Critical Point Energies Research Articles

Optical properties study of In.08Ga.92As/GaAs using spectral reflectance, photoreflectance and near-infrared Photoluminescence

Optical properties of In.08Ga.92As/GaAs structure grown by metalorganic vapor phase epitaxy have been investigated. Spectral reflectance (SR) and photoreflectance (PR) as well as near-infrared Photoluminescence (PL) were performed in this study. In fact, SR signals in the range 200–1700nm provided specific parameters of materials such as optical constant spectra, sensitivity to wavelength and critical point energies. In addition, band gap energy was determined by both PR and optical absorption measurements at room temperature. Spin-orbit splitting, internal electric field and electro-optical energy were also calculated. Results provided by previous techniques present a good correlation and complementarities and agree well with the literature. On the other hand, the origins of 12K PL peaks at 1.42, 1.38 and 1.29eV, have been identified by performing excitation power (Pex) study. Finally, the peak at 1.38eV has two regimes of variation with Pex separated by a critical power around 50mW.

Comprehensive investigations on DNa⋯A (D = H/F) complexes show why ‘sodium bonding’ is not commonly observed

A comprehensive study of D-Na⋯A (D=H/F) complexes has been done using advanced ab initio and atoms in molecule (AIM) theoretical analyses. The correlation between electron density at bond critical point and binding energy gives a distinguishing feature for hydrogen bonding, different from the ‘electrostatic complexes’ formed by LiD and NaD. Moreover, the LiD/NaD dimers have both linear and anti-parallel minima, as expected for electrostatic dipole–dipole interactions. The HF dimer has a quasi-linear minimum and the anti-parallel structure is a saddle point. Clearly, characterizing hydrogen bonding as ‘nothing but electrostatic interaction between two dipoles’ is grossly in error.

Interband transitions and dielectric functions of InGaSb alloys

We report pseudodielectric functions of In1−xGaxSb ternary alloy films from 1.5 to 6.0 eV determined by spectroscopic ellipsometry. Artifacts were minimized by real-time assessment of overlayer removal, leading to accurate representations of the bulk dielectric responses of these materials. Critical-point (CP) energies were obtained from numerically calculated second energy derivatives, and their Brillouin-zone origins identified by band-structure calculations. The E2′ and E2 + Δ2 CP energies cross with increasing In content as a result of increasing spin-orbit splitting Δ2.

Valence-band structure and critical point energies of diamond along [100

Valence-band structure and critical point energies of diamond along [100

Dielectric function of Cu(In, Ga)Se2-based polycrystalline materials

The dielectric functions of Cu(In, Ga)Se2(CIGS)-based polycrystalline layers with different Ga and Cu compositions have been determined by applying spectroscopic ellipsometry (SE) in a wide energy range of 0.7–6.5 eV. To suppress SE analysis errors induced by rough surface and compositional fluctuation, quite thin CIGS layers (<60 nm) with high uniformity toward the growth direction have been characterized using a self-consistent SE analysis method. We find that the optical model used in many previous studies is oversimplified particularly for the roughness/overlayer contribution, and all the artifacts arising from the simplified analysis have been removed almost completely in our approach. The CIGS dielectric functions with the variation of the Ga composition [x = Ga/(In + Ga)] revealed that (i) the whole CIGS dielectric function shifts toward higher energies with x, (ii) the band gap increases linearly with x without the band-gap bowing effect, and (iii) the overall absorption coefficients are significantly smaller than those reported earlier. Furthermore, the reduction of the Cu composition [y = Cu/(In + Ga)] leads to (i) the linear increase in the band-edge transition energy and (ii) the decrease in the absorption coefficient, due to the smaller interaction of the Cu 3d orbitals near the valence band maximum in the Cu-deficient layers. When y > 1, on the other hand, the free-carrier absorption increases drastically due to the formation of a semi-metallic CuxSe phase with a constant band gap in the CIGS component. In this study, by using a standard critical-point line-shape analysis, the critical point energies of the CIGS-based layers with different Ga and Cu compositions have been determined. Based on these results, we will discuss the optical transitions in CIGS-based polycrystalline materials.

A Model Dielectric Function for Graphene from the Infrared to the Ultraviolet

ABSTRACTA modified critical point model dielectric function for graphene is derived here and used to analyze spectroscopic ellipsometry data obtained over a wide spectral range from 3 to 9 eV. Critical point and exciton resonance energies are extracted and discussed. Our findings indicate that epitaxial graphene on SiC to exhibits equivalent exciton behavior to that of suspended graphene. We further apply our model dielectric function to evaluate dielectric function data for highly oriented pyrolytic graphite reported in the literature. Excellent agreement is found between the critical point model developed here and the literature data even for the low energy spectral range up to 1 eV.

Dielectric function spectra at 40 K and critical-point energies for CuIn0.7Ga0.3Se2

We report ellipsometrically determined dielectric function ε spectra for CuIn0.7Ga0.3Se2 thin film at 40 and 300 K. The data exhibit numerous spectral features associated with interband critical points (CPs) in the spectral range from 0.74 to 6.43 eV. The second-energy-derivatives of ε further reveal a total of twelve above-bandgap CP features, whose energies are obtained accurately by a standard lineshape analysis. The ε spectra determined by ellipsometry show a good agreement with the results of full-potential linearized augmented plane wave calculations. Probable electronic origins of the CP features observed are discussed.

Optical study of bulk and thin-film tin dioxide

We grew nano-crystalline SnO2 thin films on Si substrates by using RF magnetron sputtering deposition method. We examined the microstructure of the SnO2 thin films via X-ray diffraction (XRD) and the optical properties of the SnO2 thin films via photoluminescence (PL) spectroscopy and spectroscopic ellipsometry. We obtained the dielectric functions (e = e1 + ie2) of the SnO2 thin films in the visible to deep ultraviolet spectral range, as well as the anisotropic dielectric functions of the bulk SnO2 single crystal. The band edge blue shift and the larger peak maximum of e2z compared to those of e2x, in the directions parallel and perpendicular to the optical c-axis, respectively, are consistent with calculations found in the literature. We estimated the critical point energies by using the second derivatives of the dielectric functions with respect to energy, and the results matched well with the calculated band structures in the literature. We also found critical point energies in the experimental data which were forbidden by selection rules in the calculations. The PL study of the SnO2 thin films and bulk single crystals showed similar PL peaks associated with the band gap energy, suggesting that even the RT-grown thin film contained a very small number of crystalline nanograins even though the XRD spectra did not show any crystalline peaks.

An experimental and theoretical study on the reaction of Cl with CF3CF2CH2OH

An absolute kinetic study of the reaction of Cl atoms with CF3CF2CH2OH is reported as a function of temperature (T = 268–377 K) and at a total pressure of 100 Torr by the Pulsed Laser Photolysis - Resonance Fluorescence (PLP-RF) technique. No pressure dependence of the rate coefficient for the title reaction, k, was observed between 50 and 200 Torr of He at 298 K. The derived Arrhenius expression in that T-range was k(T) = (2.18 ± 0.24) × 10−12 exp(–(333 ± 34)/T) cm3 molecule−1 s−1, where the uncertainties are ±2σ. From these results, the average tropospheric lifetime of CF3CF2CH2OH due to the reaction with Cl was estimated to be 50 years, considering a global Cl concentration of 103 atom cm−3 and an average temperature of 272 K. Additionally, a theoretical study of the Cl + CF3CF2CH2OH reaction has been carried out by ab initio Möller–Plesset second-order perturbation treatment with 6-311G** basis set to investigate the reaction mechanism. Molecular energies of the different critical points of the potential energy surface have been calculated at QCISD(T) level. The theoretical study shows that the H-atom abstraction from the –CH2– group is the most favourable reaction pathway.

Dielectric functions and interband critical points of anisotropic chain structured TlSe single crystals

Spectroscopic ellipsometry measurements were carried out on TlSe single crystals for orientations of electric field, parallel (E∥c), and perpendicular (E⊥c) to optic axis c. The experiments were performed in the 1.2–6.2 eV spectral range at room temperature. The real and imaginary parts of the pseudodielectric function as well as pseudorefractive index and pseudoextinction coefficient were calculated from the analysis of ellipsometric data under the light of ambient-substrate optical model. The energies of interband transitions (critical points) have been found from the analysis on second derivative spectra of the pseudodielectric function. The analysis revealed four and five interband transition structures for E∥c and E⊥c configurations, respectively. The obtained critical point energies were assigned tentatively to interband transitions using the available electronic energy band structure given in literature.

Optical properties and electronic band structure of Cu2ZnSnSe4kesterite semiconductor

AbstractOptical properties of a kesterite‐type semiconductor Cu2ZnSnSe4 have been studied by optical absorption, spectroscopic ellipsometry, and thermoreflectance measurements. Optical absorption measurements suggest that Cu2ZnSnSe4 is a direct‐gap semiconductor having the band gap of ∼1.02 eV at 300 K. The complex dielectric‐function spectra, ϵ (E)=ϵ1(E)+iϵ2(E), measured by spectroscopic ellipsometry reveal distinct structures at energies of the critical points in the Brillouin zone. Thermoreflectance spectrum facilitates the precision determination of the critical point energy. By performing the band‐structure calculation, these critical points are successfully assigned to specific points in the Brillouin zone (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optical constants and interband transitions of anisotropic layered structured Tl2GaInS4 crystals by spectroscopic ellipsometry

Spectroscopic ellipsometry measurements were carried out on Tl2GaInS4 layered crystals for orientations of electric field vector, parallel (E//c∗) and perpendicular (E⊥c∗) to optical axis c∗. The measurements were performed in the 1.2–6.2eV spectral range at room temperature. The real and imaginary components of the pseudodielectric function, pseudorefractive index and pseudoextinction coefficient were calculated from the analysis of ellipsometric data. The energies of interband transitions (critical points) have been found from the least-square fitting of the second derivative spectra of the pseudodielectric function. The results indicated five each interband transition structures for E//c∗ and E⊥c∗ configurations. The obtained critical point energies were assigned tentatively to interband transitions using the available electronic energy band structure given in literature.

Interband transitions in gallium sulfide layered single crystals by ellipsometry measurements

Abstract Spectroscopic ellipsometry measurements on the GaS single crystals are presented in the energy range of 1.2−6.2 eV at room temperature. Optical constants; pseudorefractive index, pseudoextinction coefficient, real and imaginary parts of the pseudodielectric function were determined. Analysis of the second derivative of real and imaginary parts of the pseudodielectric constant revealed five transitions with critical point energies of 3.95, 4.22, 4.51, 4.75 and 5.50 eV. These energies were assigned to interband transitions according to theoretical study of GaS band structure available in literature.

Pseudodielectric function and critical-point energies of iron pyrite

Spectroscopic ellipsometry was used to determine the pseudodielectric function � e �=� e1 �+ i� e2� spectrum of a natural single crystal of iron pyrite (cubic FeS2) from 0.5 to 4.5 eV with the sample at 77 K. The � e� spectrum exhibits several pronounced optical features associated with the interband critical points (CPs). Accurate CP energies are obtained by fitting standard line shapes to second energy derivatives of the � e� data. The electronic origins of the six observed CP features are identified through density functional theory calculations and momentum matrix analyses.

Effects of stress on the dielectric function of strained pseudomorphic Si1−xGex alloys from 0 to 75% Ge grown on Si (001)

The dielectric function of bi-axially strained, intrinsic, and pseudomorphic Si1−xGex alloys was measured at room temperature using spectroscopic ellipsometry from 0.74 eV to 5.06 eV. Un-doped Si1−xGex with germanium compositions ranging from 0 to 75% was grown on Si (001) using chemical vapor deposition. High resolution x-ray diffraction was used to confirm sample composition, thickness, and strain. X-ray relaxation scans showed that all the samples were fully strained. All the alloy films in this study have low values of surface roughness, which allowed determination of the dielectric function. The presence of strain in the Si1−xGex alloys clearly altered the dielectric response. The bi-axial stress induced shift of the E1 and El + Δ1 critical point energies of pseudomorphic alloys can be described by the elastic response to the strain based on k*p theory [Lange et al., J. Appl. Phys. 80, 4578 (1996)]. Although the critical point energies of the alloys having higher germanium concentration showed deviations from the large shear approximation, the strain induced shift in critical point energy and the relative intensities of E1 and El + Δ1 were reasonably well described by the full elastic theory.

Investigation of InSb critical-point energies at 25 K by using spectroscopic ellipsometry

We report dielectric function data from 0.74 to 6.6 eV for InSb at 25 K obtained using spectroscopic ellipsometry. The values of the critical-point (CP) energies were determined from numerically calculated second energy derivatives of the data. The CP structures are blue shifted and significantly sharpened relative to those at room temperature (RT). The E1, E1 + Δ1, E′0, Δ5cu−Δ5vu, E′0 + Δ′0, and Δ5cl−Δ5vu CP structures are clearly observed at energies below 4 eV. We also report the E2, E′2, E2 + Δ2, E′2 + Δ2, E′1, E′1 + Δ′1, and E′1 + Δ′1 + Δ1 features in the E2−E′1 energy range of 4 to 6 eV. These cannot be resolved at RT, but are clearly separated at 25 K. In particular, several CPs in the E′2 and the E′1 + Δ′1 + Δ1 transitions have not previously been observed.

Spectroscopic ellipsometry study of above-band gap optical constants of layered structured TlGaSe2, TlGaS2 and TlInS2 single crystals

Spectroscopic ellipsometry measurements on TlGaSe2, TlGaS2 and TlInS2 layered crystals were carried out on the layer-plane (0 0 1) surfaces, which are perpendicular to the optic axis c⁎, in the 1.2–6.2 eV spectral range at room temperature. The real and imaginary parts of the pseudodielectric function as well as pseudorefractive index and pseudoextinction coefficient were found as a result of analysis of ellipsometric data. The structures of critical points in the above-band gap energy range have been characterized from the second derivative spectra of the pseudodielectric function. The analysis revealed four, five and three interband transition structures with critical point energies 2.75, 3.13, 3.72 and 4.45 eV (TlGaSe2), 3.03, 3.24, 3.53, 4.20 and 4.83 eV (TlGaS2), and 3.50, 3.85 and 4.50 eV (TlInS2). For TlGaSe2 crystals, the determined critical point energies were assigned tentatively to interband transitions using the available electronic energy band structure.

Temperature dependence of the dielectric function and critical-point energies of InAs

We report the complex dielectric function of InAs for energies from 0.74 to 6.54 eV and temperatures from 22 to 675 K. The complex dielectric function was determined by using spectroscopic ellipsometry. The critical-point (CP) structures at low temperatures are blue-shifted and are sharpened significantly relative to those observed at high temperatures, which can be explained by using the reduction of the electron-phonon interaction and the thermal expansion. The CP energies are determined by using lineshape fittings to numerically calculated second energy derivatives of the dielectric function. The obtained CP energies are fit to a phenomenological expression that contains the Bose-Einstein statistical factor and to a linear equation.

Ellipsometry study of interband transitions in TlGaS2xSe2(1−x) mixed crystals (0≤x≤1)

In this paper, the spectroscopic ellipsometry measurements on TlGaS2xSe2(1−x) mixed crystals (0≤x≤1) were carried out on the layer-plane (001) surfaces with light polarization E⊥c⁎ in the 1.2–6.2eV spectral range at room temperature. The real and imaginary parts of the dielectric function, refractive index and extinction coefficient were calculated from ellipsometric data using the ambient-substrate optical model. The critical point energies in the above-band gap energy range have been obtained from the second derivative spectra of the dielectric function. Particularly for TlGaSe2 crystals, the determined critical point energies were assigned tentatively to interband transitions using the available electronic energy band structure. The effect of the isomorphic anion substitution (sulfur for selenium) on critical point energies in TlGaS2xSe2(1−x) mixed crystals was established.

Complete parameterization of the dielectric function of microcrystalline silicon fabricated by plasma-enhanced chemical vapor deposition

The dielectric functions of microcrystalline silicon (μc-Si:H) layers deposited by plasma-enhanced chemical vapor deposition have been determined by applying real-time spectroscopic ellipsometry (SE) in an attempt to construct an optical database for μc-Si:H. The μc-Si:H dielectric functions have been parameterized completely by a dielectric function model that employs two Tauc-Lorentz peaks combined with one Harmonic oscillator peak. This parameterization scheme has been applied successfully to describe the structural variation from hydrogenated amorphous silicon (a-Si:H) to highly crystallized μc-Si:H. Moreover, to express the microstructure of μc-Si:H, the μc-Si:H structural factor κ has been defined based on the amplitude of the E2 optical transition with a critical point energy of 4.3 eV. From the value of κ, a variety of Si microstructures, including complete a-Si:H phase (κ = 0), μc-Si:H with a-Si:H-rich grain boundaries (κ ∼ 0.5), and μc-Si:H with void-rich grain boundaries (κ = 1), can be distinguished. The μc-Si:H structures estimated from the above SE analyses show excellent correlation with those deduced from the Raman spectroscopy. From the SE analysis procedure developed in this study, the layer thickness as well as the microstructure of μc-Si:H can be characterized rather easily.