Rotating-compensator Ellipsometer Research Articles

Transient dielectric functions of Ge, Si, and InP from femtosecond pump-probe ellipsometry

Transient dielectric functions with a 120 fs time resolution of Ge, Si, and InP were acquired from 1.7 to 3.5 eV with a femtosecond pump-probe rotating-compensator ellipsometer. The intensity of the pump laser (with 1.55, 3.10, or 4.65 eV photon energy) was adjusted to create an initial near-surface carrier density of 1020 cm−3. In Ge, there is a significant (∼15%) decrease in the E1 and E1 + Δ1 critical point absorption and a Kramers–Kronig consistent change in the refractive index because photoexcited electrons at L block these transitions and reduce their amplitudes. Only a small redshift of the E1 critical point is observed, which we attribute to lattice heating and exchange-correlation effects. Minimal changes were found for Si and InP, where electrons near Δ and Γ do not participate in interband transitions between 1.7 and 3.5 eV.

Determination of Anisotropic Crystal Optical Properties Using Mueller Matrix Spectroscopic Ellipsometry

In this paper the Mueller matrix ellipsometry in the spectral range from 0.73 to 6.4eV measured using dual rotating compensator ellipsometer RC2 (Woollam company) is applied to study anisotropic crystals. First we summarize the effects of optical anisotropy to Mueller matrix spectra. As an example of an uniaxial sample we have characterized a Rutile (TiO2) tetragonal crystal. The optical axis of the sample is parallel to its surface. The sample is characterized at variable angle of incidence and variable azimuthal rotation angle. The Mueller matrix spectra are fitted to the model based on Kramers-Kronig consistent Basis spline and obtained optical functions are compared with tabulated data and ab-initio models based on first-principle calculated electronic structure.

Optical Constants Determination of Pseudomorphic Si1-XGex Layers on Si(001), with 0

Spectroscopic ellipsometry (SE) is the technique of choice for the fast, non-destructive characterization of pseudomorphic Si1-xGex/silicon heterostructures in a manufacturing environment. Because of its small spot, SE can indeed be used on blanket wafers for epitaxial process monitoring and on patterned wafers for measurement in dedicated structures as small as 50 x 50 μm². Still, SE analysis is sometimes plagued by correlation effects, i.e. difficulties in determining the thickness and optical properties in a de-convoluted manner. A reliable alloy model that would accurately describe the optical constants of fully strained Si1-xGex material in a large range of germanium content is thus required to minimize correlation in the SE analysis of Si1-xGex/Si heterostructures. Such an alloy model must be based on a set of high-quality epitaxial films characterized with i/ an accurate spectroscopic ellipsometer in order to access to the Ψ and Δ angles over a wide spectral range and ii/ analytical techniques such as X-ray reflectometry (XRR) or high-resolution X-ray diffraction (XRD), in order to accurately gain access to the thickness of the epitaxial film and its germanium content and confirm that films are indeed fully pseudomorphic.The pseudodielectric function <ε>=<ε1>+i<ε2> deduced from the Ψ and Δ angles (figure) contains contributions from surface over-layers (native oxide, surface roughness, airborne molecular contamination) and from the substrate, since the penetration depth is most of the time higher that the critical thickness for plastic relaxation of Si1-xGex, above which such layers are not fully pseudomorphic anymore. Pickering et al. described the impact of surface over-layers and provided ways to access the true dielectric function of the Si1-xGex alloy. The most effective approach is a SE measurement immediately after removing the sample from the growth reactor together with a modelling of the SE data with a {overlayer/Si1-xGex /substrate} system. Some micro-roughness and potentially some excess Ge segregating on the growing surface can indeed contribute to this over-layer. Supposing that it is in fact a 0.5-0.7nm thick SiO2layer will however introduce negligible errors. Other authors did not include time constraints between process and measurement and determined the thickness of the overlayer from the non-vanishing pseudoabsorption below the bandgap, resulting in oxide thickness up to 2 nm, depending on the aging of the layer.Optical constants of strained Si1-xGex are usually available in the x = 0 - 0.35 range. This abstract describes variable-angle spectroscopic ellipsometry (VASE) measurements from 0.73 to 6.48 eV on a Woollam M2000 rotating compensator ellipsometer on a series of high-quality pseudomorphic Si1-xGex films (0<x<0.54) grown by Reduced Pressure Chemical Vapor Deposition (RP-CVD) on Si(001) substrates. XRD and XRR were used to determine the germanium content and the thickness of the Si1-xGex films, respectively. The management of the surface over-layer combined a “HF-last” wet cleaning step immediately followed by SE and XRR measurements, so as to get rid of the contributions of airborne molecular contamination and aging of the epitaxial layer. The dielectric function of each Si1-xGex film of this reference wafer set was calculated using XRR-deduced thickness as a reference and describing the over-layer as SiO2 with fixed thickness equal to 0.7nm. The Si1-xGex optical constants determined at ten compositions were interpolated for arbitrary Ge composition up to 54%. This alloy model was then tested on a large number of Si1-xGex films (evaluation wafer set) in order to demonstrate its ability to accurately characterize inline pseudomorphic Si1-xGex films over a wide range of germanium contents (0.5-1 at.% accuracy concerning the determination of the Ge content).

Ellipsometric study of the temperature dependences of the dielectric function and the critical points of AlSb at temperatures from 300 to 803 K

We report the complex pseudodielectric function = + i of an oxide-free AlSb film for energies from 0.7 to 5.0 eV and temperatures from 300 to 803 K. The 1.5-μm-thick film was grown on a (001) GaAs substrate by using molecular beam epitaxy. We maintained the film in an ultrahigh vacuum to prevent oxidation artifacts and used a rotating-compensator ellipsometer to obtain the optical properties. Critical-point (CP) energies were obtained by numerically calculating second energy derivatives of the data. Blue shifts of the CP energies and sharper structures were observed with decreasing temperature. The calculated CP energies were fit to a linear equation.

Construction of Rotating Compensator Ellipsometer Using a MgF$_2$ Monoplate Retarder and its Application to the Study of GaAs

Construction of Rotating Compensator Ellipsometer Using a MgF$_2$ Monoplate Retarder and its Application to the Study of GaAs

Optical Mueller matrix modeling of chiral AlxIn1 − xN nanospirals

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.

Optical characterization of patterned thin films

The present study investigates the use of imaging and mapping ellipsometry to determine the properties of non-ideal and patterned thin film samples. Samples which are candidates for future references and standards were prepared for this purpose. The samples investigated were lithographically patterned SiO2 and photoresist layers. The thickness and the optical constants of the two materials were determined using spectroscopic ellipsometry in the visible spectral range. On a larger lateral scale of several mm lateral resolution, the homogeneity was investigated using a goniospectral rotating compensator ellipsometer. A nulling imaging ellipsometer was used to determine the properties of the sample on a smaller scale of 25–150μm.

Characterization of e-beam patterned grating structures using Mueller matrix based scatterometry

Scatterometry is one of the most useful metrology methods for the characterization and control of critical dimensions and the detailed feature shape of periodic structures found in the microelectronics fabrication processes. Spectroscopic ellipsometry (SE) and normal incidence reflectometry (NI)-based scatterometry are widely used optical methodologies for metrology of these structures. Evolution of improved optical hardware and faster computing capabilities led to the development of Mueller matrix (MM)-based scatterometry (MMS). Unlike SE and NI, MM data provides complete information about the optical reflection and transmission of polarized light interacting with a sample. This gives MMS an advantage over traditional SE scatterometry due to the ability to characterize samples that have anisotropic optical properties and depolarize light. In this paper, we present the study of full MM (16-element) scatterometry over a wide spectral range from 245 to 1700 nm on a series of one-dimensional, two-dimensional symmetric, and asymmetric grating structures. A series of laterally complex nanoscale structures were designed and fabricated using a state-of-the-art e-beam patterning. Spectroscopic MM and SE data were collected using a dual rotating compensator ellipsometer. Commercial modeling software based on the rigorous coupled-wave approximation was used to precisely calculate the critical dimensions. Results from MMS were compared with scanning electron microscopy.

Optical and structural characterization of epitaxial graphene on vicinal 6H-SiC(0001)–Si by spectroscopic ellipsometry, Auger spectroscopy, and STM

The authors report results of spectroscopic ellipsometry (SE) measurements in the near-IR, visible, and near-UV spectral ranges using a Woollam dual rotating-compensator ellipsometer, analyzing data in terms of both epitaxial graphene and interface contributions. The SiC samples were cleaned by standard methods of CMP and HF etching prior to mounting in UHV and growing epitaxial graphene by thermal annealing at ∼1400 °C. Most samples were vicinally cut 3.5° off (0001) toward [11−20]. STM measurements show that the initial regular step edges were replaced by somewhat irregular edges after graphene growth. From growth-temperature and Auger data the authors estimate that the graphene is ∼3–4 ML thick. The authors find significant differences among the spectral features of the interface “buffer” layer and those of graphene. Specifically, the hyperbolic-exciton peak reported previously at ∼4.5 eV in graphene shifts to a similarly shaped peak at ∼4 eV in the interface buffer layer. The authors attribute this shift to a significant component of sp3 bonded carbon in the buffer, which occurs in addition to the sp2 bonded carbon that is present in the graphene layer. SE data in the terahertz range obtained by Hoffman et al. [Thin Solid Films 519, 2593 (2011)] show that the mobility values of graphene grown on the carbon face of SiC vary with proximity to the substrate. This leads to the question as to whether an interface layer at the Si face has properties (i.e., dielectric function/complex refractive index) that are different from and/or affect those of the graphene layers.

Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators

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.

Optical properties of thin films of mixed Ni–W oxide made by reactive DC magnetron sputtering

Thin films of NixW1−x oxides with x=0.05, 0.19, 0.43 and 0.90 were studied. Films with thicknesses in the range 125–250nm were deposited on silicon wafers at room temperature by reactive DC magnetron co-sputtering from targets of Ni and W. The films were characterized with X-ray diffraction (XRD), scanning electron microscopy (SEM), and spectroscopic ellipsometry (SE). XRD spectra and SEM micrographs showed that all films were amorphous and possessed a columnar structure. The ellipsometric angles Ψ and Δ of as-deposited films were measured by a rotating analyzer ellipsometer in the UV–visible-near infrared range (0.63–6.18eV) and by an infrared Fourier transform rotating compensator ellipsometer in the 500–5200cm−1 wavenumber range. SE measurements were performed at angles of incidence of from 50° to 70°. Parametric models were used to extract thicknesses of the thin films and overlayers of NixW1−x oxide at different compositions, band gaps and optical constants. Features in the optical spectra of the NixW1−x oxides were compared with previous data on tungsten oxide, nickel oxide and nickel tungstate.

Dual rotating compensator ellipsometry: Theory and simulations

Systematic methods for data reduction have been developed for the dual rotating-compensator ellipsometer in the PC1r(ω1)SC2r(ω2)A configuration, where P, C1r(ω1), S, C2r(ω2), and A represent the polarizer, first rotating compensator, reflecting sample, second rotating compensator, and analyzer, respectively. The approach used here is more general than previous treatments in that it incorporates dichroic compensators that rotate synchronously at a frequency ratio ω1:ω2 of p:q, where p and q are integers. For specific frequency ratios, the 24 ac Fourier coefficients of the irradiance waveform at the detector over-determine the 15 real elements of the (1,1)-normalized Mueller matrix and the 3 complex elements of the (2,2)-normalized Jones matrix. Alternative data reduction approaches resulting from this capability of over-determination are shown through numerical simulations to have different performance characteristics under non-ideal experimental conditions. Finally, the importance of using an achromatic retarder design in the dual rotating-compensator ellipsometer is emphasized through these simulations.

Random errors and optimum estimation of measurements photometric ellipsometers

AbstractA method of calculation of ellipsometric parameters, which allows to minimize random errors and simultaneously obtain their covariance matrix, is developed for photometric ellipsometry and polarimetry systems on the basis of Generalized least‐squares method (GLSM). As examples of application for rotating compensator ellipsometer the optimum value of retardation of the compensator equal to 132° is calculated, and also the technique of determination of the spectral range is offered. For shot‐noise limited systems the basic equation R = D (R)U is obtained, where R is the vector of measured parameters, D (R) is the covariance matrix of these parameters, and U is a constant vector describing the measuring system. All the results are applicable both for Stokes‐ and for Muller‐ellipsometry. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers.

I investigate the dependence of shot-noise-limited uncertainties of the ellipsometric parameters psi, and delta for the rotating-analyzer ellipsometer (RAE) and the rotating-compensator ellipsometer (RCE) of the polarizer-sample-compensator-analyzer type. The development is general and takes into account correlations among the Fourier coefficients of the transmitted intensity, in particular the average intensity, which is necessarily correlated with all other coefficients through normalization. The results are expressed in terms of the traditional uncertainties delta(psi) and delta(delta) of the ellipsometric parameters psi and delta, respectively, although a more appropriate measure of uncertainty is the differential area 2delta(psi) x sin psi(delta)delta on the unit-radius Poincaré sphere. Numerical results for broadband operation from 1.5 to 6.0 eV with a Si sample show that the optimum measurement conditions for both configurations occur when the intensity of light reflected from the sample is approximately balanced between the TE and the TM modes, and, for the RCE, when the analyzer azimuth is essentially equal to that of the polarizer. Under typical broadband operating conditions in which components cannot be optimized on a wavelength-by-wavelength basis, the RCE is better at determining delta, whereas the RAE is better at determining psi. The approach is easily generalized to other configurations and other types of experimental uncertainty, both random and systematic.

Dielectric function of thin metal films by combined in situ transmission ellipsometry and intensity measurements

The dielectric function and layer thicknesses of thin metal films are simultaneously determined by combined in situ spectroscopic ellipsometric (SE) transmission and transmission intensity ( T) measurements. Adding the transmission intensity data to the SE data alleviates the difficulty of correlation between thickness and optical constants of very thin absorbing films. The SE+ T data are acquired by a rotating compensator ellipsometer (RCE), using only the AC signal components. Experimental results from the deposition of Al, Co, Mo, and Ti thin films on fused silica substrates are presented. The growing films were analyzed using the real-time acquired data. The dielectric function of Al changed most dramatically as a function of film thickness, while the Ti dielectric function exhibited the least changes.

Precision in ellipsometrically determined sample parameters: simulation and experiment

A methodology for evaluating the precision of ellipsometrically determined model parameters (such as thickness) as a function of the measured data set (wavelength(s) and angle(s) of incidence) is presented and experimentally validated. This methodology is used to determine acceptable angle of incidence ranges for ellipsometric measurements and to study the merits of including multiple angles in the data set. Simulations and experimental results are presented for rotating analyzer ellipsometer and rotating compensator ellipsometer systems, using examples of thin and thick films on silicon substrates. A rigorous noise model is used to predict the ellipsometric measurement noise and Monte Carlo simulations are used to determine the parameter precision for a given data set.

Application of in situ ellipsometry in the fabrication of thin-film optical coatings on semiconductors

Thin-film interference filters, suitable for use on GaAs- and InP-based lasers, have been fabricated by use of the electron-cyclotron resonance plasma-enhanced chemical vapor deposition technique. Multilayer film structures composed of silicon oxynitride material have been deposited at low temperatures with an in situ rotating compensator ellipsometer for monitoring the index of refraction and thickness of the deposited layers. Individual layers with an index of refraction from 3.3 to 1.46 at 633 nm have been produced with a run-to-run reproducibility of 0.005 and a thickness control of 10 A. Several filter designs have been implemented, including high-reflection filters, one- and two-layer anitreflection filters, and narrow-band high-reflection filters. It is shown that an accurate measurement of the filter optical properties during deposition is possible and that controlled reflectance spectra can be obtained.

IR ellipsometry studies of polymers and oxygen plasma-treated polymers

An infrared variable angle spectroscopic ellipsometer (IR-VASE) was used to study organic polymers in the infrared (2.5–14 μm wavelength) spectral region. For the analysis of thin film polymers IR spectroscopic ellipsometry has greater sensitivity over traditional FTIR spectroscopy providing an exciting way to characterize these materials optically. The IR-VASE used in this study is of high accuracy, rotating polarizer, rotating compensator ellipsometer that uses an FTIR spectrometer as a light source. The IR-VASE was used to measure the infrared optical constants of various polymers in both solid and liquid form. These optical constants were then used to model the percentage of water in a thin film of gelatin and the percentage of residual solvent in a thin film of silicone. In addition, the IR-VASE provided a sensitive measurement of silicone chemistry and chemical changes caused by exposure to an oxygen plasma.

Broadband spectral operation of a rotating-compensator ellipsometer

We show that a rotating-compensator ellipsometer (RCE) with a zero-order retarder can be used for broadband spectroscopy, for example from 200 to 800 nm, when the compensator retardation δ is known as a function of wavelength and sample properties are determined by least-squares methods. The resulting instrument offers the standard advantages of an RCE and is no less sensitive than a rotating-analyzer or -polarizer ellipsometer under worst-case conditions, where the sin (2ω t) component vanishes at δ=180°C. Sensitivity and operation are illustrated by application to the measurement of crystalline Si.

Error analysis in rotating compenstator ellipsometer

The Rotating Compensator Ellipsometer (RCE) which are measured comparatively fast and higher accuracy can be determined all Stokes-parameters. But alignment of the RCE equipped with many optical components is tedious work. Use of the RCE and its attendant problems are discussed.