Critical Point Energies Research Articles

Temperature Dependence of Optical Properties of MoS2 and WS2 Heterostructures Assessed by Spectroscopic Ellipsometry.

We report the complex dielectric function ε = ε1 + iε2 of MoS2/WS2 and WS2/MoS2 heterostructures and their constituent monolayers MoS2 and WS2 for an energy range from 1.5 to 6.0 eV and temperatures from 39 to 300 K. Comparisons between the optical properties of the heterostructures and their monolayers were conducted. Critical-point (CP) energies of the heterostructures were traced back to their origins in the monolayers. Low-temperature measurements confirmed the existence of only three excitonic CPs from 1.5 to 2.5 eV due to the overlap of trion B- of the MoS2 monolayer and exciton A0 of the WS2 monolayer. Due to the dielectric screening effect, most CPs exhibit red shifts in the heterostructures compared to their monolayer counterparts.

Lattice constant, bandgap energy, absorption coefficient and dielectric function of the antimony-rich InBixSb1-x alloy using first-principles calculations

So far, little is known about the electronic and optical properties of InBixSb1-x. In this work, the first-principles calculations are performed to research the lattice constant, the bandgap energy, the absorption coefficient and the dielectric function of the antimony-rich InBixSb1-x. The results show that the bowing coefficient for the lattice constant is merely −0.012 Å. According to the band structures, it is found that the Sb-rich InBixSb1-x possesses a direct bandgap at G point. Its bandgap reduction is due to the ascending of the valence band maximum (VBM) and the descending of the conduction band minimum (CBM). For the sake of providing a good description for the bandgap energy in the Sb-rich range, the modified valence band anticrossing (MVBAC) model plus a linear equation is utilized. The result shows that the predicted positive to negative bandgap transition occurs at x = 0.13. Besides, the valence band offset between InSb and InBi is identified to be 0.27eV. For the optical properties, it is found that the Bi component is effective in raising the static dielectric constant of InBixSb1-x. However, it has a minor effect on the transition ability of the electrons. In the Sb-rich component range, the critical point energies E0+Δ0E1, E1+Δ1E2 and E1′ are found to shift toward the low energy direction. The result of the absorption spectra supports this opinion as increasing Bi component leads to a redshift of the absorption spectra. The adjustable bandgap energy and the optical properties of InBixSb1-x demonstrate that it is a strong candidate for fabricating the photodetectors in the 8–12 μm spectral region.

Effects of applied pressure on structural, electronic, and optical properties of magnesium incorporated wurtzite beryllium oxide at different magnesium compositions

The effects of applied pressure on the structural, electronic, and optical properties of magnesium-incorporated wurtzite beryllium oxide (w-BeO) at different magnesium compositions are calculated. Each compound at different applied pressures confirms stability in the wurtzite phase. At different applied pressures, the equilibrium lattice constants (a0, c0) increase, but the bulk modulus (B0) and the c0/a0 ratio decrease with increasing magnesium composition. With increasing pressure, the lattice constants of each specimen decrease nonlinearly. Each compound possesses a wide direct band gap (Г-Г) at different applied pressures. The calculated band gap decreases with increasing magnesium composition at different applied pressures. With an increase in applied pressure, the band gap of each compound increases. Each wurtzite specimen is optically anisotropic and exhibits birefringence. Electronic excitations from O-2p to Be-2s, 3p and Mg-3s, 3p are responsible for the various optical features of the considered alloys. At different applied pressures, static optical constants ε1(0), n(0), and R(0) increase, but critical points in the ε2(ω), k(ω, σ(ω), and α(ω) spectra decrease with increasing magnesium composition. For each specimen, components of static optical constants reduce, while components of critical point energies increase with an increase in applied pressure.

Determination of the Complex Refractive Index of GaSb1−xBixby Variable‐Angle Spectroscopic Ellipsometry

Variable‐angle spectroscopic ellipsometry is used to determine the room temperature complex refractive index of molecular beam epitaxy grown GaSb1−xBixfilms withx ≤ 4.25% over a spectral range of 0.47–6.2 eV. By correlating to critical points in the extinction coefficientk, the energies of several interband transitions are extracted as functions of Bi content. The observed change in the fundamental bandgap energy (E0, −36.5 meV per %Bi) agrees well with previously published values; however, the samples examined here show a much more rapid increase in the spin‐orbit splitting energy (Δ0, +30.1 meV per Bi) than previous calculations have predicted. As in the related GaAsBi, the energy of transitions involving the top of the valence band are observed to have a much stronger dependence on Bi content than those that do not, suggesting the valence band maximum is most sensitive to Bi alloying. Finally, the effects of surface droplets on both the complex refractive index and the critical point energies are examined.

Interpretation of complex optical properties and optical transitions of epitaxial LaMnO3 thin films

An in-depth analysis of the optical properties of epitaxial (001) oriented LaMnO3films grown on SrTiO3and LaAlO3single crystal substrates is performed by spectroscopic ellipsometry to determine the complex dielectric function (ε = ε1 + iε2) spectra from 0.12 to 5.89 eV. Density Functional Theory and many body perturbation theory within the G0W0 and the Bethe-Salpeter Equation approximations, are also employed to generate theoretical spectra in ε. Critical point energies (CPs) from 0.91 to 1.49 eV are interpreted as energy separation between eg and t2g orbitals. CPs from 3.31 to 3.53 eV and 3.75 to 5.23 are interpreted as Mn d exchange splitting and strong charge transfer transitions, respectively. Direct and indirect bandgaps from Tauc-plots are identified in the range of 0.100–0.594 eV. Anisotropy presents in LaMnO3 on LaAlO3 is attributed to substantial distortion in the out-of-plane epitaxial strain compared to LaMnO3 on SrTiO3. These findings provide a comprehensive understanding of the origins and characteristics of features observed in optical properties of epitaxial LaMnO3, offering insights for development of optical and electronic applications based on these materials.

A Systematic Study of the Temperature Dependence of the Dielectric Function of GaSe Uniaxial Crystals from 27 to 300 K.

We report the temperature dependences of the dielectric function ε = ε1 + iε2 and critical point (CP) energies of the uniaxial crystal GaSe in the spectral energy region from 0.74 to 6.42 eV and at temperatures from 27 to 300 K using spectroscopic ellipsometry. The fundamental bandgap and strong exciton effect near 2.1 eV are detected only in the c-direction, which is perpendicular to the cleavage plane of the crystal. The temperature dependences of the CP energies were determined by fitting the data to the phenomenological expression that incorporates the Bose-Einstein statistical factor and the temperature coefficient to describe the electron-phonon interaction. To determine the origin of this anisotropy, we perform first-principles calculations using the mBJ method for bandgap correction. The results clearly demonstrate that the anisotropic dielectric characteristics can be directly attributed to the inherent anisotropy of p orbitals. More specifically, this prominent excitonic feature and fundamental bandgap are derived from the band-to-band transition between s and pz orbitals at the Γ-point.

Performance of machine learning algorithms in spectroscopic ellipsometry data analysis of ZnTiO3 nanocomposite

In this research, the optical properties of the PVP: ZnTiO3 nanocomposite are studied using the spectroscopic ellipsometry technique. The preparation procedure of the ZnTiO3 nanocomposite is explained in detail. The absorbance/transmittance, surface morphology, structural information, chemical identification, and surface topography of the ZnTiO3 nanocomposite is studied using UV–Vis spectroscopy, field-emission scanning electron microscopy, Raman spectroscopy, Fourier transform infra-red, and atomic force microscopy, respectively. The ellipsometry method is used to obtain the spectra of the real and imaginary parts of the dielectric function and refractive index in the photon energy range of 0.59–4.59 eV. Moreover, using two machine learning algorithms, namely artificial neural network and support vector regression methods, the ellipsometric parameters ψ and Δ are analyzed and compared with non-linear regression. The error and accuracy of each three methods, as well as the time required for their execution, are calculated to compare their suitability in the ellipsometric data analysis. Also, the absorption coefficient was used to determine the band gap energy of the ZnTiO3 nanocomposite, which is found to be 3.83 eV. The second-energy derivative of the dielectric function is utilized to identify six critical point energies of the prepared sample. Finally, the spectral-dependent optical loss function and optical conductivity of the ZnTiO3 nanocomposite are investigated.

Photoreflectance spectroscopy of BiOCl epitaxial thin films

We have observed a new optical transition in the photoreflectance spectra of indirect-gap BiOCl thin films, which were grown on SrTiO3 substrates. The position of this transition is close in energy to its bulk critical point (CP) energy. Moreover, these are significantly lower than a higher-lying direct-type CP from an energetic point of view. The spectral line shape analysis for our observed signal suggests the presence of an excitonic effect of this compound. We determined its dependence of the optical anomaly on temperature ranging from 80 K to RT. We adopted the Varshni model for this analysis. At last, we compared photonic properties of BiOCl with those of an element and binary semiconductors.

Analytical Determination of Irrotational Flow Profiles in Open-Channel Transitions

Transitional free surface flow profiles with a critical point occur with weak vorticity and viscosity effects and thus can be modeled with an irrotational flow approach. Important examples in hydraulic engineering include flow over low obstacles, transition structures in canals, and flow over high spillways. While solving Laplace’s equation is relatively simple, the determination of the unknown free surface and energy head of the flow is challenging. Both hydraulic quantities need to be iterated before solving the Laplace equation. Former models iterated the energy head on a trial-and-error basis, assuming that the linked free surface profile is smooth, i.e., free of waves. The iteration of the free surface for a given head is frequently accomplished using the Newton–Rapshon method, which is difficult for the challenging case of spillway flow, giving no solution in some cases. An alternative method of computing irrotational flow profiles in transitional flows involving a critical point is proposed in this work. The model contains three elements: mapping of Laplace’s equation to directly track the streamlines, determination of the critical point and unknown energy head using a critical flow condition for irrotational flows, and determination of the water surface position using an exact analytical solution. The proposed model is favorably compared with experimental data from different sources and CFD results, indicating a reasonable agreement.

Investigation of linear and nonlinear optical properties of PbWO4 single crystal

In this manuscript, PbWO4 single crystals having great importance for device applications were studied in terms of linear and nonlinear optical properties. For this purpose, transmission and reflection experiments were performed in the wavelength range of 350–1000 nm. X-ray diffraction analysis presented crystalline structure as scheelite type tetragonal. Spectral dependencies of absorption coefficient, skin depth, refractive index, dielectric function were reported. Optical band gap of the crystal was estimated as 3.25 eV from the Tauc and derivative spectral methods. Urbach, critical point, single oscillator and dispersion energies, static refractive index and dielectric constant were revealed for PbWO4 single crystal. First- and third-order nonlinear susceptibilities, and nonlinear refractive index were also computed for the studied crystal.

Photoreflectance system based on vacuum ultraviolet laser at 177.3 nm

Photoreflectance (PR) spectroscopy is a powerful and non-destructive experimental technique to explore interband transitions of semiconductors. In most PR systems, the photon energy of the pumping beam is usually chosen to be higher than the bandgap energy of the sample. To the best of our knowledge, the highest energy of pumping laser in reported PR systems is 5.08 eV (244 nm), not yet in the vacuum ultraviolet (VUV) region. In this work, we report the design and construction of a PR system pumped by VUV laser of 7.0 eV (177.3 nm). At the same time, dual-modulated technique is applied and a dual channel lock-in-amplifier is integrated into the system for efficient PR measurement. The system’s performance is verified by the PR spectroscopy measurement of well-studied semiconductors, which testifies its ability to probe critical-point energies of the electronic band in semiconductors from ultraviolet to near-infrared spectral region.

Optical properties of Sub-30 nm-thick ZnS films studied by spectroscopic ellipsometry

The sub-30 nm-thick ZnS thin films with different thicknesses were deposited on Si substrates by electron beam evaporation (EBE). The thickness and optical constants of ZnS films were obtained by fitting spectroscopic ellipsometry (SE) data using Tauc-Lorentz Model. The variation of refractive index, extinction coefficient, optical band gap, the complex dielectric function of the samples with film thickness was analyzed. Due to the increase of film density, the refractive index increases with the thickness, and the extinction coefficient has the same trend. Due to the quantum size effect, the optical band gap decreases from 3.56 eV to 3.23 eV with increasing film thickness. Two peaks (E0 and E1) are obtained from the complex dielectric function spectrum, which most likely corresponds to the central energy of the exciton optical transition. Three critical points (CP) energies (EA, EB, and EC) and the types of interband optical transitions were extracted from the standard linear analysis of the second-order derivatives of the dielectric function. The three CPs energies have a significant thickness dependence, which is mainly attributed to quantum size effects. This result is beneficial for the design and application of photonic and optoelectronic devices with sub-30 nm-thick ZnS films.

Determination of optical constants and scattering properties of transparent polymers for use in optoelectronics

Knowledge of optical constants, i.e. refractive index n and extinction coefficient k, and light scattering properties of optical polymers are required to optimize micro-optics for light-emitting diodes in terms of efficiency, color properties and light distribution. We present here a model-based diagnostic approach to determine the optical properties of polymers, which should be particularly useful in the development of plastics for optical applications. Optical constants and scattering coefficients were obtained from transmission and reflection measurements in a wavelength range from UV to NIR taking into account scattering effects due to rough surfaces and volume inhomogeneity. Based on the models for the dielectric function, the molecular optical transition energies Eg, critical point energies, Urbach energies and exciton transition energies were determined. Rayleigh and Mie scattering model and van de Hulst's anomalous diffraction theory were applied to characterize scattering due to volume inhomogeneities. Scalar diffraction theory was applied to account for surface roughness scattering. Atomic force microscopy with nanomechanical characterization was used to characterize domains in size and shape and to assign optical scattering to a suitable morphological model. The combined optical and mechanical characterization help to improve the qualification of new polymer materials for optical applications.

Characterization of In(Ga,Al)As/GaAs metamorphic heterostructures for mid-IR emitters by FTIR photoreflectance spectroscopy

Infrared photoreflectance (PR) spectra of In(Ga,Al)As/GaAs metamorphic heterostructures have been obtained using a novel photomodulation FTIR spectroscopy technique. An analysis of the PR spectra features allowed us to estimate the critical point energies corresponding to the direct interband transitions in various regions of the In(Ga,Al)As heterostructures, and distinguish the PR signals originating from Fabry-Perot interference. Observation of Franz-Keldysh oscillations originating from the InAlAs virtual substrate and an InGaAs waveguide layer has enabled determination of the built-in electric field intensities within the heterostructures. The obtained results open up possibilities for contactless control of free carrier concentration in In(Ga,Al)As/GaAs metamorphic heterostructures developed for growth of emitters of mid-IR spectral range.

Pressure induced structural, electronic and optical properties of wurtzite beryllium monoxide (w-BeO) from first-principle calculations

All-electron density functional calculations of structural, electronic and optical properties of wutrzite beryllium oxide (w-BeO) are carried out at different applied hydrostatic pressure. Calculated lattice constants decrease (a, c), while bulk modulus increases with increasing pressure. Direct fundamental band-gap (Eg) of w-BeO increases with increasing pressure and vice versa and the variation provides first and second order pressure coefficient of band-gap. The calculated volume deformation potential of band-gap of w-BeO is −11.5972 eV. Optical properties of w-BeO at zero and high pressures have been studied in terms of dielectric function ε(ω) and related ancillary optical parameters. Each optical parameter is marginally anisotropic. Calculated components of refractive index at each pressure signify uniaxial characteristics of the w-BeO. Calculated components of static dielectric constant, refractive index and reflectivity decreases, while critical point energy in the spectra of each component of ε2(ω), k(ω), σ(ω) and α(ω) increases with increasing pressure and vice versa. Calculated optical energy-gap (Eopt) of w-BeO increases like Eg with increasing pressure and vice versa. The transmission cutoff energy (ECutoff) is shifted towards the higher energy region with increasing pressure.

Band structure critical point energy in germanium–tin alloys with high tin contents

The dielectric functions of germanium–tin alloy thin-films, deposited by molecular beam epitaxy on bulk Ge substrates, with relatively high Sn contents from 15 to 27 at. %, were measured by variable angle spectroscopic ellipsometry over the wavelength range from 0.190 to 6 μm, using a combination of ultraviolet-visible and infrared ellipsometers. The band structure critical point energies, specifically the E1 and E1 + Δ1 optical transitions, were extracted from the measurements by a method of parametric oscillator modeling and second derivative analysis. With increasing Sn content, the transitions shifted to lower energies, and for alloys with less than 20% Sn, the numerical values agreed reasonably with predictions based on deformation potential theory that accounted for film strain. For the higher Sn alloys, the critical point energies from measurements agreed less well with deformation potential theory. These results provide information on the band structure of GeSn alloys with high Sn contents, which are increasingly important for long-wave infrared devices and applications.

Optical properties of freestanding GaN nanomembranes using monochromated valence-EELS

In the present study, the dielectric function of freestanding GaN nanomembranes was described using valence electron energy loss spectroscopy coupled to a monochromated electron probe in a Sub-Electron-volt Sub-Angstrom transmission electron Microscope. Such a technique has proven to be very efficient in handling nanometer-scale freestanding nanomembranes and provided local and direct measurements of optical characteristics. Indeed, core-state along with outer-shell electrons transitions were first measured in the configuration where the GaN c→-axis was normal to the transferred momentum q→. With the help of Kramers-Kroning analyses and density functional theory, critical points energies were extracted and assigned. Finally, optical data such as the real refractive index n, extinction coefficient k, absorption coefficient α and reflectivity R were numerically deduced from the real and imaginary parts of the dielectric function.

Effect of thallium (Tl) substitution for indium (In) on ellipsometric characteristics of TlInSe2 single crystals

TlMeSe2 (Me: Tl, In) semiconducting compounds exhibiting chain structure have been attractive ternary materials in various technological devices. In the TlMeSe2 structure, Tl1+ is monovalent while Me3+ is trivalent ions. The present paper reports the results of spectroscopic ellipsometry measurements performed on Tl1+(Tl0.2In0.8)3+Se2 (abbreviated as Tl1.2In0.8Se2) single crystals which were grown by substituting thallium for indium. The measurements were performed for orientations of E//c and E丄c (E: electric field and c: optical axis). The analyses of ellipsometry data considering air-sample optical model presented the spectral dependencies of dielectric function, refractive index and extinction coefficient in the 1.2–5.0 eV range. Critical point energies of studied single crystal were obtained by fitting second-energy derivative spectra of dielectric function. The determined energies were compared with those of TlInSe2 to understand the effect of thallium-indium substitution in the compound. The crystal structure and atomic compositions of the constituent elements were also reported throughout the paper.

A Systematic Study of Compositionally Dependent Dielectric Tensors of SnSxSe1-x Alloys by Spectroscopic Ellipsometry

We report the dielectric tensors on the cleavage plane of biaxial SnSxSe1-x alloys in the spectral energy region from 0.74 to 6.42 eV obtained by spectroscopic ellipsometry. Single-crystal SnSxSe1-x alloys were grown by the temperature-gradient method. Strongly anisotropic optical responses are observed along the different principal axes. An approximate solution yields the anisotropic dielectric functions along the zigzag (a-axis) and armchair (b-axis) directions. The critical point (CP) energies of SnSxSe1-x alloys are obtained by analyzing numerically calculated second derivatives, and their physical origins are identified by energy band structure. Blue shifts of the CPs are observed with increasing S composition. The fundamental bandgap for Se = 0.8 and 1 in the armchair axis arises from band-to-band transitions at the M0 minimum point instead of the M1 saddle point as in SnS. These optical data will be useful for designing optoelectronic devices based on SnSxSe1-x alloys.

Band gap and emission wavelength tuning of Sr-doped BaTiO3 (BST) perovskites for high-efficiency visible-light emitters and solar cells

A numerical full-potential linearized augmented plane method within density functional theory is performed to study the electronic structure include, energy band gap, total and partial density of states and chemical bonding as well as optical constants of Ba1−xSrxTiO3 (BST) (0≤ x ≤ 1) crystalizes in the paraelectric and ferroelectric phases. Results obtained using the improved [Koller-Tran-Blaha]-mBJ potential show excellent agreement with the experimental data. It is observed that the band gap in BST crystals increases with increasing Sr dopants due to the resonant interaction of O_2p orbitals mixed with co-doping Sr_4d states with the top of the valence band. BST exhibits a direct band gap at x range ~0.04–0.88 covering the wavelengths range ~397–436 nm within the visible spectrum region. The dielectric functions and optical constants such as refractive index, reflectivity and absorption coefficient are computed for radiation range 0–10 eV in comparison with measured data. The critical-point energies in various optical spectra are due to interband transitions from occupied O_2p states and little admixture of Sr_4p/d and Ba_4p orbitals localize in the top of the valence band to unoccupied Ti_3d, Sr_4p, and Ba_4d orbitals localize in the bottom of the conduction band. Excellent ultraviolet absorption (~4–8 eV) and visible regime transparency are achieved. BaSrTiO3 (BST) perovskite is a promising candidate for manufacturing low-cost high-efficiency solar cells and designing of novel sources of light operating in the visible spectrum region.