Forouhi Bloomer Model Research Articles

Optical properties of silicon nanocrystals embedded in aSiO2matrix

Optical properties of isolated silicon nanocrystals $(\mathit{nc}\text{\ensuremath{-}}\mathrm{Si})$ with a mean size of $\ensuremath{\sim}4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ embedded in a ${\mathrm{SiO}}_{2}$ matrix that was synthesized with an ion beam technique have been determined with spectroscopic ellipsometry in the photon energy range of 1.1--5.0 eV. The optical properties of the $\mathit{nc}\text{\ensuremath{-}}\mathrm{Si}$ are found to be well described by both the Lorentz oscillator model and the Forouhi-Bloomer (FB) model. The $\mathit{nc}\text{\ensuremath{-}}\mathrm{Si}$ exhibits a significant reduction in the dielectric functions and optical constants and a large blueshift $(\ensuremath{\sim}0.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ in the absorption spectrum as compared with bulk crystalline silicon. The band gap of the $\mathit{nc}\text{\ensuremath{-}}\mathrm{Si}$ obtained from the FB model is $\ensuremath{\sim}1.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, showing a large band gap expansion of $\ensuremath{\sim}0.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ relative to the bulk value. The band gap expansion is in very good agreement with the first-principles calculation of the $\mathit{nc}\text{\ensuremath{-}}\mathrm{Si}$ optical gap based on quantum confinement.

Deposition and characterization of copper oxide thin films

In the present work we study thin films of copper oxide that were deposited by oxidation of copper thin films on silicon substrates in temperatures varying from 150 °C up to 450 °C. Copper films were deposited by vacuum evaporation and their thickness was estimated from the evaporated mass. X-rays diffraction (XRD) patterns showed that in the copper oxide films coexist two phases: CuO and Cu2O their proportion varying with oxidation temperature. At temperatures up to 225 °C Cu and Cu2O is formed while above this temperature CuO forms. Pure Cu2O was obtained at 225 °C while pure CuO above 350 °C. FTIR transmittance spectra confirmed the results from the XRD. The index of diffraction was calculated from spectroscopic ellipsometry measurements within the energy range 1 to 3 eV, which were analysed using the Forouhi-Bloomer model.

Dependence of Structure and Haemocompatibility of AmorphousCarbon Films on Substrate Bias Voltage

Tetrahedral amorphous hydrogenated carbon (ta-C:H) films on Si(100)substrates were prepared by using a magnetic-field-filter plasma streamdeposition system. Samples with different ratios of sp3-bond tosp2-bond were obtained by changing the biasvoltage applied to the substrates. The ellipsometric spectra of variouscarbon films in the photon energy range of 1.9–5.4 eV were measured.The refractive index n and the relative sp3 C ratio ofthese films were obtained by simulating their ellipsometric spectrausing the Forouhi–Bloomer model and by using the Bruggeman effectivemedium approximation, respectively. The haemocompatibility of theseta-C:H films was analysed by observation of platelet adhesion andmeasurement of kinetic clotting time. The results show that the sp3C fraction is dependent on the substrate bias voltage, andthe haemocompatibility is dependent on the ratio of sp3-bond tosp2-bond. A good haemocompatibility material ofta-C:H films with a suitable sp3 C fraction can be preparedby changing the substrate bias voltage.

Optical properties of SiO2-TiO2sol-gel thin films

The optical properties of thin SiO2-TiO2 sol-gel composite films were investigated using exact optical models and the Forouhi-Bloomer model, (Phys. Rev. B34, 7018 (1986)), which describes the optical dispersion of amorphous dielectrics. Films deposited on glass and silicon substrates, were characterized by optical transmission and reflection measurements. Theoretical spectra have been generated and fitted to the experimental ones via standard regression analysis techniques. The (five) adjustable Forouhi-Bloomer parameters describing the dispersion of the complex refractive index, as well as the film thickness were determined. The refractive index and absorption coefficient of the films were found to depend on the molar contents of the component oxides.

Optical absorption threshold of low pressure chemically vapor deposited silicon oxynitride films from SiCl 2H 2NH 3N 2O mixtures

Amorphous silicon oxynitride thin films were deposited on 4 inch (100) Si wafers in a conventional low pressure chemical vapor deposition reactor at 812 °C and 230 mTorr, using SiCl 2H 2NH 3N 2O gas mixtures. Depositions were carried out keeping the flows of SiCl 2H 2 and of NH 3 constants at 20 and 60 sccm, respectively, while that of N 2O was varying between 0 and 180 sccm. The optical properties of deposits were studied with the aid of the Forouhi–Bloomer model (Phys. Rev. B34, 7018 (1986)) for amorphous semiconductors. From the analysis of the optical spectra the complex refractive index of the films as well as their thicknesses were derived. Moreover, an approximate picture of the energetic distribution of the density of electronic states near the absorption threshold of these films was obtained. This picture was found to be consistent with theoretical calculations found in the literature for crystalline silicon nitride and oxynitride. Thus, the increase of oxygen content in films does not cause a shift of valence and conduction band towards lower and higher energies, respectively, but it implies rather an increase of the band gap and a decrease of the energetic distance between their centers of gravity due to the appearance of a local maximum near the top of the valence band. This maximum is due to the additive effect of the N 2 p and the O 2 p non-bonding orbitals. The study of optical properties provides also useful information regarding the presence of electronic states within the forbidden gap due to film defects, coherent with electrical measurements.

Determination of the Optical Properties of Sol-Gel-Derived Pb(Zr x Ti (1 − x ) )O 3 Thin Films by Spectroscopic Ellipsometry

Optical properties of polycrystalline Pb(Zr x Ti (1 m x ) )O 3 (PZT) thin films with different Zr/Ti ratios deposited on Si(100) substrates by the sol-gel techniques have been investigated by spectroscopic ellipsometry (SE) in the UV-visible region. The measured SE spectra were fitted by a model consisting of air/roughness/PZT/substrate. The roughness was modeled using the Bruggeman effective medium approximation. The optical constants of the PZT films were parameterized using the Forouhi-Bloomer model. The refractive index n, extinction coefficient k and thickness of samples with different Zr/Ti ratios have been obtained by analyzing the SE spectra. The influence of Zr/Ti ratios on the optical properties was discussed. The optical band gap energies E g for these films were reported under the assumption of a direct band-to-band transition. It has been found that the refractive index, extinction coefficient and optical band gap energy of the films were functions of the film compositions. The refractive index of polycrystalline PZT films increase with increasing Ti content. On the other hand, the optical band gap energy of polycrystalline PZT films decreases with increasing Ti content.

Study of the electronic structure of amorphous and crystallized low pressure chemically vapor deposited silicon films near the absorption threshold

Silicon films were chemically vapor deposited on quartz substrates from SiH4 decomposition in a conventional reactor at 230 mTorr and at a temperature of 550 °C. Samples were subsequently doped with phosphorus at a concentration of 1018 cm−3 and oxidized, in order to increase the grain size and to enhance crystallization. The optical properties of these films were studied with optical transmission measurements below their absorption threshold taken after every processing step, which were analyzed with the aid of a two-band model proposed by R. Forouhi and I. Bloomer [Phys. Rev. B 34, 7018 (1986)]. It was found that the energetic distance, separation, and magnitude of the Forouhi–Bloomer (FB) bands change with the various post-deposition treatments. For the as-deposited (amorphous) films, the FB model provides a picture of the distribution of the density of states (DOS) in very good agreement with that of vacuum evaporated films measured in the past with photoelectron spectroscopy. X-ray diffraction measurements taken on crystallized samples have shown that grains were oriented with the (111) and (220) crystallographic axes normal to the substrate. It was shown that the orientation of grains affects significantly the DOS and hence the optical properties of films, which are in this case influenced by electronic transitions near the L and K points of the Brillouin zone of Si [corresponding to the (111) and (220) crystallographic directions].

Spectroscopic ellipsometry analysis of nanocrystalline silicon carbide obtained at low temperature

Thin films of silicon carbide obtained by hydrogen-reactive magnetron sputtering with various substrate temperatures T S (100–600 °C) were analysed by transmission electron microscopy (TEM) and spectroscopic ellipsometry (SE). The TEM images show evidence of the growth of hydrogenated nanocrystalline silicon carbide (nc-SiC:H) deposited at T S as low as 300 °C, with an average grain size of 4–5 nm. The SE spectra were reproduced by using the Forouhi–Bloomer model and assuming a 7 nm thick overlayer with a void fraction of 45%. The observed increase of the refractive index with T S is assigned to the improvement of both crystallinity and compactness of the layer. The expected increase of the optical gap seems to be offset by the drop of hydrogen content, leaving the gap unchanged. The fabrication and characteristics of nc-SiC:H/c-Si diode are finally described and the data indicate a good rectifying behaviour, together with a low leakage current.

Spectroellipsometric study of sol–gel derived potassium sodium strontium barium niobate films

Spectroscopic ellipsometry (SE) was used to characterize the sol–gel derived (K0.5Na0.5)0.4(Sr0.6Ba0.4)0.8Nb2O6 (KNSBN) thin films as a function of sol concentration. In the analysis of the measured SE spectra, a modified double-layer Forouhi–Bloomer model was adopted to represent the optical properties of the KNSBN films. In this model, the films were assumed to consist of two layers—a bottom bulk KNSBN layer and a surface layer that composed of bulk KNSBN as well as void. Good agreement was obtained between the measured spectra and the model calculations in the chosen spectral region. Effective medium approximation theory was used to evaluate the effective refractive index for the surface layer. The results of SE have been correlated with atomic force microscopy measurements of surface roughness. Our analyses have shown that the surface layer had a lower refractive index than the bottom one. In addition, the refractive index and the surface roughness of the KNSBN films increase with the sol concentration.

Spectroscopic ellipsometric study of tetrahedral amorphous carbon films: optical properties and modelling

We present a spectroscopic ellipsometric (SE) study of ta-C and ta-C:N films obtained in a filtered cathodic vacuum arc system with an improved S-bend filter that yields high values of sp 3 content and mass density. The films consist of an ambient/roughness/film/interface/substrate structure, as demonstrated by X-ray reflectivity (XRR) and SE. The optical properties of the films have been derived by using four different approaches for the optical function: (i) Cauchy's absorbent dispersion formula; (ii) the contribution of three classical oscillators; (iii) the Forouhi–Bloomer model; and (iv) the Tauc–Lorentz model. The interface appears to be a mixture of a-Si and ta-C material, due to an amorphisation process originated by the carbon ion bombardment. The comparison of SE with XRR results, as well as the dependence of the fitted parameters with mass density, allows the Tauc–Lorentz model to be applied with confidence.

Spectroscopic ellipsometry characterization of Er 3+-dopedtitania thin films prepared by the sol-gel method

Abstract Titania thin films prepared by the sol-gel method were optically characterized by spectroscopic ellipsometry. These films were doped with Er 3+ and supported on silicon wafers chemically activated by using the dipping method. The dielectric function was modeled using the Forouhi-Bloomer model, which provides also the refractive index and the thickness of the film.

Optical properties of Ge:Sb:Te ternary alloys

The complex dielectric function of the three stoichiometric compositions GeSb4Te7, GeSb2Te4, and Ge2Sb2Te5 has been measured by spectroscopic ellipsometry in the energy range of 1.4–5.1 eV. Each composition was measured in the amorphous and in the two crystalline states, the metastable face-centered-cubic and the stable hexagonal phases. The complex dielectric function shows strong differences between the amorphous and the crystalline samples, these differences are responsible for the drastic contrast in the reflectivity spectra. The ellipsometric spectra are fitted with models which fulfilling the Kramers–Kronig relations. Thus the Forouhi–Bloomer model was used for the amorphous samples and the Lorentz harmonic oscillator model for the crystalline samples. The temperatures at which the phase transformations are achieved were determined by measuring the ac electrical resistance at 100 Hz while the samples were heated. The temperature derivative of the electrical conductivity shows two well defined peaks at critical temperatures where the phase transformation occurs as is revealed by the x-ray data.

Optical properties of very thin (

Very thin TiO 2 films (<100 nm) were prepared by a sol–gel dip-coating process on glass substrates. The films were characterized with optical transmission measurements and atomic force microscopy. The optical properties of these films were analyzed within the Forouhi–Bloomer model, [A. Forouhi, I. Bloomer, Phys. Rev., B34 (1986) 7018], describing the optical dispersion in disordered dielectrics. Theoretical spectra were generated and fitted, using standard regression analysis techniques, to the experimental ones having as adjustable parameters, the five Forouhi–Bloomer physical model constants and the film thickness. It was found that the model describes satisfactorily the optical properties of very thin sol–gel TiO 2 films within the range of 200–2500 nm. The energy difference between bonding–antibonding states was found to be approximately 4.3 eV, while the energy gap values (as defined by the physical model) obtained, ranged between 2.8 and 3.2 eV. The energy gap values using Tauc's formula have also been estimated and found to be approximately 3.6 eV, slightly higher than other corresponding values found in the literature.

Optical characterisation of thin organic films by analysing transmission measurements with the Forouhi-Bloomer model

The application of the Forouhi-Bloomer model, designed to describe the refractive index dispersion in solid inorganic insulators, in order to obtain film thickness and (complex) refractive index dispersion of organic films of the type encountered in microlithographic and micromachining applications using only transmission measurements is presented. Films with various compositions of the miscible polymers, cresol epoxy novolac (EPNOV) and poly hydroxy styrene (PHS), were prepared on quartz substrates by the standard spin coating techniques and their transmission spectra were recorded. Theoretical transmission spectra were generated simulating the optical dispersion of these films with the aid of the Forouhi-Bloomer model and fitted to the experimental ones using standard regression analysis techniques. The fit (adjustable) parameters were those describing the optical dispersion and the film thickness. The fits were very satisfactory permitting the determination of the film thickness and of the dispersion of the real and of the imaginary parts of the refractive index of the samples. The dispersions of the real and of the imaginary parts of the refractive index were found to vary from one film to the other with a way dependent on film composition. Information with respect to the electronic structure of the films was obtained using this analysis.

Silicon (Oxy)Nitride Thin Films Deposited by Lpcvd From SiCl2H2-NH3-N2O Mixtures Of Variable Composition

AbstractSilicon (oxy)nitride thin films were deposited on (100) 4″ silicon substrates in a conventional LPCVD reactor at 812°C and 230 mTorr, using mixtures of SiCl2H2 -NH3-N2O of variable composition in order to evaluate their optical properties for potential applications in SOI based Si technology. The depositions were carried out keeping the flow of SiCl2H2 and NH3 constant at 20 and 60 sccm respectively while that of N2O was varying between 0 and 180 sccm. Optical reflection measurements within the range 190 to 860 nm, performed on our films were analyzed within the Forouhi-Bloomer model (Phys. Rev. B34, 7018 (1986)) for amorphous semiconductors. From the analysis of the optical spectra, the constants of the model were derived. It was shown that the refractive index of the films varies between the limits set by those of silicon nitride and silicon dioxide, the increase of the N2O flow implying a decrease of the refractive index of the films. The film thicknesses were also derived from the analysis of the optical spectra. Capacitance - voltage measurements made on Metal-Insulator-Semiconductor (MIS) structures using our films as the insulator, have shown that, the electric charge density within the dielectric initially increases and then decreases with increasing the amount of oxygen into the deposition ambiance. Our films are suitable for optoelectronic applications in SOI structures compatible with C-MOS technology.