Bruggeman Effective Medium Research Articles

Wettability of Heterogeneous Substrates

Incomplete organic monolayers grafted on silicon wafer are characterized by spectroscopic ellipsometry (SE) using the Bruggeman effective-medium approximation. The formation of the monolayer, as a condensed liquid (LC*) phase, is investigated. The time evolution of the surface fractions occupied by the different phases allows the determination of a reaction model and of the associated thermodynamic constants. Furthermore, the high spacial resolution spectroscopic ellipsometry (HRSE) is used to study the spreading of silicon oils on such heterogeneous substrates. A simple model is proposed, in agreement with the experimental results, showing that the inverse of the diffusion coefficient of the liquid molecules is proportional to concentration of the heterogeneities.

Spectroscopic ellipsometry studies of nanocrystalline carbon thin films deposited by HFCVD

Nanocrystalline carbon thin films were grown by hot-filament chemical vapor deposition (HFCVD) using a relatively high concentration of methane in hydrogen. The films were deposited on molybdenum substrates at 900°C, and under various substrate-biasing conditions. The optical properties were examined ex situ using spectroscopic phase-modulated ellipsometry (SPME) from the near IR to the near UV region (1.5–5.0 eV). The ellipsometry data [ψ(λ i), Δ(λ i)] were modeled using Bruggeman effective-medium approximation (EMA) and the dispersion relation for the amorphous semiconductor (Forouhi and Bloomer Model; Phys. Rev. B 34, 7018, 1986). We performed these simulations by least-square regression analysis (LRA) and obtained the true dielectric function of our nanocrystalline carbon material and the energy band-gap ( E g ), along with the film thickness, bulk void fraction and roughness layer. We discuss the possible physical meaning of the five parameters in the amorphous dispersion model applied to the case of nanocrystalline carbon. Micro-Raman spectroscopy and profilometry were used to guide and validate the simulations.

Calculation of electron-energy-loss spectra of composites and self-similar structures

We calculate electron-energy-loss spectra for self-similar systems of polarizable spheres using a previously developed theory for the electron-energy loss of a system of identical spheres. We do this by means of a recursive procedure and an effective ``local'' dielectric function, which contains, implicitly, the effects of spatial nonlocality due to correlations and multipolar interactions among the spheres, as well as some characteristics of the experimental setup. We also apply the procedure to systems of spheres with a continuum distribution of sizes. Finally, we propose a simple nonlocal generalization of Bruggeman's differential effective medium theory.

Optical Characterization and Modeling of Sulfur Incorporated Nanocrystalline Carbon Thin Films Deposited By Hot Filament CVD

ABSTRACTSulfur incorporated nanocrystalline carbon (n-C:S) thin films grown on molybdenum substrates by hot-filament chemical vapor deposition (HFCVD) using gas mixtures of methane, hydrogen and a range of hydrogen sulfide (H2S) concentrations are optically examined using Raman spectroscopy (RS) and ex situ spectroscopic phase modulated ellipsometry (SPME) from near IR to near UV (1.5-5.0 eV) obtaining their vibrational frequencies and pseudodielectric function, respectively. The ellipsometry data (<εr(E)>, <εi(E)>) were modeled using Bruggeman effective-medium theory (BEMT) and five parameters Forouhi and Bloomer (FB) dispersion Model. A simplified two-layer model consisting of a top layer comprising an aggregate mixture of sp3C+sp2C+void and a bulk layer (L2), defined as a dense amorphized FB-modeled material was found to simulate the data reasonably well. Through these simulations, it was possible to estimate the dielectric function of our n-C: S material, along with the optical bandgap (Eg), film thickness (d), and roughness layer (σ) as a function of [H2S]. The physical interpretation(s) of the modeling parameters obtained were discussed. The Raman and ellipsometry results indicate that the average size of nanocrystallites in the sulfur-incorporated carbon thin films becomes smaller with increasing H2S concentration, consistent with AFM measurements. The bandgap was found to decrease systematically with increasing H2S concentration, indicating the enhancement of midgap states and sp2 C network, in agreement with RS results. These results are compared to those obtained for the films grown without sulfur (n-C), in order to study the influence of sulfur addition to the CVD process. This analysis led to a correlation between the film microstructure and its electronic properties.

Optical properties of fully amorphous silicon

We have determined the complex dielectric function, $\ensuremath{\varepsilon}(E)={\ensuremath{\varepsilon}}_{1}(E)+i{\ensuremath{\varepsilon}}_{2}(E),$ for self-implanted amorphous silicon (a-Si) by spectroscopic ellipsometry (SE) in the 1.5--5.2-eV photon-energy range at room temperature. The measured SE spectra show a single broad peak in ${\ensuremath{\varepsilon}}_{2}(\ensuremath{\sim}26.6)$ at $E\ensuremath{\sim}3.45\mathrm{eV},$ which is typically observed in amorphous tetrahedral semiconductors. The SE $\ensuremath{\varepsilon}(E)$ data, together with the literature data which exhibit the largest peak in ${\ensuremath{\varepsilon}}_{2}(\ensuremath{\sim}30)$ at $E\ensuremath{\sim}3.7\mathrm{eV}$ and have been widely used as a reference of ``dense'' a-Si, are analyzed by means of the Bruggeman effective-medium approximation. The results clearly indicate that the self-implanted a-Si sample is in the fully amorphous state, while the literature data contain microcrystalline component $(\ensuremath{\mu}c\ensuremath{-}\mathrm{Si})$ in its spectra. The volume fraction of $\ensuremath{\mu}c\ensuremath{-}\mathrm{Si}$ is estimated to be about 53%. The optical spectra of $\ensuremath{\mu}c\ensuremath{-}\mathrm{Si}$ are found to be quite different from those of single-crystalline silicon, especially in the vicinity of the sharp critical-point features. The SE $\ensuremath{\varepsilon}(E)$ data of the self-implanted a-Si are successfully parametrized using Jellison-Modine's dispersion expression.

Ellipsometric Study of Silicate Treatment of Aluminum Offset Printing Plates

The silicate treatment of aluminum offset printing plates has been studied by ellipsometry. Aluminum is very reactive with oxygen and the aluminum surface is easily oxidized in the atmosphere. The presence of the oxide layer on the aluminum surface brings about some ambiguities in the analysis of the ellipsometric data of the overlaid film. Few researchers have estimated the thickness of a siliceous film on aluminum plates as far as we know. However their estimations are very vague, ranging from one monolayer (∼0.3 nm) to 1 µm.1,2) We carried out a series of experiments to determine the thickness of a siliceous film on an aluminum surface by means of ellipsometry. The thicknesses of the siliceous films on the aluminum film surface were successfully estimated by applying Bruggeman's effective medium approximation to the composite layer of the aluminum and the aluminum oxide. In our experiments, the thicknesses of the composite layer and the siliceous film were estimated to be in the range from 1.3 nm to 1.6 nm and about 0.7 nm, respectively.

Self-consistent effective-medium approximations with path integrals

We study effective-medium approximations for linear composite media by means of a path integral formalism with replicas. We show how to recover the Bruggeman and Hori-Yonezawa effective-medium formulas. Using a replica-coupling ansatz, these formulas are extended into ones which have the same percolation thresholds as those of the Bethe lattice and Potts model of percolation, and critical exponents s=0 and t=2 in any space dimension d>/=2. Like the Bruggeman and Hori-Yonezawa formulas, the obtained formulas are exact to second order in the weak-contrast and dilute limits. The dimensional range of validity of the four effective-medium formulas is discussed, and it is argued that out formulas are of better relevance than the classical ones in dimensions d=3,4 for systems obeying the nodes-links-blobs picture, such as random-resistor networks.

In situ spectroscopic ellipsometry for the characterization of polysilicon formation inside a vertical furnace

A spectroscopic ellipsometer was integrated in a vertical furnace for measurement and control during chemical vapor deposition and thermal oxidation processes. The major goal of this activity was to adapt the ellipsometer arrangement to the furnace geometry with a minimum impact on the furnace process performance. Modifications in the furnace geometry were restricted as far as possible, to show that a fast integration in existing industrial equipment with minor costs can be done. This aim led to a novel beam-guiding system. This setup has been used for the in situ characterization of polysilicon formation, inside the vertical furnace during high temperature processes. The polysilicon-on-oxide structures were modeled using the Bruggeman effective-medium approximation (B-EMA). The crystallization process of amorphous silicon layers during annealing at 600°C has been monitored. Layer thickness and the degree of crystallinity can be obtained simultaneously. The crystallinity can be described in the optical model using a ‘mixture’ of amorphous silicon and single-crystalline silicon in the B-EMA.

Ellipsometric study of polycrystalline silicon films prepared by low-pressure chemical vapor deposition

Polysilicon layers with thicknesses between 8 and 600 nm deposited by low-pressure chemical vapor deposition at temperatures ranging from 560 to 640 °C were characterized by spectroscopic ellipsometry (SE) to determine the layer thicknesses and compositions using multilayer optical models and the Bruggeman effective-medium approximation. The dependence of the structural parameters on the layer thickness and deposition temperature have been investigated. A better characterization of the polysilicon layer is achieved by using the reference data of fine-grained polysilicon in the optical model. The amount of voids in the polysilicon layer was independently measured by Rutherford backscattering spectrometry (RBS). The SE and RBS results show a good correlation. The comparison of the surface roughness measured by SE and atomic force microscopy (AFM) shows that independently of the AFM window sizes, a good correlation of the roughness determined by SE and AFM was obtained.

Effect of Polycarboxylate Superplasticizer on Contribution of Interfacial Transition Zone to Electrical Conductivity of Portland Cement Mortars

This study evaluated the effect of a polycarboxylate high-range water-reducing admixture on the electrical conductivity and interfacial transition zone characteristics of portland cement mortars using alternating current (AC) impedance spectroscopy, mercury intrusion porosimetry, and two electrical conductance models: the interfacial excess conductance and Bruggeman's asymmetrical effective medium theories. Mechanical tests were also performed. Mortar specimens used had sand-cement ratios of 0.5, 1.0, and 1.5; aqueous high-range water-reducing admixture dosages of 0%, 0.3%, and 0.75% (by mass of cement); and a water-cement ratio of 0.35. The results showed that the presence of the polycarboxylate high-range water-reducing admixture had positively modified the interfacial transition zone performance and the microstructural characteristics of the hardened mortars. It was found, however, that this high-range water-reducing admixture reduced the rate of hydration during the first day.

Optical characterization of hydrogenated amorphous silicon thin films deposited at high rate

The aim of this paper is to provide a better understanding of hydrogenated amorphous silicon thin films (a-Si:H) in relation to their optical properties: refractive index, optical gap, absorption coefficient, thickness and surface roughness. The transmission spectrum of the films, deposited with various rf discharge power densities by an optimized plasma enhanced chemical vapor deposition (PECVD) method, at a high rate (>10 A/sec), was measured over a range in wavelength from 500 to 1100 nm. An approximate model is utilized to describe the surface roughness. In this model, the surface roughness is modeled as a mixed layer of 50 percent of a-Si:H and 50 percent of air and the optical constant of the rough layer is derived using the Bruggemann effective medium approximation (EMA). The gradient iteration method of numerical analysis is used to solve the nonlinear equations in the study. Our results show that the potential underestimation of refractive index and resulting overestimation of film thickness can be overcome by considering the reflection of the rough surface. The method is carried out on the transmission data and the influence of rf discharge power density on the properties of the film is discussed in detail.

In situ infrared investigation of metals electrodeposited for SEIRAS

We report on the use of in situ infrared spectroscopy for monitoring the electrodeposition of metals on semiconductors. The deposit is modelled as a slice of an effective medium consisting of a mixture of the deposited metal and the electrolyte, and the infrared absorption is fitted using Bruggeman's and Bergman's effective medium theories. In the case of Ag deposition on Si, this analysis brings information not only on the amount of deposited metal but also on the morphology of the deposit, as confirmed by ex situ SEM observations. In situ monitoring of the morphology provides a means for realizing surface enhanced infrared absorption geometry with electrodeposited metal islets.

The effective medium approximations: Some recent developments

We provide a brief and highly selective review of the Landauer– Bruggeman effective-medium approximation as applied to random composite media. We first discuss this approximation as applied to linear composites, i.e., to those materials in which there is a linear relation between a curl-free electric field and a divergence-free current density. We then describe extensions of this approach to random composites with cubic nonlinearities in addition to a dominant linear term, and to composites in which the components have a fluctuating conductivity (‘conductivity noise’). Finally, we mention one novel application: to conductivity noise in a random composite of normal metal (N) and perfect conductor (S). It is shown that the extension of the EMA leads to a prediction of a frequency range in which the conductivity noise has a 1/ω frequency dependence, even if the noise in the individual components is frequency independent.

Anisotropic dielectric response and surface aging of mercuric iodide crystal studied by variable angle spectroscopic ellipsometry

Variable angle spectroscopic ellipsometry (VASE) was employed to study the anisotropic optical properties and surface aging phenomena of mercuric iodide (HgI 2) — a material for room-temperature radiation detectors. In the optical property study, two surface orientations of this tetragonal crystal were selected, i.e. an a-plane and a c-plane sample. Room temperature multiple-angle SE measurements from both samples with three different optical configurations along with polarized transmission measurements were analyzed simultaneously by the VASE analysis through multiple-sample, multiple-model methods. Anisotropic dielectric functions of single crystal HgI 2, ε ⊥(ω) and ε ‖(ω), for optical electric field vectors oriented perpendicular and parallel to the c axis, respectively, were obtained over the range of 1.24–5.1 eV. In the surface aging characterization, three different initial HgI 2 surface conditions were selected, i.e. an as-grown surface, a cleaved surface, and a surface chemically etched by 10% KI solution. A model of the HgI 2 crystal including top surface roughness and subsurface defects was established and characterized, as a function of time, by the VASE analysis. In this model, the surface defects associated with the surface aging were modeled by the Bruggeman effective-medium approximation (EMA) as a HgI 2/void mixed overlayer. The relative 2-dimensional (2D) surface-defect-densities were then monitored as the surface aging proceeded.

Carbon nitride thin films prepared by reactive r.f. Magnetron sputtering

Nitrogenated amorphous carbon thin films (CN x ) were prepared by reactive r.f. magnetron sputtering from a graphite target in a nitrogen containing plasma (up to 4.4 at%) on Si substrates. All main controllable deposition conditions (such as base and deposition pressure, power at target, target-substrate distance, substrate bias voltage) were kept constant throughout the series of experiments and the only variable parameter was the nitrogen flux (0–2 sccm). In situ spectroscopic ellipsometry (SE) in the energy region 1.5–5.5 eV in combination with Bruggeman's effective medium theory analysis was used per iterative deposition layer to monitor the film thickness and diamond character. The C:N chemical bonding characteristics of the films were also examined with the new Fourier transform IR ellipsometry technique. It was found that the films have a mixed character composed of constituents (phases) of sp 3 and sp 2 type bonding. The film composition in terms of sp 3, sp 2 and void concentration as a function of film thickness and nitrogen concentration in the plasma was determined. The plasma nitrogen concentration seems to directly affect the film deposition rate and diamond character of the films by favoring sp 3 bond formation.

Optical properties of excimer laser annealed polycrystalline Si by spectroscopic ellipsometry

Using spectroscopic ellipsometry (SE), optical properties of poly-Si obtained by excimer laser annealing of amorphous silicon (α-Si) are evaluated. Both, amorphous silicon and SiO 2 are deposited on Si substrate (α-Si/SiO 2/Si) by low temperature chemical vapor deposition (LPCVD). SE measurement shows that the crystallization starts with laser annealing of energy 144–280 mJ/cm 2 and above at which it remains amorphous. A linear regression analysis (LRA) and a Bruggeman effective-medium approximation (EMA) indicate that the laser annealed layer consists of 91.3% crystalline Si and 8.7% amorphous Si for samples irradiated in two steps, i.e., 344 and 276 mJ/cm 2 of each pulse. The thickness of each layer determined by SE is in good agreement with that of cross-section transmission electron microscopy (TEM).

Modified effective-medium theory for magneto-optical spectra of magnetic materials

We have modified the Bruggeman effective-medium theory (EMT) to study the microstructural dependence of the magneto-optical spectra in magnetic materials having the off-diagonal elements of the dielectric tensor. To verify the modified theory, optically thick (4-\AA{} Co/9-\AA{} Pt${)}_{77}$ multilayers were prepared at various Ar sputtering gas pressures of 2, 10, and 30 mTorr. The modified effective-medium theory was confirmed to match well with the experimental values of the dielectric tensors of Co/Pt multilayers. We have also applied this modified EMT to a 20-\AA{}-thick Co film having island structure and observed that this modified EMT exhibited a better match to the experimental data than any other existing theories.

In situ monitoring of CdTe nucleation on GaAs (100) using spectroscopic ellipsometry

Abstract In situ spectroscopic ellipsometry was used to monitor the nucleation behavior of CdTe grown on vicinal GaAs (100) substrates by organometallic vapor phase epitaxy. CdTe was grown on GaAs (100) substrates of exact and 2° off towards 〈110〉 orientations. A spectroscopic ellipsometer was used to collect in situ data at 44 wavelengths from 4000–7000 A. The Bruggeman's effective medium approximation was employed to determine the variation of the epilayer volume fraction with thickness, which was an indirect way of monitoring the expected island growth behavior. The Stranski-Krastonov (layer plus island) mode of growth was clearly observed for CdTe growth. The growth on the 2° off substrate was also “denser” than that on exact (100), which implied that coalescence of the islands occurred at lower thickness. This was expected since island nucleation is most favored along the ledges on the surface whose spacing decreases with increasing misorientation. A simple nucleation model, assuming cylinder-like islands, was able to fit the experimental data quite well, lending support to the island growth model.

Spectro-ellipsometric Studies of Amorphization and Thermal Annealing in Ion-implanted Silicon

The damage profiles in the P+, BF2+, As+ and B+ ion-implanted silicon specimens are investigated using the nondestructive spectroscopic ellipsometry (SE) technique. The effective dielectric functions of the damaged layers are calculated using the Bruggeman's effective medium approximation, assuming that the damaged layer can be optically represented by the mixture of crystalline and amorphous silicon. By selectively using either the dielectric function of implanted amorphous silicon, or that of the relaxed amorphous silicon as the reference data for the amorphous silicon, we have improved the accuracy in modeling. The model parameters regarding the damaged layer thickness and the degree of amorphization are found to depend on implanting ion species, implantation energies, and total doses. Also, the implantation induced damage profiles are computer simulated and compared with the SE results. When annealed at lower temperatures, implanted amorphous silicon turns into the relaxed amorphous silicon and starts to recrystallize from the interface of the c-Si side due to solid-phase epitaxial growth. At annealing temperatures higher than 600°C, relaxed amorphous layers become crystalline silicon.

Effect of sample density on the resistivity and Hall coefficient of polycrystalline La 1.83Sr 0.17CuO 4

The resistivity and Hall coefficient ( R H) of polycrystalline La 1.83Sr 0.17CuO 4 has been studied as a function of sample density (i.e. porosity). R H is inversely proportional to the density and can be corrected to give a good estimate of the in-plane value for single crystals. The resistivity is much more strongly dependent on sample density and grain boundary effects are shown to be important. Bruggeman's symmetrical effective medium theory reproduces some of the features of the density dependence of the resistivity, but is unable to model grain boundary resistances and consequently predicts a percolation threshold at a lower density than is actually observed. It is noted that direct comparisons of cot( θ H) between different porous materials is more difficult because of these density dependent behaviours.