Optical Dispersion Model Research Articles

New optical dispersion models for the accurate description of the electrical permittivity in direct and indirect semiconductors

We propose new optical dispersion models to describe the imaginary part of the electrical permittivity of dielectric and semiconductor materials in the fundamental absorption region. We work out our procedure based on the well-known structure of the semi-empirical Tauc–Lorentz dispersion model and the band-fluctuations approach to derive a five-parameter formula that describes the Urbach, Tauc and high-absorption regions of direct and indirect semiconductors. Main features of the dispersion models are the self-consistent generation of the exponential Urbach tail below the bandgap and the incorporation of the Lorentz oscillator behavior due to electronic transitions above the fundamental region. We apply and test these models on optical data of direct (MAPbI3, gallium arsenide and indium phosphide), indirect (gallium phosphide and crystalline silicon), and amorphous hydrogenated silicon semiconductors, accurately describing the spectra of the imaginary part of the electrical permittivity. Lastly, we compare our results with other similarly inspired dispersion models to assess the optical bandgap, Urbach tail and oscillator central resonance energy.

In-situ observation of nucleation and property evolution in films grown with an atmospheric pressure spatial atomic layer deposition system

Atmospheric pressure—spatial atomic layer deposition (AP-SALD) is a promising open-air deposition technique for high-throughput manufacturing of nanoscale films, yet the nucleation and property evolution in these films has not been studied in detail. In this work, in situ reflectance spectroscopy was implemented in an AP-SALD system to measure the properties of Zinc oxide (ZnO) and Aluminum oxide (Al2O3) films during their deposition. For the first time, this revealed a substrate nucleation period for this technique, where the length of the nucleation time was sensitive to the deposition parameters. The in situ characterization of thickness showed that varying the deposition parameters can achieve a wide range of growth rates (0.1–3 nm/cycle), and the evolution of optical properties throughout film growth was observed. For ZnO, the initial bandgap increased when deposited at lower temperatures and subsequently decreased as the film thickness increased. Similarly, for Al2O3 the refractive index was lower for films deposited at a lower temperature and subsequently increased as the film thickness increased. Notably, where other implementations of reflectance spectroscopy require previous knowledge of the film’s optical properties to fit the spectra to optical dispersion models, the approach developed here utilizes a large range of initial guesses that are inputted into a Levenberg-Marquardt fitting algorithm in parallel to accurately determine both the film thickness and complex refractive index.

Study of the Dispersive Contribution Effect for Neutrons Scattering by <sup>60</sup>Cu Nucleus Using Variational Moment Approach

The variational moment approach for the neutrons scattering analysis by 60Cu nucleus within the energy range (60-80) MeV is applied to the construction of the complex single-particle mean field felt by neutrons in 60Cu, starting from negative energy values to the positive energy values. The experimental data of the scattering neutron has been analysis by using one of the methods for optical dispersion model which depending on the afferent between the real and imaginary parts and this led to a derivation decrease in determining the optical parameters from the experimental data. Also on the stripe expending of the real potential parameters from high energy to low energy to the close area of the Coulomb barrier which characterized the lack of information about the experimental data for each, using the program SPI-GINOA in order to determine the value of the volume integral for the real and imaginary parts (surface and volume). The Value of the volume integral for the real part and integrals oh – Fock was pointed and then determined the value of real part of the potential Hartree – fock potential. In addition we also has been determined the imaginary potential (two parts the surface and the volume) and studied on function of energy for all the specific pointed ingredients. The potential dispersion was determined (surface – volume) and studied their functional energy. Therefore, we determined the radius neutron optical model and also we found its energy way match close to what reveal the correctness of method of dispersive optical model at one hand, and the accuracy in the determination of optical model parameters at other hand.

Continuous-discontinuous Galerkin time domain (CDGTD) method with generalized dispersive material (GDM) model for computational photonics.

The discontinuous Galerkin time domain (DGTD) method and its recent flavor, the continuous-discontinuous Galerkin time domain (CDGTD) method, have been extensively applied to simulations in the radio frequency (RF) and microwave (MW) regimes due to their inherent ability to efficiently model multiscale problems. We propose to extend the CDGTD method to nanophotonics while exploiting its advantages which have already been established in the RF and MW regimes, such as domain decomposition, non-conformal meshing, high-order elements, and hp-refinement. However, at optical frequencies many materials are highly dispersive, so the modeling of nanophotonic devices requires accurate handling of different dielectric functions, including those of plasmonic elements, dielectrics, and tunable materials. In this paper, we propose a CDGTD method that incorporates a generalized dispersive material (GDM) model which is an efficient way to implement a wide range of optical dispersion models with a universal analytic function. Physics-based dispersion models, such as the Drude, Debye, Lorentz, and critical points as well as more complicated behavior founded on ab-initio principles can all be obtained as special cases of the universal GDM approach. The accuracy and convergence of this GDM-incorporated CDGTD are verified by numerical examples. The CDGTD method, equipped with the GDM model, paves the way to the efficient design and optimization of large scale photonic devices with a diverse range of optical dispersive materials.

The Uncertain Limits Between Classical and Quantum Physics: Optical Dispersion and Bohr's Atomic Model

AbstractIt is commonplace to recount the history of quantum physics on the basis of phenomena that have found no satisfactory explanation in the context of so‐called classical physics. This is the case of, for example, blackbody radiation, the photoelectric effect, specific heats, and series of spectral lines. This story goes in another direction: new knowledge about quantum physics not only emerged from the need to explain new phenomena that conflicted with old theoretical structures, but also from the attempts to provide a quantum explanation of phenomena, like optical dispersion, which for a long time had found a very convincing explanation in old physical models, such as the resonance model. The boundary between classical and quantum domains of knowledge was not fixed a priori, but historically negotiated in the context of specific problems, including the problem of optical dispersion.

Optical characterization and bandgap engineering of flat and wrinkle-textured FA0.83Cs0.17Pb(I1–xBrx)3 perovskite thin films

The complex refractive indices of formamidinium cesium lead mixed-halide [FA0.83Cs0.17Pb(I1– xBrx)3] perovskite thin films of compositions ranging from x = 0 to 0.4, with both flat and wrinkle-textured surface topographies, are reported. The films are characterized using a combination of variable angle spectroscopic ellipsometry and spectral transmittance in the wavelength range of 190 nm to 850 nm. Optical constants, film thicknesses and roughness layers are obtained point-by-point by minimizing a global error function, without using optical dispersion models, and including topographical information supplied by a laser confocal microscope. To evaluate the bandgap engineering potential of the material, the optical bandgaps and Urbach energies are then accurately determined by applying a band fluctuation model for direct semiconductors, which considers both the Urbach tail and the fundamental band-to-band absorption region in a single equation. With this information, the composition yielding the optimum bandgap of 1.75 eV for a Si-perovskite tandem solar cell is determined.

Modeling of a selective solar absorber thin film structure based on double TiNxOy layers for concentrated solar power applications

By using double TiNxOy absorption layers with low N/O ratio (TiNO_L) and high N/O ratio (TiNO_H), a spectral selective solar absorber (SSA) with the structure of SiO2-TiO2-TiNO_L-TiNO_H-Cu has been proposed. Optical properties of the TiNO_L and TiNO_H layers are investigated with spectroscopic ellipsometry (SE) in the wavelength range of 0.3–2.5μm using an optical dispersion model in which the absorption mechanisms in TiNxOy including the localized surface plasmon resonance (LSPR), free electron absorption and interband transitions are taken into account. Because TiNO_H has a higher free electron concentration than that of TiNO_L, the absorption due to both the LSPR and free electron absorption in TiNO_H is found larger than that in TiNO_L. With the model parameters of the dispersion model obtained from the SE modeling, the reflectance spectrum of the SSA in the wide wavelength range of 0.3–25μm covering both the solar radiation and heat radiation of a hot surface has been simulated; and the simulated result agrees well with the experimental result.

Role of Isopropyl Alcohol Solvent in the Synthesis of Organic–Inorganic Halide CH(NH2)2PbIxBr3–x Perovskite Thin Films by a Two-Step Method

Spectroscopic ellipsometry (SE) was used to investigate the role of isopropyl alcohol (IPA) solvent in the synthesis of organic-lead-halide perovskite CH(NH2)2PbIxBr3–x [FAPbIxBr3–x] thin films by the two-step reaction of an amorphous (a-)PbIxBr2–x layer and FAIxBr1–x solution diluted in IPA. An optical dispersion model was developed to extract the complex refractive index N (=n+ik), optical transition, and film thickness of FAPbIxBr3–x perovskites by SE analysis as a function of immersion time in a solution of FAIxBr1–x diluted in IPA. SE combined with X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), and scanning microscopy (SEM) revealed that IPA promoted film crystallization of a-PbIxBr2–x accompanied by the formation of surface roughness, grain boundaries, and voids, followed by enhanced diffusion of FAIxBr1–x into the grain boundaries/voids in the mesoporous crystallized PbIxBr2–x network. These processes contribute synergistically to the growth of the perovskite structure.

Ellipsometric study of the optical properties of n-type superconductor La_19Ce_01CuO_4

Two thin La2-xCexCuO4 (x = 0.1) films were deposited on [001]-oriented SrTiO3 substrates by pulsed-laser deposition. The as-prepared LCCO films were well studied by X-ray diffraction, atomic force microscopy, transmission electron microscopy and spectroscopic ellipsometry. Spectroscopic ellipsometry provides a nondestructive, fast, and accurate method to explore the optical properties of the superconductive materials. The thickness and the optical dispersion model of the LCCO films in the visible range are presented for the first time. The results show that minor differences in the annealing progress will cause a relatively large change in the optical properties of the LCCO films.

Spectroscopic ellipsometry studies of as‐prepared and annealed CdS:O thin films

AbstractCadmium sulfide thin films on soda lime substrates were obtained by rf‐magnetron sputtering in argon‐oxygen atmosphere. As‐prepared and vacuum annealed films were then studied by spectroscopic ellipsometry at room temperature over photon energy range from 0.5 to 6 eV. The obtained ellipsometric data were treated using optical dispersion models based on Gaussian type oscillators. Dielectric function of oxygen‐free films, as well as those obtained under 3% of O/Ar partial pressure was reliably restored. At the same time, dielectric function obtained for 5% CdS:O can be regarded only as an average over several materials since our XPS examination disclosed presence of several compounds in thin films deposited at O/Ar ratios higher than 3%. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The effects of thermally-induced biaxial stress on the structural, electrical, and optical properties of Cu2O thin films

The effects of biaxial stress in Cu2O thin films grown by rf magnetron sputtering at different growth temperatures were investigated using X-ray diffraction (XRD), atomic force microscopy (AFM), electrical transport, and ellipsometric measurements. A predominant diffraction peak in the XRD patterns corresponds to the (111) plane direction of the Cu2O phase. Biaxial tensile stress was induced by thermal mismatch between the film and substrate and increased with increasing growth temperature. As the growth temperature and biaxial stress increased, the electrical resistivity decreased, while the carrier concentration and Hall mobility both increased. The ellipsometric data were fit using an optical dispersion model, and the decrease in refractive index was attributed to contraction of the lattice parameter with increasing biaxial stress. The optical absorption peaks shifted slightly toward higher energy with increasing stress. Our experimental data suggest that the mechanisms of stress are important for understanding the properties of Cu2O thin films and for the fabrication of devices using them.

DNA strand breaks induced by electrons simulated with Nanodosimetry Monte Carlo Simulation Code: NASIC.

The method of Monte Carlo simulation is a powerful tool to investigate the details of radiation biological damage at the molecular level. In this paper, a Monte Carlo code called NASIC (Nanodosimetry Monte Carlo Simulation Code) was developed. It includes physical module, pre-chemical module, chemical module, geometric module and DNA damage module. The physical module can simulate physical tracks of low-energy electrons in the liquid water event-by-event. More than one set of inelastic cross sections were calculated by applying the dielectric function method of Emfietzoglou's optical-data treatments, with different optical data sets and dispersion models. In the pre-chemical module, the ionised and excited water molecules undergo dissociation processes. In the chemical module, the produced radiolytic chemical species diffuse and react. In the geometric module, an atomic model of 46 chromatin fibres in a spherical nucleus of human lymphocyte was established. In the DNA damage module, the direct damages induced by the energy depositions of the electrons and the indirect damages induced by the radiolytic chemical species were calculated. The parameters should be adjusted to make the simulation results be agreed with the experimental results. In this paper, the influence study of the inelastic cross sections and vibrational excitation reaction on the parameters and the DNA strand break yields were studied. Further work of NASIC is underway.

A practical method for optical dispersion model selection and parameters variations in scatterometry analysis with variable n&k's

Optical critical dimension (OCD) scatterometry in recent years became a well-accepted and powerful technique to determine the properties and grating profiles of 2D and 3D microelectronic structures (critical dimensions, side-wall angles, grating and underlying thin film thicknesses) in modern semiconductor manufacturing. However, the optical scatterometry, as any model-based metrology technique, relies on the accuracy of the OCD model which highly depends on the optical properties (the n&k's) of the materials in the structure. In practice, even small deviations in material's optical properties (from nominal model inputs) due to process condition variations might significantly affect the scatterometry measurements. A logical way to deal with this problem is to allow some degree of the n&k's variability of the most affected layer(s) in the OCD model describable by relevant dispersion model(s) (floating n&k's). Essentially, one of the largest complications for the end users (process engineers) is to decide which optical dispersion model (Cauchy, Lorentz, Tauc–Lorentz, etc.) needs to be selected to describe a material under production conditions and which parameters are more sensitive and need to be floated in the OCD model. We developed an approach which, we believe, will result in more straightforward and fast development of the OCD models. This approach provides a possibility to automatically select a most proper dispersion model which has been always an ambiguous decision for most of the end users. This methodology will allow determination of most influential model parameters to vary, eliminating potential sources of modeling error at the initial steps of the OCD modeling. A few examples to illustrate the key ideas and practical use of our procedure have been provided.

Investigation of the optical properties of MoS2 thin films using spectroscopic ellipsometry

Spectroscopic ellipsometry (SE) characterization of layered transition metal dichalcogenide (TMD) thin films grown by vapor phase sulfurization is reported. By developing an optical dispersion model, the extinction coefficient and refractive index, as well as the thickness of molybdenum disulfide (MoS2) films, were extracted. In addition, the optical band gap was obtained from SE and showed a clear dependence on the MoS2 film thickness, with thinner films having a larger band gap energy. These results are consistent with theory and observations made on MoS2 flakes prepared by exfoliation, showing the viability of vapor phase derived TMDs for optical applications.

Complexation of WPI and microwave-assisted extracted agars with different physicochemical properties

The complex formation between whey protein isolate (WPI) and agar has been investigated and their interactions were monitored as a function of the physicochemical properties of agar, the pH and the ionic strength of the medium. Agars from Gracilaria vermiculophylla were extracted under different MAE conditions and characterized according to their physicochemical properties. By using microwave irradiation a wide variety of agars was obtained, as different MAE conditions results in polyelectrolytes with distinct properties. UV–vis (in optical dispersion (O.D.) model) spectroscopy and isothermal titration calorimetry (ITC) have been used to study the formation of insoluble (coacervate) complexes. MAE agars revealed excellent properties for complex formation with WPI. The binding of WPI to MAE agar samples has been shown to be the result of different contributions. O.D. and ITC results showed that the molecular mass and the sulfate content of different agars had a determinant effect on coacervate formation.

Optical constants and band gap expansion of size controlled silicon nanocrystals embedded in SiO 2 matrix

Silicon nanocrystals (Si-NCs) with different sizes embedded in SiO 2 matrix were synthesized by phase separation and thermal crystallization of SiO x/SiO 2 supperlattice approach. The optical constants and band gap expansion of Si-NCs have been investigated by spectroscopic ellipsometry, based on the Maxwell–Garnett effective medium approximation and the Forouhi–Bloomer optical dispersion model. Similar spectra shapes but smaller values of Si-NCs optical constants with respect to bulk crystalline Si is observed. With the size of Si-NCs decreasing from 6 nm to 2 nm, the band gap increases from 1.64 eV to 2.56 eV. The band gap expansion, as compared to bulk crystalline Si, which agrees with the prediction of first-principles calculations based on quantum confinement effect, is presented in this paper.

Ellipsometric studies on TiO 2 thin films synthesized by spray pyrolysis technique

TiO 2 thin films were synthesized on quartz substrates at substrate temperatures of 350 °C and 450 °C by thermal spray pyrolysis technique using titanium oxy-acetyl acetonate as a precursor. The optical properties of the thin films were characterized by a Spectroscopic Ellipsometer (SE). The surface morphology of the thin films was studied using Atomic Force Microscopy (AFM). The surface roughness values obtained using AFM and SE was compared. The refractive indices of the films were computed using a point by point ellipsometric data extraction procedure. The porosity of the films were modeled from the optical data by effective medium approximation and corroborated from empirical relations. Using Forouhi–Bloomer optical dispersion model, further treatment of SE data was carried out. The experimental investigations and modeling of the data were directed towards optical benchmarking of spray pyrolyzed titania thin films.

Bandgap expansion and dielectric suppression of self-assembled Ge nanocrystals

The bandgap and optical properties (dielectric functions and optical constants) of dome-shaped Ge nanocrystals (nc-Ge) with average sizes of ∼6 nm in height and ∼13 nm in diameter have been investigated using spectroscopic ellipsometry based on the Forouhi-Bloomer optical dispersion model. As compared to bulk crystalline Ge, the nc-Ge exhibited a bandgap expansion of ∼0.2 eV and a significant reduction in the dielectric function. The bandgap expansion and dielectric suppression are discussed in terms of the quantum confinement effect as well as the bond contraction model.

Description of TiO 2 thin films treated in NH 3 atmosphere by optical dispersion models

The influence of a reductive ammonia atmosphere on TiO 2 sol-gel film structural and optical characteristics was investigated. X-ray Diffraction technique, X-ray photoelectron spectroscopy and Rutherford Back Scattering analysis were applied to study the crystallinity, oxidation state and element concentration profile of the modified films. Their optical properties were investigated by UV–Vis spectroscopy. The refractive index and extinction coefficient were obtained by fitting theoretical transmittance curves to experimental ones using Forouhi–Bloomer (FB) and Tauc–Lorentz (TL) physical models. Both models revealed slight decrease (up to 2.6–2.7 eV) of the FB and TL band gaps with increase of the treatment temperature. These results were discussed in terms of the additional energy levels creation due to the defect TiO 2 structure formation during thermal treatment in reductive atmosphere.

Spectroscopic ellipsometry studies of GaN films deposited by reactive rf sputtering of GaAs target

GaN films have been deposited by reactive rf sputtering of GaAs target in 100% nitrogen ambient on quartz substrates at different substrate temperatures ranging from room temperature to 700°C. A series of films, from arsenic-rich amorphous to nearly arsenic-free polycrystalline hexagonal GaN, has been obtained. The films have been characterized by phase modulated spectroscopic ellipsometry to obtain the optical parameters, viz., fundamental band gap, refractive index, and extinction coefficient, and to understand their dependence on composition and microstructure. A generalized optical dispersion model has been used to carry out the ellipsometric analysis for amorphous and polycrystalline GaN films and the variation of the optical parameters of the films has been studied as a function of substrate temperature. The refractive index values of polycrystalline films with preferred orientation of crystallites are slightly higher (2.2) compared to those for amorphous and randomly oriented films. The dominantly amorphous GaN film shows a band gap of 3.47eV, which decreases to 3.37eV for the strongly c-axis oriented polycrystalline film due to the reduction in amorphous phase content with increase in substrate temperature.