Blaine D. Johs

Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO 2

For what is the first time, to our knowledge, we report on the extension of spectroscopic rotating-analyzer ellipsometry to generalized ellipsometry to define and to determine three essentially normalized elements of the optical Jones matrix J [ R. M. A. Azzam N. M. Bashara , J. Opt. Soc. Am.62, 1521 ( 1972)]. These elements are measured in reflection over the spectral range of 3.5–4.5 eV on different surface orientations of uniaxial TiO2 cut from the same bulk crystal. With a wavelength-by-wavelength regression and a 4 × 4 generalized matrix algebra, both refractive and absorption indices for the ordinary and the extraordinary waves, no, ko, ne, and ke, are determined. The inclinations and the azimuths of the optic axes with respect to the sample normal and plane of incidence were determined as well. The latter are confirmed by x-ray diffraction and polarization microscopy. Hence the spectrally dependent dielectric function tensor in laboratory coordinates is obtained. Very good agreement between measured and calculated data for the normalized Jones elements for the respective sample orientations and positions are presented. This technique may become an important tool for investigating layered systems with nonscalar dielectric susceptibilities.

Overview of variable-angle spectroscopic ellipsometry (VASE): I. Basic theory and typical applications

Variable angle spectroscopic ellipsometry (VASE) is important for metrology in several industries, and is a powerful technique for research on new materials and processes. Sophisticated instrumentation and software for VASE data acquisition and analysis is available for the most demanding research applications, while simple to use software enables the use of VASE for routine measurements as well. This article gives a basic introduction to the theory of ellipsometry, references “classic” papers, and shows typical VASE applications. In the following companion paper, more advanced applications are discussed.

Techniques for ellipsometric measurement of the thickness and optical constants of thin absorbing films

Abstract The determination of both the optical constants and thickness of thin, optically absorbing films, particularly on opaque substrates, is a difficult problem when approached solely with ellipsometric techniques. This is due to the strong statistical correlation which exists between the optical constants of the film (primarily the extinction coefficient) and the thickness of the film when adjusting these parameters to fit the experimental ellipsometric data. In this paper we present several techniques which are useful for the solution of this problem, and illustrate the success of these individual techniques with analysis of several thin films of amorphous hydrogenated carbon.

Modeling AlxGa1−xAs optical constants as functions of composition

Three models for the dielectric function ex(hν) of AlxGa1−xAs are reviewed. All are based on measured optical constants at discrete compositions. The validity of each model near critical point energies, and otherwise, is evaluated. Only the energy‐shift model is appropriate over the entire available spectrum (1.5–6.0 eV), including the band‐gap (E0) region.

Regression calibration method for rotating element ellipsometers

Abstract A new method for calibrating rotating element ellipsometers is described. This procedure is similar in concept to the residual calibration procedure developed by Aspnes (D. E. Aspnes, J. Opt. Soc. Am., 64 (1974) 812; D. E. Aspnes and A. A. Studna, Appl. Opt., 14 (1975) 220). However, instead of using a parabolic approximation to fit the calibration data, the calibration data are fitted to the exact expressions that model the response of the optical system, using an iterative regression algorithm. The regression calibration method offers many advantages: (1) accurate calibration can be obtained on nearly any sample; (2) highly accurate values of the ellipsometric parameters ψ and Δ are also extracted from the regression analysis; (3) the quality of the regression fit can be used to quantify the accuracy of the optical system. The method may also be easily extended to account for non-ideal elements in the optical system, such as polarization-dependent sensitivity in the detector system.

Overview of variable-angle spectroscopic ellipsometry (VASE): II. Advanced applications

A preceding companion paper provides a general introduction to Variable Angle Spectroscopic Ellipsometry (VASE), and also describes many typical applications of the technique. In this paper, more advanced VASE applications are discussed. These applications rely on recent advances in ellipsometric hardware, which allow extremely accurate ellipsometric data to be acquired over a broad spectral range, from the IR to VUV. This instrumentation can also quantitatively measure the optical response of nonisotropic samples. Advanced data analysis techniques are also presented.

Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals

We report on the application, for the first time to our knowledge, of spectroscopic generalized ellipsometry to liquid crystal materials. We have measured the three normalized elements of the Jones transmission matrix t at various sample temperatures within the spectral range from 340 to 1700 nm (0.73 to 3.65 eV) on thin cells filled with twisted nematic mixtures 4-cyano-4′-pentylbiphenyl (5CB) and 4-cyano-4′-(2 methyl)-butylbiphenyl (CB15) (Ref. 4). The Berreman 4 × 4 matrix for electromagnetic plane waves in a biaxial medium homogeneously twisted along the sample normal is derived and presented. Analytic expressions in the case of light propagation along the helical axis permit the calculation of the transmission and reflection coefficients simultaneously without numerical approximations. This solution is valid for any biaxial configuration of chiral liquid crystals, including the case of absorption. We have fully analyzed the measured Jones transmission matrix elements and obtained the geometrical sample properties and, as a function of the photon energy and the temperature, the refractive indices no, and ne of the chiral liquid crystals. We found that within the experimental error the main refractive indices of the mixtures 5CB and CB15 are those of pure 5CB at the same reduced temperatures. The handedness of the optical activity of the samples can be obtained immediately from the phase information of the Jones transmission matrix coefficients.

Real-time monitoring and control during MOVPE growth of CdTe using multiwavelength ellipsometry

Abstract New multi-wavelength in-situ ellipsometer hardware and data analysis software are described. The hardware can simultaneously acquire accurate ellipsometric data at 12 wavelengths in less than 1 s, is simple and compact and is well suited for in-situ monitoring. The data analysis software implements a “virtual interface” approach to determine in real time the characteristics (growth rate and composition) of the near-surface region of the film. These new tools were used to study the metal-organic vapor phase epitaxy (MOVPE) growth of CdTe on GaAs. From a post-deposition analysis of the in-situ data, dielectric constants of CdTe at growth temperature were obtained. Non-uniformity in the CdTe film thickness, and film nucleation during the initial stages of growth, were also observed in the post-deposition analysis. The determined CdTe dielectric constants were utilized in subsequent depositions to determine the growth rate of a CdTe film in real time. Feedback control of the CdTe growth rate was effected by connecting an analog control voltage line from the data acquisition/analysis computer to the Cd mass flow controller.

Progress in spectroscopic ellipsometry: Applications from vacuum ultraviolet to infrared

Spectroscopicellipsometry (SE) is a noncontact and nondestructive optical technique for thin film characterization. In the past 10 yr, it has migrated from the research laboratory into the semiconductor, data storage, display, communication, and optical coating industries. The wide acceptance of SE is a result of its flexibility to measure most material types: dielectrics, semiconductors, metals, superconductors, polymers, biological coatings, and even multilayers of these materials. Measurement of anisotropic materials has also made huge strides in recent years. Traditional SE measurements cover the ultraviolet, visible, and near infrared wavelengths. This spectral range is now acquired within seconds with high accuracy due to innovative optical configurations and charge coupled device detection. In addition, commercial SE has expanded into both the vacuum ultraviolet (VUV) and midinfrared (IR). This wide spectral coverage was achieved by utilizing new optical elements and detection systems, along with UV or Fourier transform IR light sources. Modern instrumentation is now available with unprecedented flexibility promoting a new range of possible applications. For example, the VUVspectral region is capable of characterizing lithographic materials for 157 nm photolithography. The VUV also provides increased sensitivity for thin layers (e.g., gate oxides or self-assembled monolayers) and allows investigation of high-energy electronic transitions. The infrared spectral region contains information about semiconductor doping concentration, phonon absorption, and molecular bond vibrational absorptions. In this work, we review the latest progress in SE wavelength coverage. Areas of significant application in both research and industrial fields will be surveyed, with emphasis on wavelength-specific information content.

Cuticle structure of the scarab beetle Cetonia aurata analyzed by regression analysis of Mueller-matrix ellipsometric data

Since one hundred years it is known that some scarab beetles reflect elliptically and near-circular polarized light as demonstrated by Michelson for the beetle Chrysina resplendens. The handedness of the polarization is in a majority of cases left-handed but also right-handed polarization has been found. In addition, brilliant colors with metallic shine are observed. The polarization and color effects are generated in the beetle exoskeleton, the so-called cuticle. The objective of this work is to demonstrate that structural parameters and materials optical functions of these photonic structures can be extracted by advanced modeling of spectral multi-angle Mueller-matrix data recorded from beetle cuticles. A dual-rotating compensator ellipsometer is used to record normalized Mueller-matrix data in the spectral range 400 - 800 nm at angles of incidence in the range 25-75°. Analysis of data measured on the scarab beetle Cetonia aurata are presented in detail. The model used in the analysis mimics a chiral nanostructure and is based on a twisted layered structure. Given the complexity of the nanostructure, an excellent fit between experimental and model data is achieved. The obtained model parameters are the spectral variation of the refractive indices of the cuticle layers and structural parameters of the chiral structure.