Spectroscopic ellipsometry data analysis: Measured vs. calculated quantities

Spectroscopic ellipsometry is a very powerful technique for optical characterization of thin-film and bulk materials, but the technique measures functions of complex reflection coefficients, which are usually not of interest per se. The interesting characteristics such as film thickness, surface roughness thickness, and optical functions can be determined only by modeling the near-surface region of the sample. However, the measured quantities are not equivalent to those determined from the modeling. Ellipsometry measurements determine elements of the sample Mueller matrix, but the usual result of modeling calculations are elements of the sample. Often this difference is academic, but if the sample depolarizes the light, it is not. Ellipsometry calculations also include methods for determining the optical functions of materials. Data for bulk materials are usually accurate for substrates, but are not appropriate for most thin films. Therefore, reasonable parameterizations are quite useful in performing spectroscopic ellipsometry data analysis. Recently, there has been an increased interest in anisotropic materials, both in thin-film and bulk form. A generalized procedure will be presented for calculating the elements of the Jones matrix for any number of layers, any one of which may or may not be uniaxial

The calculation of thin film parameters from spectroscopic ellipsometry data

Spectroscopic ellipsometry (SE) has proven to be a very powerful diagnostic for thin film characterization, but the results of SE experiments must first be compared with calculations to determine thin film parameters such as film thickness and optical functions. This process requires 4 steps: (1) The quantities measured must be specified and the equivalent calculated parameters identified. (2) The film structure must be modeled, where the number of films is specified and certain characteristics of each layer specified, such as whether or not the film is isotropic or anisotropic, homogeneous or graded. (3) The optical functions of each layer must be specified or parameterized. (4) The data must be compared with the calculated spectra, where a quantifiable figure of merit is used for the comparison. The last step is particularly important because without it, no {open_quotes}goodness of fit{close_quotes} parameter is calculated and one does not know whether or not the calculated spectrum fits the data

Development of the Two-Modulator Generalized Ellipsometer (2-MGE) for Commercial Application

The two-modulator generalized ellipsometer (2-MGE) is an instrument that measures the change of light polarization upon interacting with a sample. The 2-MGE can operate in either reflection or transmission. In reflection, it acts as a generalized ellipsometer, measuring the standard ellipsometry parameters, as well as the cross-polarization parameters. In transmission, it measures all parameters associated with a general diattenuation and retarder. In this CRADA, Hinds and ORNL have explored the commercial possibilities of the 2-MGE. This exploration has taken two primary paths. First, prototypes were built at both ORNL and Hinds. Second, various scientific applications were explored, including characterization of Polaroid-like materials and various materials under electric field. The main purpose of this CRADA was to develop the two-modulator generalized ellipsometer (2-MGE) into a commercial product. The 2-MGE is an ORNL patented technology (U. S. Patent No. 5956147 (1999)). Associated with the 2-MGE is the computer program EllipsCalc, which is used to simulate spectroscopic ellipsometry data in order to determine useful parameters, such as film thickness, surface roughness, interface thickness, and spectroscopic refractive indices, from the 2-MGE data. To this end, the CRADA had several objectives contained in two phases

Spectroscopic ellipsometry characterization of thin-film silicon nitride

We have measured and analyzed the optical characteristics of a series of silicon nitride thin films prepared by plasma-enhanced chemical vapor deposition on silicon substrates for photovoltaic applications. Spectroscopic ellipsometry measurements were made by using a two-channel spectroscopic polarization modulator ellipsometer that measures N, S, and C data simultaneously. The data were fit to a model consisting of air / roughness / SiN / crystalline silicon. The roughness was modeled using the Bruggeman effective medium approximation, assuming 50% SiN, 50% voids. The optical functions of the SiN film were parameterized using a model by Jellison and Modine. All the {Chi}{sup 2} are near 1, demonstrating that this model works extremely well for all SiN films. The measured dielectric functions were used to make optimized SiN antireflection coatings for crystalline silicon solar cells

Proximity induced metal/insulator transition in YBa2Cu3O7/La2/3Ca1/3MnO3Y Ba_2 Cu_3 O_7 / La_{2/3} Ca_{1/3} Mn O_3 superlattices

The far-infrared dielectric response of superlattices (SL) composed of superconducting YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO) and ferromagnetic La$_{0.67}$% Ca$_{0.33}$MnO$_{3}$ (LCMO) has been investigated by ellipsometry. A drastic decrease of the free carrier response is observed which involves an unusually large length scale of d$^{crit}\approx$20 nm in YBCO and d$^{crit}\approx$10 nm in LCMO. A corresponding suppression of metallicity is not observed in SLs where LCMO is replaced by the paramagnetic metal LaNiO$_{3}$. Our data suggest that either a long range charge transfer from the YBCO to the LCMO layers or alternatively a strong coupling of the charge carriers to the different and competitive kind of magnetic correlations in the LCMO and YBCO layers are at the heart of the observed metal/insulator transition. The low free carrier response observed in the far-infrared dielectric response of the magnetic superconductor RuSr$_{2}$GdCu$_{2}$O$_{8}$ is possibly related to this effect

Optical properties of MgH2 measured in situ in a novel gas cell for ellipsometry/spectrophotometry

The dielectric properties of alpha-MgH2 are investigated in the photon energy range between 1 and 6.5 eV. For this purpose, a novel sample configuration and experimental setup are developed that allow both optical transmission and ellipsometric measurements of a transparent thin film in equilibrium with hydrogen. We show that alpha-MgH2 is a transparent, colour neutral insulator with a band gap of 5.6 +/- 0.1 eV. It has an intrinsic transparency of about 80% over the whole visible spectrum. The dielectric function found in this work confirms very recent band structure calculations using the GW approximation by Alford and Chou [J.A. Alford and M.Y. Chou (unpublished)]. As Pd is used as a cap layer we report also the optical properties of PdHx thin films.Comment: REVTeX4, 15 pages, 12 figures, 5 table

Interdiffusion at Sb/Ge interfaces induced in thin multilayer films by nanosecond laser irradiation

Thin films consisting of 3 or 4 Sb and Ge alternating layers are irradiated with single nanosecond laser pulses (12 ns, 193 nm). Real time reflectivity (RTR) measurements are performed during irradiation, and Rutherford backscattering spectrometry (RBS) is used to obtain the concentration depth profiles before and after irradiation. Interdiffusion of the elements takes place at the layer interfaces within the liquid phase. The reflectivity transients allow to determine the laser energy thresholds both to induce and to saturate the process being both thresholds dependent on the multilayer configuration. It is found that the energy threshold to initiate the process is lower when Sb is at the surface while the saturation is reached at lower energy densities in those configurations with thinner layers

Molecular-jet chemical vapor deposition of SiC

SiC films have been deposited by molecular-jet chemical vapor deposition (MJCVD) on Si(001) substrates. Methylsilane (MS) diluted in He was used as a precursor for deposition under conditions which produced a MS molecular beam with 0.365 eV translational energy. Films grown at temperatures between 1000 and 1150 C and above {approx}1200 C were single crystal as judged by electron channeling, while those grown at intermediate temperatures were polycrystalline. Films grown at lower temperatures generally had a smoother surface morphology for moderate thicknesses, although all films showed at least some degree of faceting. The best thick films, up to 4 {mu}m, were obtained for substrate temperatures of {approx}1210 C under flow conditions which produced a deposition rate of {approx}1200 {angstrom} per minute

Calibration Procedures for a Two-Modulator Generalized Ellipsometer

A Two-Modulator Generalized Ellipsometer (2-MGE) has been extremely useful in characterizing optical properties of uniaxial bulk materials, thin films and diffraction gratings. The instrument consists of two polarizer-photoelastic modulator pairs, one operating as the polarization state generator and the other as the polarization state detector. Each photoelastic modulator operates at a different remnant frequency (such as 50 kHz and 60 kHz), making it possible to measure eight elements of the reduced sample Mueller matrix simultaneously. In certain configurations, light reflection from non-depolarizing anisotropic samples can be completely characterized by a single measurement, and the entire reduced Jones matrix can be determined, including the cross polarization coefficients. The calibration of the instrument involves the measurement of the azimuthal angle of the polarizer with respect to the modulator, the modulation amplitude, and the modulator strain for each polarizer photoelastic modulator pair, where the last two are functions of wavelengths. In addition, it is essential to calibrate the azimuthal angles of the polarization state generator and the polarization state detector with respect to the plane of incidence in the ellipsometry configuration that is used in the measurements. Because two modulators operating at different frequencies are used, these calibrations are actually easier and more accurate than for one modulator ellipsometers. In this paper, we will discuss these calibrations and the resultant accuracy limitations of the 2-MGE