Interband Transition Strength Research Articles

Electronic states and oscillator strengths for interband transitions of a graded quantum dot quantum well structure

A theoretical study of electron and hole electronic states and oscillator strength of interband transitions in a graded spherical HgS/CdS/HgS/CdS quantum dot quantum well (QDQW) nanostructure is presented; also the Coulomb interaction energies of excitons are calculated. The Finite Element Method (FEM) is used for solving the problem with the position dependent effective mass approximation. The results of calculations show that gradation of the potential decreases energies of confined particles and considerably reduces the oscillator strength for certain transitions. The gradation of the potential can be used as an additional parameter for experimental purposes to manipulate needed properties of the QDQW structure.

Optical Properties of Hexagonal and Cubic ZnS Nanoribbons: Experiment and Theory

Optical properties of hexagonal and cubic ZnS nanoribbons are studied by using valence electron energy loss spectroscopy (VEELS) and ab initio band structure calculations. The peaks in VEELS are assigned to interband transitions by comparing the interband transition strengths with the calculated densities of states. The optical properties are deduced from the experimental VEELS, and the theoretical calculations give consistent results. This combination of experimental and theoretical approaches provides a comprehensive understanding of the optical properties of polytype ZnS.

Determination of complex dielectric functions at HfO2/Si interface by using STEM-VEELS

The complex dielectric functions and refractive index of atomic layer deposited HfO2 were determined by the line scan method of the valence electron energy loss spectrum (VEELS) in a scanning transmission electron microscope (STEM). The complex dielectric functions and dielectric constant of monoclinic HfO2 were calculated by the density functional theory (DFT) method. The resulting two dielectric functions were relatively well matched. On the other hand, the refractive index of HfO2 was measured as 2.18 by VEELS analysis and 2.1 by DFT calculation. The electronic structure of HfO2 was revealed by the comparison of the inter-band transition strength, obtained by STEM-VEELS, with the density of states (DOS) calculated by DFT calculation.

Enhanced oscillator strength of interband transitions in coupled Ge∕Si quantum dots

We report a calculation of oscillator strength for the Δ1−Γ25′ interband transition in two vertically coupled pyramidal Ge quantum dots embedded in Si. A six-band k⋅p formalism was used to study the Γ25′ hole states, and a single-band approach was used to obtain the Δ1 electron state interacting with the hole. The elastic strain due to the lattice mismatch between Ge and Si was included into the problem via the Bir–Pikus Hamiltonian. We find that when two dots are brought closely together, the oscillator strength may enlarge by a factor of about 2 as compared to the single-dot system.

Valley-dependent optoelectronics from inversion symmetry breaking

Inversion symmetry breaking allows contrasted circular dichroism in different $k$-space regions, which takes the extreme form of optical selection rules for interband transitions at high symmetry points. In materials where band edges occur at noncentral valleys, this enables valley-dependent interplay of electrons with light of different circular polarizations, in analogy to spin dependent optical activities in semiconductors. This discovery is in perfect harmony with the previous finding of valley contrasted Bloch band features of orbital magnetic moment and Berry curvatures from inversion symmetry breaking [D. Xiao, W. Yao, and Q. Niu, Phys. Rev. Lett. 99, 236809 (2007)]. A universal connection is revealed between the $k$-resolved optical oscillator strength of interband transitions, the orbital magnetic moment and the Berry curvatures, which also provides a principle for optical measurement of orbital magnetization and intrinsic anomalous Hall conductivity in ferromagnetic systems. The general physics is demonstrated in graphene where inversion symmetry breaking leads to valley contrasted optical selection rule for interband transitions. We discuss graphene based valley optoelectronics applications where light polarization information can be interconverted with electronic information.

Electronic and optical properties of Cd1-xZnxS nanocrystals

We report a numerical simulation of the conduction and valence band edges of Cd1-xZnxS nanocrystallites using a one — dimensional potential model. Electron — hole pairs are assumed to be confined in nanospheres of finite barrier heights. Optical absorption measurements are used to fit the bandgap of the Cd1-xZnxS nanocrystal material. A theoretical analysis is also made to calculate the energy location of bound excitons and the oscillator strength of interband transitions as a function of zinc composition. The aim of the latter study is to investigate the optical behavior of Cd1-xZnxS nanocrystals. An attempt to explain all the results is presented.

Optical properties, electronic structure and London dispersion interactions for nanostructured interfacial and surficial films

Nanostructured amorphous films exhibit complex thermodynamic and kinetic behavior. To understand the structure and properties of nanostructured amorphous films in silicon based ceramics (Si 3N 4, SiC, Si) and in SrTiO 3 ceramics, we have focused on experimental studies to determine the interband electronic structure and optical properties. We use vacuum ultraviolet spectroscopy for bulk materials, and valence electron energy loss spectroscopy (VEELS) in either transmission mode in the transmission electron microscope for interfacial films, and are developing VEELS in reflection mode for surficial films. These experimental data are quantitatively analyzed using Kramers–Kronig analysis to determine the complex optical properties of the constituent materials. This interband electronic structure information is the fundamental input to determine from Lifshitz theory the London dispersion interaction in these low-dimensional systems. We present interband transition strengths of AlPO 4, SiO 2 and rare-earth doped MgSiON glasses, and also of SiC and SrTiO 3 and their grain boundaries. We use a new multilayer approach to produce graded interface models for the London dispersion interaction in complex nanostructured interfacial and surficial films.

Optical properties and London dispersion interaction of amorphous and crystallineSiO2determined by vacuum ultraviolet spectroscopy and spectroscopic ellipsometry

The interband optical properties of crystalline (quartz) and amorphous ${\mathrm{SiO}}_{2}$ in the vacuum ultraviolet (VUV) region have been investigated using combined spectroscopic ellipsometry and VUV spectroscopy. Over the range of 1.5--42 eV the optical properties exhibit similar exciton and interband transitions, with crystalline ${\mathrm{SiO}}_{2}$ exhibiting larger transition strengths and index of refraction. Crystalline ${\mathrm{SiO}}_{2}$ has more sharp features in the interband transition strength spectrum than amorphous ${\mathrm{SiO}}_{2}$, the energy of the absorption edge for crystalline ${\mathrm{SiO}}_{2}$ is about 1 eV higher than that for amorphous ${\mathrm{SiO}}_{2}$, and the direct band-gap energies for $X$-cut and $Z$-cut quartz are 8.30 and 8.29 eV within the absorption coefficient range $2\text{--}20\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. In crystalline ${\mathrm{SiO}}_{2}$ we report different interband transition peaks at 16.2, 20.1, 21, 22.6, and 27.5 eV, which are in addition to those lower energy transitions previously reported at 10.4, 11.6, 14, and 17.1 eV. We find the bulk plasmon energy in $X$- and $Z$-cut crystalline quartz and amorphous ${\mathrm{SiO}}_{2}$ to be at 24.6, 25.2, and 23.7 eV, respectively. The oscillator strength $(f)$ sum rules of the interband transitions for crystalline ${\mathrm{SiO}}_{2}$ is 10--10.8 electrons per formula unit for transition energies up to 45 eV. These differences in the electronic structure and optical properties, and the physical densities of crystalline and amorphous ${\mathrm{SiO}}_{2}$, can be attributed to differences in the intermediate-range order (IRO) and long-range order (LRO) of the different forms of ${\mathrm{SiO}}_{2}$. The intimate relationship between the electronic structure and optical properties and the London dispersion interaction has attracted increased interest recently, and the role of amorphous silica and other structural glass formers as a fluid in high-temperature wetting and materials processes means a detailed knowledge of the optical properties and London dispersion interaction in ${\mathrm{SiO}}_{2}$ is important. Hamaker constants for the London dispersion interaction of the configuration of two layers of $c\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ or $a\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ separated by an interlayer film have been determined, using full spectral methods, from the interband transition strength. The London dispersion interaction is appreciably larger in $c\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ than $a\text{\ensuremath{-}}{\mathrm{SiO}}_{2}$ due to the increased physical density, index of refraction, transition strengths, and oscillator strengths in quartz.

Low electron energy-loss spectroscopy study of the electronic structure of matrix and Σ19, Σ13 boundaries in SrTiO3

The dielectric properties of the bulk and at two grain boundaries of commercial SrTiO3 polycrystals have been determined by analysing the low loss region of the electron energy loss spectrum in a transmission electron microscope. For this purpose, we have made use of field emission scanning transmission electron microscopes equipped with electron energy loss spectroscopy systems which provide subnanometre electron probes and offer energy resolutions of 0.3 eV and 0.7 eV, respectively. In this paper we calculate the dielectric function by a Kramers–Kronig transformation and also the interband transition strength. The interband transitions arise from maxima in the valence-band density of states. These transition calculations compare well with published optical data and theoretical calculations. The JDOS of the boundaries is obviously and reproducibly different from that in the bulk.

Kramers–Kronig transform for the surface energy loss function

A new pair of Kramers–Kronig (KK) dispersion relationships for the transformation of surface energy loss function Im[−1/( ɛ + 1)] has been proposed. The validity of the new surface KK transform is confirmed, using both a Lorentz oscillator model and the surface energy loss functions determined from the experimental complex dielectric function of SrTiO 3 and tungsten metal. The interband transition strength spectra ( J cv) have been derived either directly from the original complex dielectric function or from the derived dielectric function obtained from the KK transform of the surface energy loss function. The original J cv trace and post- J cv trace overlapped together for the three modes, indicating that the new surface Kramers–Kronig dispersion relationship is valid for the surface energy loss function.

Insights into the Electronic Structure of Ceramics through Quantitative Analysis of Valence Electron Energy-loss Spectroscopy.

Valence electron energy-loss (VEEL) spectroscopy was performed on six ceramic materials in a dedicated scanning transmission electron microscope (STEM). Quantitative analysis of these data is described yielding access to the complex optical properties and the electronic structure of the materials. Comparisons are made on the basis of the interband transition strength describing transitions between occupied states in the valence band and empty states in the conduction band. This proves that the quantitative analysis of VEEL data is a competitive and complementary method to be considered when investigating the electronic structure of materials. Possibilities for improvement and extension of the analysis are discussed extensively.

Detailed spectroscopy of the chiral-twin candidate bands in136Pm

The chiral-twin candidate bands recently observed in 136Pm have been extended to high spins [I=(21)] using the Gammasphere γ-ray spectrometer and the Microball charged-particle detector array. A more-detailed spectroscopy of the bands was possible, where the rotational alignments and B(M1)/B(E2) ratios confirm that both sequences have the πh11/2νh11/2 configuration. Particle-rotor calculations of intraband and interband transition strength ratios of the chiral-twin bands are compared with experimental values for the first time. Good agreement was found between the predicted transition strength ratios and the experimental values, thus supporting the possible chiral nature of the πh11/2νh11/2 configuration in 136Pm.Received 22 May 2001DOI:https://doi.org/10.1103/PhysRevC.64.031304©2001 American Physical Society

Valence electron energy loss study of Fe-doped SrTiO 3 and a Σ13 boundary: electronic structure and dispersion forces

Valence electron energy loss spectroscopy in a dedicated scanning transmission electron microscope has been used to obtain the interband transition strength of a Σ13 tilt grain boundary in SrTiO 3. In a first step the electronic structure of bulk SrTiO 3 has been analysed quantitatively by comparing VEELS spectra with vacuum ultraviolet spectra and with ab initio density of states calculations. The electronic structure of a near Σ13 grain boundary and the corresponding dispersion forces were then determined by spatially resolved VEELS. Also the effects of delocalization of the inelastic scattering processes were estimated and compared with results from the literature.

Insights into the Electronic Structure of Ceramics through Quantitative Analysis of Valence Electron Energy-loss Spectroscopy

AbstractValence electron energy-loss (VEEL) spectroscopy was performed on six ceramic materials in a dedicated scanning transmission electron microscope (STEM). Quantitative analysis of these data is described yielding access to the complex optical properties and the electronic structure of the materials. Comparisons are made on the basis of the interband transition strength describing transitions between occupied states in the valence band and empty states in the conduction band. This proves that the quantitative analysis of VEEL data is a competitive and complementary method to be considered when investigating the electronic structure of materials. Possibilities for improvement and extension of the analysis are discussed extensively.

TE- and TM-polarized optoelectronic properties of HgCdTe quantum wells

A systematic investigation of the strength of TE-polarized and TM-polarized intersubband and interband transitions in narrow-gap HgCdTe quantum wells is performed using an eight-band finite-element k·p formalism. Effects of varying the well composition, well width, and applied electric field are explored for both polarizations, and the possibility of fabricating low-threshold quantum cascade lasers using this system is pointed out. Especially promising are the prospects for optically-pumped terahertz lasers based on interband transitions. Lasers emitting in the 30–45 µm wavelength range (falling in the phonon bands of III–V quantum wells), are projected to operate above liquid-nitrogen temperature.

Variable optical absorption edge in ion beam sputtered thin ytterbium oxide films

Thin films of ytterbium oxide have been deposited by ion beam sputtering from the oxide target on to fused silica substrates. The films that were in the thickness range 50 to 150 nm were characterised for spectral transmittance and reflectance and the refractive index, extinction coefficient and optical absorption edge. It is demonstrated that all these quantities are extremely sensitive to variation in thickness of the films. The refractive index increases with thickness while the extinction coefficient decreases with increase in thickness. The thickest films (∼150 nm) have a refractive index of 1.75 at 600 nm which decreases to 1.55 for the 50 nm thick film. Most significantly the optical absorption edge varies from 4.85 to 4.63 eV over the same range of thickness. The observed behaviour has been fitted in to the single effective oscillator model and it is shown that this model predicts an increase in absorption edge with decreasing thickness. It is also shown, based on this model, that the variation in refractive index and absorption edge are inter-related. The dispersion energy, which is a measure of the strength of interband transitions increases with increase in thickness.

Optical Properties of Aluminum Oxide: Determined from Vacuum Ultraviolet and Electron Energy‐Loss Spectroscopies

The optical properties of alpha‐Al2O3 have been determined by two independent methods, vacuum ultraviolet (VUV) spectroscopy and electron energy‐loss spectroscopy (EELS) over the energy range from 6 to 142 eV. For each experimental method two sets of high‐quality data have been measured and analyzed from alpha‐Al2O3. The evolution of the differences between the data for each experimental method and its associated analytical method indicate the reliability of the results, and the comparison between the methods emphasizes the relative advantages of each. VUV spectroscopy offers a higher energy resolution, resolving sharper features in the spectra, whereas EELS significantly extends the energy range, which has been exploited here to 140 eV but can be extended even further. Good overall consistency is found, but there are pronounced differences in the valence region from 10 to 30 eV, where strong absorptions are present, increasing the relative variability of the analysis. This demonstrates that accuracy estimates of the optical properties are meaningful only when supplied as a function of energy, because both strong intrinsic absorptions and weak experimental signals make accurate determinations difficult. Moreover, variations in the optical properties are observed most easily in the interband transition strength, Jcv, and are less evident when the optical properties are represented as the complex index of refraction. Because the optical properties can change with specimen origin and preparation and because of the details of data acquisition and numerical analysis procedures, assessing the contributions of each of these methods to our accurate knowledge of the optical constants is essential.

Quantitative analysis of valence electron energy-loss spectra of aluminium nitride.

The optical properties and electronic structure of aluminium nitride are determined using valence electron energy-loss spectroscopy in a dedicated scanning transmission electron microscope. Quantitative analysis of the experimental valence electron energy-loss spectra to determine the electronic structure encompasses single scattering deconvolution of the valence electron energy-loss spectra to calculate the energy-loss function, Kramers-Kronig analysis of the energy-loss function to reveal the complex dielectric function, transformation of the dielectric function into the optical interband transition strength via optical property relations and finally critical-point analysis of the interband transition strength. The influence of both experimental and analytical parameters on the final result was studied systematically to define and improve the understanding of the methods. To check the reliability of this technique the interband transition strength determined was compared with results of vacuum ultraviolet spectroscopy. Good agreement was found if sample preparation was taken into account. The preparation of the specimen for the transmission electron microscopy has an effect on the electronic structure. Quantitative analysis of valence electron energy-loss spectroscopy, using the methods presented, is an important and capable method to determine the electronic structure of materials and it has the benefit of high spatial resolution.

Dispersion forces and Hamaker constants for intergranular films in silicon nitride from spatially resolved-valence electron energy loss spectrum imaging

The van der Waals (vdW) dispersion forces represent one of the fundamental long range interfacial and surface forces in materials. The dispersion forces, for a set of materials in close proximity, arise from the electronic structure of the materials wherein the electrons in interatomic bonds acting as oscillating dipoles exhibit an attractive interaction energy. These vdW dispersion forces, represented by a proportionality constant, the full spectral Hamaker constant (A), can be calculated directly from optical property based electronic structure spectra such as the interband transition strength (Jcv) using the Lifshitz theory. Si3N4 exhibits equilibrium intergranular films (IGFs) whose thickness is determined by a force balance where the contribution of the van der Waals dispersion force is dictated by the IGF chemistry. Using spatially resolved-valence electron energy loss (SR-VEEL) spectroscopy in the STEM with a 0.6 nm probe permits the in situ determination of vdW forces on the IGFs in viscous sintered polycrystalline systems. In addition local variations in IGF chemistry and dispersion forces throughout the microstructure of individual silicon nitride samples can be determined using these methods. From multiplexed zero loss/plasmon loss optimized SR-VEEL spectra across IGFs with subsequent single scattering deconvolution, Kramers Kronig analysis and London dispersion analysis, the index of refraction and Hamaker constants can be determined. The method proved to be accurate and reproducible with comparison to VUV measurements for the bulk materials and repeated measurements on numerous individual IGFs. For these optimized Si3N4 materials, the dispersion forces varied over a range from 2 to 12 zJ. These showed standard deviations on the order of 1 zJ for systems with IGFs. Additional systematic errors can not be excluded. Local variations in Hamaker constants within the microstructure of a single sample correlate to the distribution of IGF thicknesses observed i.e. the thickness varies inversely with Hamaker constant. The technique of measuring Hamaker constants in situ represents an important new tool for dispersion force and wetting studies. For the first time it is observed that the thickness of the IGF scales with the local Hamaker constant of the investigated grain boundary region.

Critical point analysis of the interband transition strength of electrons

Optical and electron-energy-loss spectroscopies are well established methods of probing the electronic structure of materials. Comparison of experimental spectroscopic results with theory is complicated by the fact that the experiments extract information about the interband transition strength of electrons, whereas theoretical calculations provide information about individual valence and conduction bands. Based on the observation that prominent features in the optical response arise from critical points in the joint density of states, critical point modelling was developed to gain an understanding of these spectral features in terms of specific critical points in the band structure. These models were usually applied to derivative spectra and restricted to the consideration of isolated critical points. The authors present a new approach to critical point modelling of the undifferentiated spectra and interpret the model in terms of balanced sets of critical points which describe the interband transition strength arising from individual pairings of valence and conduction bands. This approach is then applied to achieve a direct, quantitative comparison of theoretical and experimental data on aluminium nitride.