Roger H. French

Bulk electronic structure of SrTiO3: Experiment and theory

Valence electron-energy loss spectroscopy (VEELS) in a dedicated scanning transmission electron microscope, vacuum ultraviolet spectroscopy and spectroscopic ellipsometry, and ab initio band structure calculations in the local density approximation have been used to determine the optical properties and the electronic structure of SrTiO3. Assignments of the interband transitions in the electronic structure of bulk SrTiO3 have been determined quantitatively by comparison of VEELS spectra with vacuum ultraviolet spectra and with the ab initio calculated densities of states. The experimentally determined indirect band gap energy is 3.25 eV, while the direct band gap energy is 3.75 eV. The conduction bands in SrTiO3 correspond to the bands composed of mainly Ti 3d t2g and eg states, followed at higher energies by the bands of Sr 4d t2g and eg states, and free electron like states dominating at energies above 15 eV. The upper valence band (UVB) contains 18 electrons in dominantly O 2p states, hybridized with Ti and Sr states, and has a bandwidth of 5 eV. The interband transitions from the UVB to the Ti 3d bands and to the Sr 4d bands give rise to the transitions spanning from the indirect band gap energy of 3.25 eV up to 15 eV. The lower valence band contains 12 electrons in Sr 4p and O 2s states which are separated by 2 eV, while having a bandwidth of 5 eV. The interband transitions from the Sr 4p to the Ti 3d and Sr 4d bands give rise to transition energies spanning from 15 to 24 eV. Interband transitions from the O 2s band to the conduction bands appear at 26 eV. A very narrow band at −33 eV below the top of the valence band is composed of Sr 4s and Ti 3p states and contains eight electrons.

Full spectral calculation of non-retarded Hamaker constants for ceramic systems from interband transition strengths

Abstract The van der Waals (vdW) interaction is one of the key terms in the force balances dictating wetting behavior and intergranular film thicknesses. The characteristics of thin intergranular or surficial glass films are of increasing importance due to their role in determining the properties of polycrystalline ceramics. The Hamaker constant scales the London dispersion force part of the vdW interaction for a particular configuration of grains and films and is a direct function of the interband optical properties of the interatomic bonds of the materials. For ceramics, much previous work focused on simplified models, such as the Tabor-Winterton approximation (TWA), to determine Hamaker constants based on refractive indices. Herein we develop full spectral calculations of the Hamaker constants for various ceramic systems using experimentally determined interband transition strengths (ĵcv(ω)) to directly derive the London dispersion spectra (e2(ξ)) from which spectral difference functions lead to direct determination of the Hamaker constants. The results affirm the expectation that transitions involving valence electrons provide the predominant contribution to the dispersion forces for the compounds examined. Calculations have been done for the planar case of a gap between two semi-infinite bodies containing either vacuum or an intervening glassy layer. The results indicate that the TWA is useful for oxides with relatively low refractive indices, i.e., n ~ 1.4–;1.8. However, when any of the materials have larger indices, this approximation becomes inexact, and no obvious, simple correction to the TWA gives uniformly good results, as the behavior differs for simple covalent materials and for oxides with partially filled d-shells but having similar refractive indices. An important consequence is that Hamaker constants are smaller for such high index materials, especially oxides, with intervening glassy films than might be expected from approximations. Calculations have also been done for two other geometries, i.e., for an intervening film with a layer of a third material at both interfaces and for glass coated free surfaces. The former of these provides first insights regarding the behavior with nonuniform films which often differs markedly from that expected for homogeneous films of the same average composition.

Temperature dependence of the electronic structure of oxides : MgO, MgAl2O4 and Al2O3

We have studied the room temperature optical reflectivity of MgO, MgAl2O4, and α-Al2O3 from 5 to 40eV using a novel spectrophotometer with a laser plasma light source. Structure in the imaginary component of the dielectric response is analysed using critical point line shapes, and the origins of the major transitions in MgO and MgAl2O4 are determined using an ab initio pseudofunction band structure calculation of MgO. The exciton reflectivity has been studied in the three materials at temperatures between 300 and 1500 K, and exciton-phonon coupling appears to increase from MgO to α-Al2O3. The temperature dependence of the higher lying interband transitions in MgO has been determined to 1100 K, and we find that while the temperature dependence of the onset transitions at Γ and X are nearly identical (− 1.22meV/K at Γ), higher lying transitions have very different temperature dependences. Furthermore with increasing temperature the X point valence band separation increases at a rate of 0.38meV/K, while the conduction band separation at X decreases at −0.41meV/K.

Multiple scattering from rutile TiO2 particles

The physical properties of rutile titania (TiO 2) have led to its wide use as a white pigment in many applications. The success of these applications depends not only on the optical properties of the bulk material, but also on subtle aspects of the scattering of light from collections of small TiO 2 particles embedded in a transparent medium. We consider here the problem of multiple scattering in dense systems containing particles of a size comparable to the wavelength. Our method of analysis allowed us to understand the effects that the number density of particles and the particle size distribution have on the measured diffuse reflectance of such films. We apply this analysis to films of TiO 2 particles in a transparent medium. We present the results of diffuse reflectance and transmittance measurements in the visible range of films with concentrations that span the range in which the radiation fields of adjacent particles begin to interact. We find that for l,400 nm the spectra are predominantly determined by the scattering properties of the individual single particles. At longer wavelengths, where multiple-scattering effects become important, the particles behave as independent scatterers for volume concentrations of less than approximately 1%. At higher concentrations, where the interparticle spacing becomes less than the wavelength of light in the medium, the interaction of the radiation fields of adjacent particles lowers the backscattering fraction of the multiple-scattering function. This reduction in backscattering is significant for many of the applications of films containing TiO 2, such as coatings and paper, which rely upon multiple scattering from large numbers of particles to provide the desired opacity.

Optical reflectivity measurements using a laser plasma light source

Light produced by a laser plasma light source (LPLS) is used to perform optical reflectivity measurements on single crystals from 5 to 40 eV in a single experiment. The intense continuum generated by the rare‐earth plasma allows a significantly higher resolution above 15 eV and extends the measurements to higher energies than those attainable with other laboratory based light sources. This is the first application of a LPLS to vacuum ultraviolet spectroscopy of solids and we demonstrate this capability on two insulating materials, α‐Al2O3 and MgAl2O4.

Optical properties of Teflon ® AF amorphous fluoropolymers

The optical properties of three grades of Teflon ® AF— AF1300, AF1601, and AF2400—were investigated using a J.A. Woollam VUV-VASE spectroscopic ellipsometry system. The refractive indices for each grade were obtained from multiple measurements with different film thicknesses on Si substrates. The absorbances of Teflon ® AF films were determined by measuring the transmission intensity of Teflon ® AF films on CaF2 substrates. In addition to the refractive index and absorbance per cm base 10, the extinction coefficient k, and absorption coefficient per cm base e, Urbach parameters of absorption edge position and edge width, and two-pole Sellmeier parameters were determined for the three grades of Teflon ® AF. We found that the optical properties of the three grades of Teflon ® AF varied systematically with the AF TFE/PDD composition. The indices of refraction, extinction coefficient k, absorp- tion coefficient , and absorbance A increased, as did the TFE con- tent, while the PDD content decreased. In addition, the Urbach edge position moved to a longer wavelength, and the Urbach edge width became wider.

Electronic structure of aluminum nitride: Theory and experiment

Recent efforts to develop electronic.,’ optical, and electro-optical’ -” components and applications based on wide band-gap III-V materials have generated considerable practical interest in the electronic structure of AlN. While a number of theoretical calculations5m10 of the band structure exist, the experimental work”-‘” available for comparison has been limited in either energy range or energy resolution. Extant experimental studies are mostly on thin films due to the difficulty of growing high-purity bulk crystals of 41N. Aside from techuological applications, the electronic structure of AlN is also of fundamental interest. Calculation of the electronic structure of ceramics is a developing area of theoretical physics and the nitrides are of particular importance because the bonding is more covalent than in the oxides. Experimental information about the electronic structure of AlN provides insight as to how theoretical models based on oxides should be adapted to covalent ceramics. Quantitative comparison of theory and experiment affords the best tool for gaining this insight. To this end, we present our results in terms of analytical critical point models of the interband transition strength, J,, , for both a first principles calculation and a vacuum ultraviolet (VW) optical measurement. Our method emphasizes the relationship among critical points grouping them into sets representative of transitions between pairs of bands, while other recent work” emphasizes individual critical points. A single crystal (W201), with a thermal conductivity of 275 W m -’ K-r grown by a modified Bridgman technique,r6 was studied. The oxygen content of the single crystal was 3GO ppm, as previously reported.‘” Polishing with diamond powders suspended in high-purity dry kerosene yields an oxide-free surface for reRectance measurements. Oxidized surfaces give spurious results and were avoided by nonaqueous polishing. The polished face of the single crystal was near normal to the c axis. The VIJV reflectance spectra were obtained with a laser plasma sourced VUV spectrophotometer, described elsewhere.9 Above the band gap at 6.2 eV, t.he spectra show two main features. A sharp peak appears at about 9 eV and a smaller, somewhat brozder peak appears at about l&15 eV. A small feature also appears at about 35 eV. Small features below the band gap are due to vacancies. The single crystal response was found to be representative of commercial polycrystalline substrates also studied.” The spectrum was adjustedd, consistent with an index of jz[ 1.25 eV] = 2.1 A Kramers-Kriinig (KK) analysi?” recovered the phase information, S[h,\r], and permitted calculation of other optical properties,” including the complex dielectric function shown in Fig. 1. The energy band structure of AlN was calculated from first principles, using the orthogonalized linear combination of atomic orbitals (OL.CAOj method with the local density approximation (LDA

Room‐temperature optical absorption in undoped α‐Al2O3

Optical absorption over a large dynamic range obtained by two different experimental techniques is reported for an undoped α‐Al2 O3 single crystal. Absorption data are presented in two energy ranges: 0.94–3.5 eV and 4.5–8.6 eV. Vacuum ultraviolet (vuv) absorption measurements were performed on three boules of Czochralski‐grown single‐crystal Al2 O3 with differing starting material purities. The initial powder purities were 99.99%, 99.999%, and 99.999999%. In addition to the vuv measurements, calorimetric absorption results obtained in the visible and near‐infrared (ir) are presented. An empirical formula is obtained that provides an estimate of the absorption coefficient from the near‐ir to the vuv for undoped Al2 O3 . Detailed impurity analyses and sample histories are given for the optical‐quality α‐Al2 O3 utilized herein.

Optical properties of AlN determined by vacuum ultraviolet spectroscopy and spectroscopic ellipsometry data

Precise and accurate knowledge of the optical properties of aluminum nitride (AlN) in the ultraviolet (UV) and visible (VIS) regions is important because of the increasing application of AlN in optical and electro-optical devices, including compact disks, phase shift lithography masks, and AlN/GaN multilayer devices. The interband optical properties in the vacuum ultraviolet (VUV) region of 6–44 eV have been investigated previously because they convey detailed information on the electronic structure and interatomic bonding of the material. In this work, we have combined spectroscopic ellipsometry with UV/VIS and VUV spectroscopy to directly determine the optical constants of AlN in this range, thereby reducing the uncertainty in the preparation of the low-energy data extrapolation essential for Kramers–Kronig analysis of VUV reflectance. We report the complex optical properties of AlN, over the range of 1.5–42 eV, showing improved agreement with theory when contrasted with earlier results.

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 inter- facial 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 oscillat- ing dipoles exhibit an attractive interaction energy. These vdW dispersion forces, represented by a propor- tionality 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 individ- ual 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 devi- ations 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 con- stant of the investigated grain boundary region. # 1998 Acta Metallurgica Inc.