L. Broch

Systematic errors for a Mueller matrix dual rotating compensator ellipsometer.

The characterization of anisotropic materials and complex systems by ellipsometry has pushed the design of instruments to require the measurement of the full reflection Mueller matrix of the sample with a great precision. Therefore Mueller matrix ellipsometers have emerged over the past twenty years. The values of some coefficients of the matrix can be very small and errors due to noise or systematic errors can induce distored analysis. We present a detailed characterization of the systematic errors for a Mueller Matrix Ellipsometer in the dual-rotating compensator configuration. Starting from a general formalism, we derive explicit first-order expressions for the errors on all the coefficients of the Mueller matrix of the sample. The errors caused by inaccuracy of the azimuthal arrangement of the optical components and residual ellipticity introduced by imperfect optical elements are shown. A new method based on a four-zone averaging measurement is proposed to vanish the systematic errors.

Fixed polarizer, rotating-polarizer and fixed analyzer spectroscopic ellipsometer: accurate calibration method, effect of errors and testing

Abstract We present a detailed description of fixed polarizer, rotating-polarizer and fixed analyzer spectroscopic ellipsometer called PRPSE. This configuration is especially interesting in that it eliminates the residual polarization of the light source. For the first time, to our knowledge, the optimized calibration procedure of PRPSE and the systematic and statistical errors are reported. Three calibration steps are necessary to determine all azimuthal angles of the instrument. The reflection measurement from a sample 109 nm SiO 2 on silicon substrate is used as an example for the calibration procedure. The main sources of errors in PRPSE are presented and discussed. The tracking method is used to minimize the random errors and new functions are found to position the analyzer. Experimental verification of error reductions and stability tests are also achieved. The average values of ellipsometric parameters are obtained with a standard deviation of approximately 10 −3 for tanΨ and cosΔ.

Real time in situ ellipsometric and gravimetric monitoring for electrochemistry experiments

This work describes a new system using real time spectroscopic ellipsometer with simultaneous electrochemical and electrochemical quartz crystal microbalance (EQCM) measurements. This method is particularly adapted to characterize electrolyte/electrode interfaces during electrochemical and chemical processes in liquid medium. The ellipsometer, based on a rotating compensator Horiba Jobin-Yvon ellipsometer, has been adapted to acquire Psi-Delta spectra every 25 ms on a spectral range fixed from 400 to 800 nm. Measurements with short sampling times are only achievable with a fixed analyzer position (A=45 degrees ). Therefore the ellipsometer calibration is extremely important for high precision measurements and we propose a spectroscopic calibration (i.e., determination of the azimuth of elements according to the wavelength) on the whole spectral range. A homemade EQCM was developed to detect mass variations attached to the electrode. This additional instrument provides further information useful for ellipsometric data modeling of complex electrochemical systems. The EQCM measures frequency variations of piezoelectric quartz crystal oscillator working at 5 MHz. These frequency variations are linked to mass variations of electrode surface with a precision of 20 ng cm(-2) every 160 ms. Data acquisition has been developed in order to simultaneously record spectroscopic ellipsometry, EQCM, and electrochemical measurements by a single computer. Finally the electrodeposition of bismuth telluride film was monitored by this new in situ experimental setup and the density of electroplated layers was extracted from the optical thickness and EQCM mass.

Microstructure and optical dispersion characterization of nanocomposite sol–gel TiO2–SiO2 thin films with different compositions

Nanocomposite TiO2-SiO2 thin films with different compositions (from 0 to 100 mol% TiO2) were deposited by sol-gel dip-coating method on silicon substrate. Crystal structure, chemical bonding configuration, composition and morphology evolutions with composition were followed by Raman scattering, Fourier transform infrared spectroscopy, energy-dispersive X-ray spectroscopy and scanning electron microscopy respectively. The refractive index and the extinction coefficient were derived in a broad band wavelength (250-900 nm) from spectroscopic ellipsometry data with high accuracy and correlated with composition and microstructure. Results showed an anatase structure for 100% TiO2 with a grain size in 6-10nm range. Whereas, the inclusion of SiO2 enlarges the optical band gap and suppresses the grain growth up to 4 nm in size. High TiO2 dispersion in SiO2 matrix was observed for all mixed materials. The refractive index (at λ=600 nm) increases linearly with composition from 1.48 (in 100% SiO2) to 2.22 (in 100% TiO2) leading to lower dense material, its dispersion being discussed in terms of the Wemple-DiDomenico single oscillator model. Hence, the optical parameters, such optical dispersion energies E0 and Ed, the average oscillators, strength S0 and wavelength λ0 and the ratio of the carrier concentration to the effective mass N/m(∗) have been derived. The analysis revealed a strong dependence on composition and structure. The optical response was also investigated in term of complex optical conductivity (σ) and both volume and surface energy loss functions (VELF and SELF).

Second-order systematic errors in Mueller matrix dual rotating compensator ellipsometry

We investigate the systematic errors at the second order for a Mueller matrix ellipsometer in the dual rotating compensator configuration. Starting from a general formalism, we derive explicit second-order errors in the Mueller matrix coefficients of a given sample. We present the errors caused by the azimuthal inaccuracy of the optical components and their influences on the measurements. We demonstrate that the methods based on four-zone or two-zone averaging measurement are effective to vanish the errors due to the compensators. For the other elements, it is shown that the systematic errors at the second order can be canceled only for some coefficients of the Mueller matrix. The calibration step for the analyzer and the polarizer is developed. This important step is necessary to avoid the azimuthal inaccuracy in such elements. Numerical simulations and experimental measurements are presented and discussed.

Near-forward Raman study of a phonon-polariton reinforcement regime in the Zn(Se,S) alloy

We investigate by near-forward Raman scattering a presumed reinforcement of the (A-C,B-C)-mixed phonon-polariton of a A1-xBxC zincblende alloy when entering its longitudinal optical-like (LO-like) regime near the Brillouin zone centre Γ, as predicted within the formalism of the linear dielectric response. A choice system to address such issue is ZnSe0.68S0.32 due to the moderate dispersion of its refractive index in the visible range, a sine qua non condition to bring the phonon-polariton insight near Γ. The LO-like reinforcement regime is actually accessed by using the 633.0u2009nm laser excitation, testified by the strong emergence of the (Zn-Se,Zn-S)-mixed phonon-polariton at ultimately small scattering angles.

Pressure-induced phonon freezing in the ZnSeS II-VI mixed crystal: phonon-polaritons and ab initio calculations.

Near-forward Raman scattering combined with ab initio phonon and bond length calculations is used to study the phonon-polariton transverse optical modes (with mixed electrical-mechanical character) of the II-VI ZnSe1-x S x mixed crystal under pressure. The goal of the study is to determine the pressure dependence of the poorly-resolved percolation-type Zn-S Raman doublet of the three oscillator [1u2009u2009×u2009u2009(Zn-Se), 2u2009u2009×u2009u2009(Zn-S)] ZnSe0.68S0.32 mixed crystal, which exhibits a phase transition at approximately the same pressure as its two end compounds (~14u2009GPa, zincblendeu2009u2009→u2009u2009rocksalt), as determined by high-pressure x-ray diffraction. We find that the intensity of the lower Zn-S sub-mode of ZnSe0.68S0.32, due to Zn-S bonds vibrating in their own (S-like) environment, decreases under pressure (Raman scattering), whereas its frequency progressively converges onto that of the upper Zn-S sub-mode, due to Zn-S vibrations in the foreign (Se-like) environment (ab initio calculations). Ultimately, only the latter sub-mode survives. A similar phonon freezing was earlier evidenced with the well-resolved percolation-type Be-Se doublet of Zn1-x Be x Se (Pradhan et al 2010 Phys. Rev. B 81 115207), that exhibits a large contrast in the pressure-induced structural transitions of its end compounds. We deduce that the above collapse/convergence process is intrinsic to the percolation doublet of a short bond under pressure, at least in a ZnSe-based mixed crystal, and not due to any pressure-induced structural transition.

Spectroscopic ellipsometric characterization of approximant thin films of Al–Cr–Fe deposited on glass substrates

The reflection spectroscopic ellipsometric study of optical properties of thin films of Al–Cr–Fe is presented. PRPSE (polarizer, rotating polarizer spectroscopic ellipsometer) equipped with a quarter wave achromatic is used for thin films/ glasses analysis. Al–Cr–Fe approximant thin films were deposited from the vapor phase on the glass substrates. The optical constants were determined at room temperature in the spectral range from 500 to 800 nm. Surface layer on the glass substrates was treated as a mixture of voids and Al–Cr–Fe by using Bruggeman effective medium approximation. The surface oxidation has been identified as Al2O3 and the thin film thickness were found to be a few nanometers, and in agreement with transmission electron microscopy (TEM).

Ellipsometry of Colloidal Solutions: New Experimental Setup and Application to Metallic Colloids

An ellipsometric cell is developed to simultaneously determine the shape distribution, the volume fraction, and the complex refractive index of gold and silver colloids. Simulation reveals that this cell drastically improves the detection limit of ellipsometry. Indeed, Ag and Au nanoparticles (NPs) are detected at the ppmv level. We demonstrate that the NPs shape distribution can be estimated from ellipsometric measurements by analyzing them with a shape distributed effective medium theory (SDEMT). The obtained distributions from ellipsometry are in agreement with those deduced from transmission electron microcopy (TEM). Contrary to TEM, ellipsometry probes a large number of NPs estimated at about 1011 NPs. Finally, we show that the complex refractive index of colloids as determined from ellipsometry is sensitive to the optical properties of the solvent and the plasmonic properties of NPs.

Near-forward Raman selection rules for the phonon-polariton in (Zn, Be)Se alloys

The Raman selection rules of the (Zn-Se, Be-Se)-mixed phonon-polariton ( PP) created by “alloying” in the three-mode [1u2009×u2009(Zn-Se), 2u2009×u2009(Be-Se)] Zn1−xBexSe system, whose dramatic S-like dispersion (∼200u2009cm−1) covers the large frequency gap between the Zn-Se and Be-Se spectral ranges, are studied in its wave vector ( q) dependence by near-forward Raman scattering. Both the “collapse” regime away from the Γ point (qu2009=u20090) and the “reinforcement” regime near Γ are addressed, using appropriate laser lines and Be contents. We find that in both regimes the considered PP, in fact a transverse mode with the mixed mechanical-electrical character, obeys the same nominal Raman selection rules as its purely mechanical variant observed in the standard backscattering geometry. The discussion is supported by contour modeling of the multi- PP Raman lineshapes in their q-dependence within the linear dielectric approach.