FB Dispersion Equation Validation

Publications & Papers

Since the Forouhi-Bloomer Dispersion (FB) theory was published in 1986, research institutes all over the world have utilized the FB Dispersion to characterize semiconductor thin films and achieved results successfully. Representative publications are listed below:

Optical Absorption Parameters of Amorphous Carbon Films from Forouhi–Bloomer and Tauc–Lorentz Models: A Comparative Study

Source: Journal of Physics: Condensed Matter, Volume 20, Issue 1, pp. 015216 (2008)
Authors: N Laidani, R Bartali, G Gottardi, M Anderle and P Cheyssac
Abstract: A comparative study of TaucLorentz (TL), ForouhiBloomer (FB), and modified Forouhi-Bloomer models. The models are applied to the interband absorption of amorphous carbon films. The modified Forouhi-Bloomer model shows a relative superiority over the Tauc-Lorentz for the determination of the band gap energy, as it is the only one to be validated by an independent, though indirect, gap measurement by x-ray photoelectron spectroscopy.

 


Effect of Y-radiation on the Optical Properties of Soda-lime-silicate Glasses

Source: Technical Physics Letters, Volume 33, Issue 11, pp.980-982 (2007)
Authors: E. A. Vanina, M. A. Chibisova, and A. N. Chibisov
Abstract: The effect of γ-radiation on the optical constants of soda-lime-silicate glasses was studied theoretically and experimentally. The energy band gaps calculated using Forouhi-Bloomer dispersion show good correlations with experimental results.

 


Forouhi-Bloomer and Tauc-Lorentz optical dispersions applied using spectroscopic ellipsometry to plasma-deposited fluorocarbon films

Source: Journal of Applied Phyics 101, 073102 (2007)
Authors: T. Easwarakhanthan, D. Beyssen, L. Le Brizoual, and P. Alnot
Abstract: Optical properties of the fluorocarbon (FC) films plasma deposited on Si substrates are evaluated in this work using multiple sample analysis (MSA)-based spectroscopic ellipsometry _SE_ with representing the film optical constants by the Forouhi-Bloomer (FB) and Tauc-Lorentz (TL) optical dispersions. This SE analysis supported also with other film investigations results in a two-layer optical model consisting of an interface assimilated to FC species-permeated Si layer beneath a surface smooth, homogeneous, and isotropic FC bulk film. Both dispersions yield a low-dielectric constant quality visible range refractive index of 1.39 and almost identical model layer thicknesses. Deposition-dominated linear film growth is thus asserted. Specifically, the FB dispersion better describes the region near absorption cutoff with taking up a lower optical band gap (OBG) than that of the TL dispersion, indicating thereby that particular FC film absorptions included in the FB dispersion are excluded in the other. Also, the FB index spectrum tends to peak towards a broad maximum in the ultraviolet (UV) wavelength range, whereas this trend is absent in the TL index spectrum probably removed by the TL parameter cross correlations although reduced by MSA. Sample to sample analysis further shows that the TL parameter correlation is accentuated by the instrument-limited UV range. The FB parameters are much less affected by cross correlation such that even the sample to sample analysis may be readily used in conjuncture with the FB dispersion for thicker FC films above 150 nm to monitor their index and OBG in tailoring desired film physical properties through deposition conditions.

 


Temperature Dependent Refractive Index of Amorphous Silicon Determined by
Time-resolved Reflectivity During Low Fluence Excimer Laser Heating

Source: Journal of Applied Physics, Volume 99, Issue 6, pp. 063516-063516-4 (2006)
Authors: J. D. Hoyland, D. Sandsa
Abstract: Forouhi-Bloomer dispersion has been used to characterize the temperature dependent refractive index of amorphous silicon after carefully comparing with Tauc-Lorentz model. The temperature dependent refractive index of amorphous silicon has been measured at a wavelength of 820 nm from room temperature up to nearly the melting point close to 1200 C. The refractive index is optimized using simulated annealing. The real part of the refractive index is found to vary linearly with a temperature coefficient of 3.85×104 while the extinction coefficient is found to vary as exp(3.82x103T), with T=0 at room temperature.

 


Extraction of optical constants of zinc oxide thin films by ellipsometry with
various models

Source: Thin Solid Films 510 32-38 (2006)
Authors: Y.C. Liu, J.H. Hsieh, S.K. Tung
Abstract: Spectroscopic ellipsometry was used to extract the optical constants of zinc oxide (ZnO) thin films deposited on (100) silicon substrate by filtered cathodic vacuum arc technique. Three dispersion models, namely, Sellmeier dispersion model, Cauchy model and Forouhi-Bloomer model, were evaluated for determining the optical constants of ZnO thin films below the energy band gap. The study shows that the Cauchy model provides the best spectral fittings among these three models. Above the energy band gap, two ellipsometric models, namely, two-phase model and three-phase point-by-point fit, were used.

 


Optical Properties of Silicon Nanocrystals Embedded in a SiO2 Matrix

Source: Physical Review B 72, 125419 (2005).
Authors: L. Ding, T. P. Chen, Y. Liu, C. Y. Ng, and S. Fung
Abstract: Optical properties of isolated silicon nanocrystals: nc-Si with a mean size of 4 nm embedded in a SiO2 matrix that was synthesized with an ion beam technique have been determined with spectroscopic ellipsometry in the photon energy range of 1.15.0 eV. A large band gap of the nc-Si obtained from the Forouhi-Bloomer model is found and is in very good agreement with the first-principles calculation of the nc-Si optical gap based on quantum confinement.

 


An approach to optical-property profiling of a planar-waveguide structure of Si nanocrystals embedded in SiO2

Source: Nanotechnology 16 (2005) 2657-2660
Authors: L. Ding, T. P. Chen, Y. Liu, C. Y. Ng, and S. Fung
Abstract: This paper reports an approach to optical-constant profiling for such a planar waveguide structure formed by Si ion implantation into a SiO2 thin film based on spectroscopic ellipsometry (SE). With the nc-Si optical constants calculated from the Forouhi-Bloomer model and the nc-Si depth profile obtained from secondary ion mass spectroscopy (SIMS) measurements, the optical properties at a given depth are simulated with the Maxwell-Garnett effective medium approximation (EMA). Then an SE fitting is carried out, and the optical constants of nc-Si are extracted from the best fitting. Finally, the depth profile of optical constants of the structure is obtained from the EMA calculation. The result also suggests that the structure has a very low optical loss in the visible to infrared spectral range.

 


Thermal Annealing Effect on the Band Gap and Dielectric Functions of Silicon Nanocrystals Embedded in SiO2 Matrix

Source: Applied Physics Letters, 87, 121903 (2005)
Authors: L. Ding, T. P. Chen, Y. Liu, C. Y. Ng, Y. C. Liu, S. Fung
Abstract: The thermal annealing effect on band gap and dielectric functions of silicon nanocrystals nc-Si_embedded in a SiO2 matrix synthesized by Si ion implantation is investigated by spectroscopic ellipsometry. The Maxwell-Garnett effective medium approximation (EMA) combined with the four-term Forouhi-Bloomer (FB) model has been used to determine the dielectric functions of nc-Si embedded in the SiO2 matrix synthesized with different annealing times. A large optical band-gap expansion and a strong dielectric suppression for nc-Si have been observed from the analysis based on the Forouhi-Bloomer model.

 


Forouhi–Bloomer analysis to study amorphization in Si

Source: Journal of Non-Crystalline Solids 351 (2005) 3866–3869
Author: S. Tripura Sundari
Abstract: Single crystal Si (100) was irradiated with 120 keV Ar+ for fluences ranging from 6 1013 to 11016 ions/cm2 and the real and imaginary parts of the dielectric function were measured using a spectroscopic ellipsometer in the energy range 1.55 eV. The pseudodielectric functions of the irradiated specimens were analyzed using ForouhiBloomer model for the first time. It was found that a minimum of four absorption terms is required to obtain good fits to the experimental data. The parameters of the fit show distinct behavior above and below amorphization threshold. This paper demonstrates that ForouhiBloomer interband model for pseudodielectric functions can be used to follow structural changes too.

 


Optical characterization of boron-doped nanocrystalline Si:H thin films

Source: Surface & Coatings Technology 198 (2005) 98– 103
Authors: H. Chen, W.Z. Shen
Abstract: This work report on the optical properties of boron-doped hydrogenated nanocrystalline silicon (nc-Si: H) thin films grown on glass substrates by plasma-enhanced chemical vapor deposition (PECVD), using X-ray diffraction (XRD), Raman scattering, and optical transmission measurements at room temperature. Wavelength-dependent optical constants (refractive index and extinction coefficient) are deduced from the optical transmission spectra by the TaucLorentz (TL) model with an empirical modification based on the comparison between the TL and ForouhiBloomer (FB) models. The extinction coefficients are very close to those obtained independently by the ForouhiBloomer (FB) model.

 


Optical properties of SiO2-TiO2 sol-gel thin films

Source: Journal of Materials Science 39 (2004) 2835 – 2839
Authors: P. Chrysicopoulou, D. Davazoglou, C. Trapalis, G. Kordas
Abstract: The optical properties of thin SiO2-TiO2 sol-gel composite films were investigated using exact optical models and the Forouhi-Bloomer model, 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.

 


Spectroscopic Ellipsometry Study of a Self-organized Ge Dot Layer

Source: Journal of Applied Physics, Volume 94, Issue 4, pp. 2248-2253 (2003).
Authors: B. Gallas and J. Rivory
Abstract: The paper reports on the determination of the dielectric function of a Ge dot layer obtained by epitaxial growth on Si(001) in the presence of Sb as surfactant and capped by Si. After growth, spectroscopic ellipsometry reveals a SiGe alloy containing Ge rich regions. After etching the Si cap, the dielectric function of the Ge rich regions exhibits critical points located at 2.92, 3.65, and 4.25 eV. It is shown that this dielectric function does not correspond either to an alloy or to bulk Ge, and is affected by confinement. In the 33.75 eV range Ge was fitted to a ForouhiBloomer dispersion law.

 


Structure, refractive index dispersion and optical absorption properties of evaporated Zn–Eu oxide films

Source: Materials Chemistry and Physics 81 (2003) 56–62
Author: A.A. Dakhel
Abstract: Zn oxide, Eu oxide and ZnEu oxide thin films were prepared by vacuum evaporation. Their structural and optical properties have been obtained by X-ray diffractometry (XRD), energy dispersion X-ray fluorescence (EDXRF) method and spectrophotometry. The EDXRF method was used to study the composition of the deposited ZnEu oxide films. The XRD patterns show that the prepared thin films of Zn oxide and ZnEu oxide with 55% ZnO were polycrystalline, while films of Eu oxide and ZnEu oxide with 28% ZnO were amorphous. Spectroscopic optical constants n(? ) and k(? ) as well as energy gap Eg were evaluated by Forouhi-Bloomer dispersion in the interband transition energy region. It was observed that ZnEu oxide thin films remain transparent in shorter wavelength range than the ZnO thin films, resulting from the increase of their band-gap. The energy gap of mixed oxide sample is controlled by the weight fraction of the constituent oxides. It was found that n, k and transmittance values for mixed-oxide film varies smoothly between the values of the pure constituent oxides in the fundamental energy gap region.

 


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

Source: Journal of applied physics, volume 89(8), pp4491, (2001)
Authors: C. L. Mak, B. Lai, K. H. Wong, C. L. Choy, D. Mo, and Y. L. Zhang
Abstract: Spectroscopic ellipsometry (SE) was used to characterize the solgel derived (K0.5Na 0.5)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 ForouhiBloomer model was adopted to represent the optical properties of the KNSBN films. In this model, the films were assumed to consist of two layersa 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.

 


Real Time Control of Plasma Deposited Optical Filters by Multiwavelength Ellipsometry

Source: 1303 J. Vac. Sci. Technol. A 18.4., Jul/Aug 2000
Authors: T. Heitz, A. Hofrichter, P. Bulkin, and B. Drevillon
Abstract: The dispersion law of Forouhi and Bloomer was used in real-time control of optical filters by multi-wavelength ellipsometry. The filters consist of SiO2/Si3N4 multilayers deposited on transparent substrates by a microwave plasma technique at room temperature. The dielectric function of the glass was found using spectroscopic ellipsometry and the dispersion law of Forouhi and Bloomer. (IS , IC) target values for the (Si3N4/SiO2). Si3N4 Bragg reflector filters were calculated using Lorentz dispersion laws for Si3N4 and SiO2 layers. The results show the excellent agreement between experimental and target values in the spectral region where the control method was used.

 


Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation

Source: Thin Solid Films 360 (2000) 96-102
Authors: D. Bhattacharyya, N.K. Sahoo, S. Thakur, N.C. Das
Abstract: Single layer TiO2 Films deposited on BK7 glass substrates by the ion-assisted electron-beam evaporation technique have been characterized by phase modulated spectroscopic ellipsometry. The ellipsometry spectra were recorded in the wavelength range of 300-1000 nm. The measured spectra were then fitted with theoretically simulated curves generated assuming different model sample structures. The absorption effect has been taken into account for fitting the data below 400 nm. In this regime, fitting has been done assuming Sato-Adachis dispersion relation for crystalline semiconductors and Forouhi-Bloomers dispersion relation for amorphous materials, and the latter has been found to give better results.

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