Standard Critical Point Model Research Articles

Composition-dependent optical, dielectric and d-orbital electron characteristic of high-throughput horizontal composition gradient Li1-xMgxTi2O4 combinatorial film

The unique physical properties of LiTi2O4 and MgTi2O4 attracted extensive research interest in various fields, including new type batteries and high-temperature superconductors. However, the intricate mechanism governing the d-orbital electron within this system still awaits further excavation. Herein, we employed the combinatorial laser molecular beam epitaxy technique to fabricate a high-quality composition-spread Li1-xMgxTi2O4 film and evaluated its structure, composition, surface morphology and phonon modes by X-ray diffraction, X-ray photoelectron spectroscopy, atomic force microscopy, and Raman scattering spectroscopy. The optical constants and dielectric properties of diverse microregions with varying Li/Mg content over a wide spectral range (189–1658 nm) were measured nondestructively using spectroscopic ellipsometry, revealing the composition-dependent optical properties of Li1-xMgxTi2O4. By fitting the second derivative spectra (d2ε/dE2) using the standard critical point model, five transitions within the detected spectral range were observed. Combining previous analyses and first-principles calculation, we attribute the critical points to crystal field (CF) transition 4A2 →4T1 originating from the spin state of tetrahedral Li/Mg ions, the binding of Ti-related pairs and electron transitions between O-2p to Ti-3d orbits. This exploration of the precise structure of the d-metal band provides a positive reference for the regulation and application of relevant devices.

Electronic and optical properties of layered chalcogenide FeIn2Se4

We investigated the spectral-dependent dielectric function and temperature-dependent bandgap energy of layered chalcogenide FeIn2Se4 crystals. The critical-point energy and Lorentzian broadening were analyzed by fitting second-derivative spectra using the standard critical point model. The temperature effect of the bandgap energy was analyzed based on an analytical model considering both thermal lattice expansion and electron–phonon interactions. We also extensively analyzed the temperature dependence of absorption tails and identified their possible origins. The dielectric functions and absorption coefficient in the photon-energy range of 0.75–4.75 eV were obtained. The results also showed that optical phonon modes associated with the electron–phonon interactions could be closely related to the average phonon energy.

Optical properties of MoO3/Ag/MoO3 multilayer structures determined using spectroscopic ellipsometry

The authors investigated the optical and electrical properties of MoO3/Ag/MoO3 multilayer structures grown using thermal evaporation on glass. For the top and bottom MoO3 layers, they found that thicknesses of 35 and 20 nm, respectively, gave the highest transmittance in the visible spectral range. Thicknesses of 5, 7, 10, 12, and 15 nm were used for the Ag layer. The MoO3 and Ag layers were amorphous and crystalline, respectively, according to transmission electron microscopy (TEM). An ultrathin, 12-nm-thick Ag layer enhances the transmittance in the visible range relative to that of a 55-nm-thick MoO3 layer (i.e., no Ag layer). The structural and morphological properties of all samples were studied using x-ray diffraction, scanning electron microscopy, and atomic force microscopy. The optical constants were obtained from the measured ellipsometric angles, Ψ and Δ, using a parametric optical constant model. The optical properties (dielectric functions and bandgap energies) of amorphous MoO3 layers were compared to literature values. The authors estimated the optical gap energy values of amorphous MoO3 layers using both the Tauc extrapolation method (Eg = 3.380 eV) and the standard critical point model (Eg = 4.044 eV). The refractive indexes (n, k) and sheet resistances of Ag ultrathin films were significantly different for layer thicknesses of 5 and 7 nm from those of thicker films. This is explained by the percolation effect, based on TEM cross-sectional images.

Exact interband transition energies of VO2 films

The temperature dependent optical constants of VO2 thin films with different thicknesses on variable substrates were measured by spectroscopic ellipsometry. The exact interband transition energies crossover metal-to-insulator transition of VO2 were obtained using a standard critical point model fitting based on the measured optical constants. The dynamic image of all critical points was obtained during the heating and cooling processes within the measured energy region. By introducing the fine orbital structure into the band model, every critical point was assigned to the corresponding band transition. The critical point of 4.7eV predicted theoretically, which is response to the transition from O2P to upper a1g, was obtained experimentally for the first time. Our work provides a new view for the complex band scheme of the monoclinic and rutile phase VO2. Moreover, the insulator-to-metal transition temperature is modified by regulating both film thickness and substrate.

Investigation of fundamental and high order optical transitions in α-Fe2O3 thin films using surface barrier electroreflectance

In this paper, we use surface barrier electroreflectance technique to probe the optical transitions in hematite (α-Fe2O3) thin film. An electric field was induced normal to the surface of α-Fe2O3 thin film in an Ag/α-Fe2O3/Ag based capacitor type structure and the corresponding electroreflectance analysis was performed. Based on the electroreflectance analysis, we observed the fundamental as well as two high order critical points associated with α-Fe2O3. Standard critical point model was used to find the exact energy locations and the broadening parameters associated with these critical points. The existence of the fundamental critical point was further confirmed by the spectrophotometric analysis. The quantitative analysis based on the electro-optic energy confirmed that the obtained electroreflectance spectrum was within the low field regime, and the obtained critical points above the fundamental transition were attributed to the high order transitions of electrons from the valence band to the deep in the conduction band.

Temperature dependent spectroscopic ellipsometry and Raman scattering of PbTiO_3-based relaxor ferroelectric single crystals around MPB region

To discover intrinsic relationship between optical bandgap and structural transformations in relaxor ferroelectric single crystals, electronic band structures and dielectric functions of xPb(In1/2Nb1/2)O3-(1 − x − y)Pb(Mg1/3Nb2/3)O3-yPbTiO3 single crystals (x∼0.27–0.28, y∼0.29–0.35) around morphotropic phase boundary have been investigated by variable-temperature (200–750 K) spectroscopic ellipsometry. It was found that the discontinuous evolution from the second derivative of dielectric functions corresponds to structural transformation patterns. Using the SCP (standard critical point) model, four typical interband transitions (Ea∼2.8 eV, Eb∼3.6 eV, Ec∼4.6 eV, and Ed∼5.4 eV) can be uniquely assigned. These interband transitions are mainly attributed to the contributions from B-O bonds and multiphase coexistence. Furthermore, a modified phase diagram based on interband transition variations with the temperature and PT composition for PIMN-PT crystals was provided. In order to verify the accuracy of phase transition temperature, temperature-dependent low-wavenumber Raman scattering was used as a support. The present results provide important supports for the theoretical model, which establish a quantitative relationship between the electronic transition and structural transformation for ferroelectric oxides.

Temperature dependence of the electronic transitions in BiFeO3 thin film studied by spectroscopic ellipsometry

The temperature dependence of the electronic response of BiFeO3 thin film grown on a SrTiO3 substrate is investigated using spectroscopic ellipsometry. By analyzing the pseudodielectric function, we identify two d-d crystal field transitions of Fe3+ ions in the energy region between 1 and 2 eV. The d-d transitions show abnormal temperature dependence that cannot be attributed to conventional electron-phonon interactions. The origin of the abnormal temperature dependence is discussed in terms of spin-charge coupling. The temperature dependence of the charge transfer transitions located above 2.5 eV is characterized by standard critical point model analysis of the 2nd derivatives of the dielectric function. This analysis provides detailed information of the critical point parameters for charge transfer transitions.

Optical properties of large-area ultrathin MoS2 films: Evolution from a single layer to multilayers

We investigated the optical properties of ultrathin MoS2 films (number of layers: N = 1, 2, 4, and 12) using Raman spectroscopy, photoluminescence (PL) spectroscopy, and spectroscopic ellipsometry. We estimated the layer thicknesses based on Raman spectra. We characterized the microstructural properties of a single-layer MoS2 film using atomic force microscopy. We measured the lowest-energy A and B excitons using PL spectroscopy. We measured the ellipsometric angles (Ψ and Δ) of MoS2 thin films using spectroscopic ellipsometry, and obtained the dielectric functions as the films' thickness changed from a single layer to multi-layers. We determined the films' optical gap energies from the absorption coefficients. Applying the standard critical point model to the second derivative of the dielectric function (d2ε(E)/dE2), we determined several critical point energies. The d2ε(E)/dE2 spectra showed doublet peaks around 3 eV corresponding to the C and D transitions, as well as doublet peaks around 2 eV corresponding to the A and B transitions. These doublet structures at 3 eV are attributed to the transitions in the Brillouin zone between the Γ and K points.

Interband electronic transitions and phase transformation of multiferroic Bi1−xLaxFe1−yTiyO3 ceramics revealed by temperature-dependent spectroscopic ellipsometry

Optical properties and phase transition of Bi1−xLaxFe1−yTiyO3 (BLFTO) ceramics with different composition (0.02 ≤ x ≤ 0.10, 0.01 ≤ y ≤ 0.06) have been investigated by spectroscopic ellipsometry (SE) in the temperature range of −70–450 °C. The real part of the complex dielectric function ε1 increases with the temperature. Meanwhile, the imaginary part ε2 in the low-energy region decreases with the temperature and has an opposite trend in the high-energy side. Four typical interband transitions (Ea ∼ 2.50 eV, Eb ∼ 2.70 eV, Ec ∼ 3.60 eV, and Ed ∼ 4.25 eV) can be observed from the second derivative of the complex dielectric functions with aid of the standard critical point model. The critical point (CP) transition becomes broadening and shifts to a lower energy side as La and Ti compositions increase. Moreover, the CP transition energies show a red-shift trend with increasing the temperature until 320 °C, due to the lattice thermal expansion and electron-phonon interaction. The typical interband transitions and partial spectral weight present anomalies in the proximity of antiferromagnetic transition owing to the coupling between magnetic and ferroelectric order parameters and spin-lattice coupling for BLFTO multiferroic materials. It was found that the Néel temperature of BLFTO ceramics decreases from 364 to 349 °C with increasing doping composition of La and Ti elements. These phenomena can be attributed to the modification of electronic structure and magnetic order because the differences of electronegativity and ionic radii between Bi and La, Fe and Ti induce the variations on the bond angle and bond length between cations and anions. Moreover, the substitution for magnetic Fe3+ ions with nonmagnetic Ti4+ ions can reduce the exchange interaction between adjacent magnetic moments. Therefore, SE technique can be sensitive for detecting the phase/structural transitions of multiferroic oxides.

Structural and optical properties of phase‐change amorphous and crystalline Ge1 − xTex (0 < x < 1) thin films

AbstractGe1 − xTex thin films were grown using thermal coevaporation deposition. The dielectric functions and the phonon modes of amorphous (a‐) and crystalline (c‐) Ge1 − xTex films were measured using spectroscopic ellipsometry and Raman spectroscopy in order to investigate electronic and vibrational properties of these alloys. Using the second derivative spectra of the dielectric functions of a‐Ge1 − xTex alloys and the standard critical point (SCP) model, we obtained optical transition energies for the a‐Ge1 − xTex alloys. The optical transition energies were not only consistent with the density of states (DOS) reported in the literature, but also provided more detailed structures for the joint density of states (JDOS) of a‐Ge1 − xTex. magnified imageThe second derivative spectra of d2ε(E)/dE2 for amorphous GeTe. The transition energies were estimated using SCP model (short arrows) and were compared to those of photoemission spectroscopy from literature (long arrows).

Microstructure, optical property, and electronic band structure of cuprous oxide thin films

Cuprous oxide (Cu2O) thin films were grown via radio frequency sputtering deposition at various temperatures. The dielectric functions and luminescence properties of the Cu2O thin films were measured using spectroscopic ellipsometry and photoluminescence, respectively. High-energy peaks were observed in the photoluminescence spectra. Several critical points (CPs) were found using second derivative spectra of the dielectric functions and the standard critical point model. The electronic band structure and the dielectric functions were calculated using density functional theory, and the CP energies were estimated to compare with the experimental data. We identified the high-energy photoluminescence peaks to quasi-direct transitions which arose from the granular structures of the Cu2O thin films.

Spectroscopic Ellipsometry Analysis of Rapid Thermal Annealing Effect on MBE Grown GaAs1−x−Nx

We report on the effect of rapid thermal annealing (RTA) on GaAs1−x−Nx layers, grown by molecular beam epitaxy (MBE), using room temperature spectroscopic ellipsometry (SE). A comparative study was carried out on a set of GaAs1−x−Nx as-grown and the RTA samples with small nitrogen content (x = 0.1%, 0.5% and 1.5%). Thanks to the standard critical point model parameterization of the GaAs1−x−Nx extracted dielectric functions, we have determined the RTA effect, and its nitrogen dependence. We have found that RTA affects more samples with high nitrogen content. In addition, RTA is found to decrease the E1 energy nitrogen blueshift and increase the broadening parameters of E1, E1+Δ1, E′0 and E2 critical points.

Optical properties of (GeTe, Sb2Te3) pseudobinary thin films studied with spectroscopic ellipsometry

The authors measure the dielectric functions of (GeTe, Sb2Te3) pseudobinary thin films by using spectroscopic ellipsometry. By using standard critical point model, they obtained the optical transition (critical point) energies of the amorphous (crystalline) thin films. The optical (indirect band) gap energies of the amorphous (crystalline) phase are estimated from the linear extrapolation of the absorption coefficients. The band structure calculations show that GeTe, Ge2Sb2Te5, and Ge1Sb2Te4 have indirect gap whereas Ge1Sb4Te7 and Sb2Te3 have direct gap. The measured indirect band gap energies match well with electronic band structure calculations.

Dielectric Function and Defect Structure of CdTe Implanted by 350-keV Bi Ions

AbstractIn this work we have developed optical models for the ellipsometric characterization of Bi-implanted CdTe. We have characterized the amount and nature of disorder using Rutherford Backscattering Spectrometry combined with channeling (RBS/C). Samples with a systematically varying degree of disorder were prepared using ion implantation of Bi into single-crystalline CdTe at an energy of 350 keV with increasing doses from 3.75×1013 cm-2 to 6×1014 cm−2. The motivation for use of the high atomic mass Bi ions was that previous studies using lighter ions revealed damage at a low level, even for doses several times higher than the amorphization threshold estimated by simulation [P. Petrik et al., phys. stat. sol. (c) 5, 1358 (2008)]. In contrast, Bi ions create sufficient disorder for investigation of the changes in dielectric function critical point (CP) features in a wider variety of structures from single-crystalline to the disordered state. The CP features can be described by numerous methods starting from the standard CP model, through the parameterization of Adachi [Adachi et al., J. Appl. Phys. 74, 3435 (1993)], and finally to the generalized CP models. The standard CP model has been demonstrated to be a reliable approach for polycrystalline CdTe characterization used in photovoltaic applications [Li et al., phys. stat. sol. (a) 205, 901 (2008)].

Dimensionality of electronic excitations in organic semiconductors: A dielectric function approach

We present a detailed investigation on the effective dimensionality (associated with the degree of delocalization) of electronic excitations in thin organic films using the dielectric function as obtained from ellipsometry. To this end, we study first the best analytical representation of the optical dielectric function of these materials and compare different approaches found in the literature: (i) the harmonic oscillator approximation, (ii) the standard critical-point model (SCP), (iii) the model dielectric function (MDF), and (iv) the Forouhi-Bloomer model. We use these models to analyze variable angle spectroscopic ellipsometry raw data for a thin poly(9,9-dioctylfluorene) (PFO) film deposited on quartz (taken as an archetypal sample). The superiority of the SCP model for PFO films and a wide range of other spin-coated conjugated polymers (and guest-molecules in polymers) is demonstrated. Moreover, we show how the SCP model can be used to gain physical information on the microscopic structure. As an example, we show that the delocalization of excitons decreases for nonconjugated polymers, such as polymethylmethacrylate and polyimide, while the conjugation length and exciton delocalization are, respectively, enhanced in cases where a planar conformation (e.g., $\ensuremath{\beta}$ phase of PFO) or a high degree of crystallinity [e.g., poly(3-hexylthiophene)] is achieved. As an additional example, we employ the SCP excitonic model to investigate the temperature dependence of the dielectric function of crystalline and glassy PFO films. We propose that the SCP excitonic model should be adopted as the standard choice to model the optical properties of polymer thin films from ellipsometry data.

Dielectric functions and critical points of PbTiO3, PbZrO3, and PbZr0.57Ti0.43O3 grown on SrTiO3 substrate

Single crystalline PbTiO3, PbZrO3, and PbZr0.57Ti0.43O3 thin films on SrTiO3 (001) substrates were grown by a combination of molecular beam epitaxy and rf sputtering methods. The authors measured the dielectric functions of the thin films using spectroscopic ellipsometry and determined the interband critical point energies using standard critical point model. They compared the critical point energies to the band structure calculations in the literature. The data suggest that anticrossing behavior occurs between Ea and Eb near Zr=0.17. This phenomenon is attributed to a coupling between X1c and X3c bands caused by intrinsic alloy disorder.

Ellipsometric study of the poling effect on nonlinear-optical side-chain polymers containing disperse red 1

The purpose of this work is to investigate the effect of corona poling on the optical functions of the nonlinear-optical (NLO) polymers. We measured the complex refractive indices of NLO polymers deposited on glasses before and after corona poling using spectroscopic ellipsometry at room temperature at various incidence angles. In addition, we observed the absorption spectral change using ultraviolet-visible spectroscopy after corona poling, which is attributed to the chromophore orientation. In order to make NLO polymers, we attached a NLO active dye and photocrosslinkable moieties as side chains of poly(4-hydroxystyrene), deposited the polymer thin films on glass substrates by spin-coating, and corona-poled it along the surface-normal direction to align the dipoles of the chromophores along the electric field direction. In detail, PSDR1-25 designates a poly(4-hydroxystyrene) where 25% of hydroxyl groups in the side chain are substituted by disperse red 1 (DR1) and PSDR1-50 means the same except for 50% substitution. PSDR1 has the second-order NLO property, which is expected to show an acentric ordering by poling electric field. We used a parametric optical constant model to estimate the complex refractive index of the polymers. We found that the poling induced the uniaxial property of the complex refractive index of the polymers by aligning the chromophores along the poling direction. With increased poling voltage, we found that the oscillator strength of the major peak near the 2.4eV (designated as Ea) peak decreases in the surface-parallel direction (x), whereas that of the surface-normal direction (z) increases. Moreover, a detailed analysis of the dielectric functions using the standard critical point model showed that the poling induced a new peak Ec (∼2.6eV) between dominant Ea (∼2.3eV) and weak Eb (∼2.9eV) peaks for PSDR1-50 polymers. With increased poling voltage, the Ec peak strength increased compared to those of Ea and Eb peaks. We tentatively attribute Ec to lower symmetry, possibly Stark effect, induced in the chromophores by the corona poling.

Optical Properties of Black NiO and CoO Single Crystals Studied with Spectroscopic Ellipsometry

Using spectroscopic ellipsometry, we measure the dielectric functions of NiO and CoO single crystals, which are grown by using the Verneuil (flame fusion) process. Taking the 2nd derivative of the dielectric function, we identify several optical structures below and near the band gap. We fit the 2nd derivative of the dielectric function by using an exciton lineshape and the standard critical point (SCP) model. The band gap energies of NiO and CoO are estimated to be 3.87 eV and 5.43 eV, respectively. The optical structures below and near the band gaps are attributed to intra-atomic d-d transitions and are estimated to be 1.2, 1.3, 1.8, 2.6, 2.9, 3.2, 3.4, 3.7, and 4.2 eV for NiO and 1.61, 2.26, 2.72, and 3.6 eV for CoO. Both the band gap and the d-d transition energies of NiO and CoO are compared to the literature values. The derivative spectra show unambiguously the d-d transitions near and above the band gap and those below the band gap. The lineshape fitting using the SCP model provides accurate values for the band gap energy and the d-d transitions. In addition, the SCP analysis verifies the exciton nature of the band gap and the d-d transitions. We attribute this to the formation of Frenkel excitons in NiO and CoO transition metal oxides.

Dielectric functions and electronic band structure of lead zirconate titanate thin films

We measure pseudodielectric functions in the visible-deep ultraviolet spectral range of Pb(ZrxTi1−x)O3 (x=0.2,0.56,0.82) (PZT), Pb0.98Nb0.04(Zr0.2Ti0.8)0.96O3, Pb0.91La0.09(Zr0.65Ti0.35)0.98O3, and Pb0.85La0.15Ti0.96O3 films grown on platinized silicon substrates using a sol-gel method and on (0001) sapphire using a radio-frequency sputtering method. Using a parametric optical constant model, we estimate the dielectric functions (ϵ) of the perovskite oxide thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard critical-point model, we determine the parameters of the critical points. In the second derivative spectra, the lowest band-gap energy peak near 4eV is fitted as a double peak for annealed PZTs due to the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest band-gap peak is fitted as a single peak. We also examine the effect of dopants La and Nb, which substitute at Pb and Zr (Ti) sites, respectively. We found three band gaps Ea(∼3.9eV), Eb(∼4.5eV), and Ec(∼6.5eV) in the order of increasing energy. The Ea and Eb band-gap energies were not sensitive to Zr composition. We discuss the change of critical-point parameters for PZTs in comparison to the band-structure calculations based on local-density approximation. The near constancy of the lowest band-gap energy independent of Zr composition is consistent with the band-structure calculations.

Visible-ultraviolet spectroscopic ellipsometry of lead zirconate titanate thin films

We measured pseudodielectric functions in the visible-ultraviolet spectral range of Pb(ZrxTi1−x)O3 (x=0.2, 0.56, 0.82) (PZT) grown on platinized silicon substrate using the sol-gel method and also on (0001) sapphire using radio frequency sputtering method. Using a parametric optical constant model, we estimated the dielectric functions of the PZT thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard critical point model, we determined the parameters of the critical points. In the second derivative spectra, the lowest bandgap energy peak near 4eV is fitted as a double peak for annealed PZTs associated with the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest bandgap is fitted as a single peak. We compared the bandgap energies with literature values.