene-terephtalate (PET), polyethylene-naphtalate (PEN), polycarbonate (PC), polypropylene (PP) and triacetylcellulose (TAC). The measurements were performed at different sample azimuths in two ellipsometric configurations giving access to both standard ellipsometric data as well as to the entire Mueller matrix. Biaxial anisotropy, a common characteristic to all polymer types, as well as the in-depth optical properties, inhomogeneity present in the sheets were clearly evidenced. The data were interpreted in terms of a model consisting of a thick substrate (several microns) coated with a simple layer. Both, substrate and layer were anisotropic and characterized by a triplet of principal refractive indexes. The orientation of the principal indexes of the bulk and the layer were different revealing the in-depth inhomogeniety of the samples.

Recent advances in the design of multichannel ellipsometers based on rotating-element principles have significantly increased their power for applications involving in-situ, real-time analysis of thin films and surfaces. These advances include: (i) extensions in the upper spectral limit beyond the typical value of 4.5 eV, and (ii) increases in the number of extracted parameters beyond the usual two, namely the ellipsometric angles (ψ, Δ). An extended spectral range is enabled, for example, by use of a tandem light source configuration and a grating spectrograph having two stages of order-sorting filters mounted over the window of the linear array detector. With an upper spectral limit of 6.5 eV, such ellipsometers are particularly useful in growth analysis for wide band gap thin films. The larger parameter set is enabled by use of dual or single rotating compensators for polarization state modulation and/or analysis, replacing the traditional rotating polarizer. For the single rotating-compensator instrument in the PSCrA configuration, one can extract the Stokes vector of the reflected beam, and thus its degree of polarization. This in turn can provide information on sample thickness variations over the beam cross-section and can suppress the effects of multiply-scattered light so that non-uniform and macroscopically rough surfaces can be analyzed. For the dual rotating compensator in the PCr1SCr2A configuration, one can extract the entire Mueller matrix of the sample and thus the characteristics of anisotropic surfaces and thin films. Applications of these advances include studies of thickness evolution of the phase for boron nitride and silicon film growth, and the nature and origin of surface-induced optical anisotropy of (110) silicon.

Mueller matrix spectroscopic ellipsometry (MMSE) can be a powerful technique for the study and accurate determination of the dielectric function, optical properties and geometric characteristics of anisotropic materials and complex systems. In this work we present the formalism we developed in order to be able to calculate the sample Mueller matrix using phase-modulated ellipsometry. In order to test the formalism and check the information we can derive spectroscopically by a Mueller matrix, in comparison with standard spectroscopic ellipsometry, we proceeded to the study of an isotropic c-Si wafer and tested the ability of the formulation to calculate correctly its dielectric function using the M 33 and M 43 components in the energy region 1.5–6.5 eV. Also, we have used this formalism to obtain the MMSE spectra of a biaxially anisotropic SnSe bulk sample. Finally, we applied the Mueller matrix formalism for the study of biaxially stretched poly(ethylene terephthalate) (PET) film, as a representative complex anisotropic material. MMSE spectra were obtained for various angles of film's orientation, determined by the angle between the axis of preferential orientation of PET's macromolecules and the plane of incidence where the optical anisotropy of PET was verified. The interpretation of the MMSE spectra is found to provide more insights to the study of anisotropic materials.

A Mueller polarimeter always comprises a polarization state generator (PSG) and a polarization state analyzer (PSA), whose configurations determine the modulation and analysis matrices W and A, involved in the linear relationship between the raw measurement matrix B and the Mueller matrix M of the sample under study. At constant noise in the raw data B, the noise in M is minimized when the condition numbers of both A and W are optimized [E. Compain et al., Rev. Sci. Instrum. 68 (1997) 2671; S. Tyo, Appl. Opt. 41 (2002) 619]. This result provides a quite general criterion for the optimization of instrument design. Typically, this optimization leads to PSG and PSA configurations, which may be difficult to calibrate accurately by usual procedures. This key issue is easily solved by the quite general eigenvalue calibration method [E. Compain et al., Appl. Opt. OT 38 (1999) 3490]. The usefulness of this approach for the development of innovative polarimeters is illustrated with two instruments. One of these comprises a photoelastic modulator and a division-of-amplitude prism, and features a high dynamical range over a broad spectrum, while the other, based on liquid crystal variable retarders, is better suited for imaging applications in the visible and the near infrared.

The Mueller matrices describing oblique incidence reflection and normal incidence transmission have been measured for sculptured thin films (STFs) by glancing angle deposition with simultaneous substrate rotation. In data reduction, the 15 parameters of the (1,1)-normalized real Mueller matrix are converted to the six parameters of the (2,2)-normalized complex Jones matrix. Two computational methods yield excellent agreement in the real and imaginary parts of the complex amplitude ratios ρps and ρsp obtained in reflection (or τps and τsp obtained in transmission). Multilayer optical analysis has been developed that employs step-wise variations of the principal axis Euler angles, associated with the local uniaxial structure in successive sublayers, in order to simulate variations in the column orientation with depth into the film. Such analysis has elucidated the Bragg resonance characteristics exhibited by the optical rotation of chiral STFs.

We have measured spectra from ∼2 to 5 eV in all 15 elements of the normalized Mueller matrix for (110) Si at an angle of incidence of θ a ∼70°, as an initial demanding performance test of a novel dual rotating-compensator multichannel ellipsometer. The Mueller matrix spectra, deduced from 36 waveform integrals collected over a single optical cycle of 0.25 s, can be analyzed to extract the bulk isotropic dielectric function e b = e 1b - ie 2b and the surface-induced dielectric function anisotropy Δe s = Δe 1s -iΔe 2s . Starting from the 15 Mueller matrix elements, six sample parameters are determined, namely the real and imaginary parts of the complex amplitude reflection ratios ρ pp , ρ ps , and ρ sp . The surface-induced anisotropic response (Δe s ) d = [e s (110)-e s (001)]d is deduced from an average of four independent spectra, two in ρ sp and two in ρ ps = - ρ sp using the first order term in d/λ from an expansion of the partial transfer matrix. Here d is the surface anisotropic layer thickness and λ is the vacuum wavelength. Because both the real and imaginary parts of (Δe s )d are now accessible, the results can be fit using a Kramers-Kronig (K-K) consistent oscillator model. The key advantage of the newly-developed instrument is the ability to perform spectroscopic measurements in real time that simultaneously provide bulk isotropic and surface- or interface-induced anisotropic optical responses.

Generalized spectroscopic ellipsometry (g-SE) and Mueller-matrix (MM) measurements are applied to twisted nematic (TN) and super twisted nematic (STN) displays. Transmitted measurements near normal incidence are used to extract twist, φ(d), and anisotropy for each display type. Angle-dependent measurements are used to determine tilt distribution, θ(d). Oblique angle measurements allow characterization of both ordinary and extraordinary indices. Finally, the liquid crystal layer thickness is accurately determined from coherent interference oscillations.

A multichannel ellipsometer in the dual rotating-compensator configuration has been designed and constructed for applications in real time Mueller matrix ellipsometry (approx. 2–5 eV) of anisotropic surfaces and films. The sequence of optical elements for this instrument is denoted PC 1r ( ω 1 ) SC 2r ( ω 2 ) A , where P , S , and A represent the polarizer, sample, and analyzer. C 1r ( ω 1 ) and C 2r ( ω 2 ) represent two MgF 2 biplate compensators that rotate at frequencies of ω 1 /2 π =10 Hz and ω 2 /2 π =6 Hz, synchronized for a ratio ω 1 : ω 2 of 5:3. Spectra in the 16 Mueller matrix elements of a transmitting or reflecting sample can be established from the 25 non-zero Fourier coefficients of the irradiance waveform acquired in a single 0.25 s optical cycle . Initial high speed Mueller matrix measurements have been performed on weakly anisotropic samples that push the instrument to its precision/accuracy limits. These include the (110) Si surface with maximum cross-polarization ellipsometric angles of ψ ps ∼0.1° and nanostructured thin films with maximum ψ ps ∼1°.

Deuterated potassium dihydrogen phosphate (DKDP) is used for third harmonic generation (frequency tripling) in high power laser applications [Ferroelectrics, 72, 1987, 397–441; Int. Mater. Rev. 47, 2002, 113–152]. DKDP is a uniaxial anisotropic crystal, which is highly transparent in the visible and infrared spectral ranges. This makes DKDP challenging but well suited for study by both transmission ellipsometry and more conventional reflection-mode ellipsometry. Mueller matrix ellipsometry measurements were required because the data included both anisotropic and depolarizing effects. A rotating analyzer ellipsometer, with computer-controlled Berek compensator after the input polarizer and before the sample, allowed measurement of 11 Mueller matrix elements in transmission mode. Spectroscopic transmission Mueller matrix measurements allow the index difference Δ n = n o − n e to be determined throughout the transparent spectral range along with the orientation of the optic axis. Reflection mode ellipsometry is used to extract the absolute index of the ordinary component over the spectral range 0.73 to 9 eV (138–1700 nm). Determination of one index component allows calculation of the other component since the difference n o − n e is known from the transmission Mueller matrix measurements.

This is the eighth in the aperiodic series of ellipsometry conferences, and the third devoted specifically to spectroscopic ellipsometry. I discuss the evolution of the field mainly from a technological perspective, and the changes that must be made in analytic procedures as accuracy requirements are increased from 1 to 0.1%. The current interest in Mueller-matrix spectroscopy motivates a discussion on how to include depolarization artifacts in Mueller-matrix calculations from first principles. Representative applications include extensions to the far infrared and vacuum ultraviolet, the determination of all elements of the Mueller matrix with a stationary sample, and the determination of critical dimensions by scatterometry.

Ellipsometry experiments normally measure two to four parameters, which are converted to the ellipsometric parameters ψ and Δ. This is usually sufficient for many samples, but more complicated situations (such as anisotropic or depolarizing samples) require more sophisticated measurements. Over the last 7 years, we have developed the two-modulator generalized ellipsometer (2-MGE), which measures eight elements of the sample Mueller matrix simultaneously either in reflection or transmission. In reflection, the 2-MGE totally characterizes light reflection from anisotropic samples, measuring the normal ellipsometry parameters, as well as the cross-polarization and depolarization effects. Applications include the determination of the spectroscopic optical functions of uniaxial materials (such as TiO2 and ZnO), and the measurement of cross-polarization from diffractive structures. In transmission, the 2-MGE completely characterizes a general linear diattenuator and retarder. Applications include the measurement of the retardation and diattenuation of film polarizers and internal electric fields in LiNbO3 and CdZnTe under bias.

A dual rotating compensator ellipsometer based on the optical PC1SC2A configuration described by Collins [1, chap. 7.3] has been developed. The systematic errors for this configuration if the compensators are quarter-wave plates have been already studied [2, 3, 4]. Smith [5] has demonstrated that the optimum retardance of a dual-rotating-retarder (DRR) instrument must be equal to 127° compared to the quarter-wave (90°) retarders generally used. In this condition random errors are optimized. The aim of this work is to used such retarders and verify if the systematic errors due to uncertainties of the optical elements (i.e. analyzer, polarizer, first and second compensators) are improved too. For each optical element in different configurations like single or 4-zone average measurements, the systematic errors are given and compared according to the compensators. It is demonstrated that using a 127° instead of quarter-wave retarders coupled with 4-zone averaging measurement is the best configuration for this instrument. These results were confirmed by a statistical study.