Kramers-Kronig Method Research Articles

The electronic structure of bismuth germanate

Reflection spectra have been measured for Bi 4Ge 3O 12 (BGO) crystals in the range from 4 to 40 eV, using synchrotron radiation. The reflection data are evaluated using a modified Kramers-Kronig method for extracting information on the optical constants. From the experimental spectra of the optical constants in a wide range and calculations of X α-scattered waves of the molecular cluster an electron structure model for bismuth germanate crystals is suggested. The most interesting feature of our model is a dominant contribution of the bismuth state in the top of the valence band.

Optical Constants of Tetracene Single Crystal within the First Absorption Band

Abstract Optical constants of tetracene single crystal within the first absorption band have been determined for various polarization states of the light incident on its crystallographic (ab) plane at room temperature. A method based on the combination of the reflectance spectra taken from the crystal interface with two different transparent media (TTM method) has been developed in order to avoid approximations needed for the analysis by usual Kramers-Kronig (KK) method. In contrast to the latter, our method does not require the knowledge of the reflectivity throughout the entire energy range and a comparison of the results with independent experimental absorption and refraction data of the crystal shows the method to be more accurate than KK method. Some possible applications of the data are briefly discussed in conjunction with intermolecular structure of crystalline tetracene.

Electron excitation and luminescence in Bi 4Ge 3O 12 and Bi 4Si 3O 12 crystals

Reflection, luminescence excitation and thermoluminescence excitation spectra have been measured for Bi 4Ge 3O 12 and Bi 4Si 3O 12 crystals in the energy range from 3 to 35 eV using synchrotron radiation. The reflection data are evaluated using a modified Kramers-Kronig method for extracting the information on optical constants of these crystals. The nature of electronic excitations in the fundamental absorption edge region is discussed, the value of forbidden-gap energy E g is estimated as 5.0 eV for Bi 4Ge 3O 12 and 5.4 eV for Bi 4Si 3O 12. Intrinsic luminescence with 2.5 eV maximum for Bi 4Si 3O 12 and 2.45 eV maximum for Bi 4Ge 3O 12 is due to both the relaxation of optically created excitons and recombination processes. The multiplication effect of electron excitations in E ⩾ 2 E g for these crystals is due to the inelastic scattering of hot photoelectrons and hot photoholes.

Infrared optical properties and vibrational behavior of anisotropic crystals: Orthorhombic Ba

The infrared (ir) optical properties and vibrational behavior of anisotropic absorbing crystals in spectral regions including strong resonances are considered. In particular, the optical parameters, namely the complex dielectric tensor and refractive indexes, of barium nitroprusside trihydrate (BNP), Ba[Fe(CN${)}_{5}$NO]\ensuremath{\cdot}${3\mathrm{H}}_{2}$O (orthorhombic, space group ${C}_{2v}^{5}$), in the range 1500--2300 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, which includes the strongly polar NO stretching mode, are determined. To this purpose, transversal electric (TE) reflectance data on (001) planes of BNP in the spectral range 250--4000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ were analyzed by the Kramers-Kronig method. The values obtained for the optical parameters were employed to get transversal (TO) and longitudinal (LO) frequencies of the NO optic stretching mode of symmetry species ${B}_{1}$ (polarized along the crystal a axis) and to show the impossibility of obtaining sharp peaks for accurate frequency measurement of the TO mode by transmission spectroscopy because too-thin crystals films (less than 1 \ensuremath{\mu}m thick) would be required. The dielectric tensor was employed to predict correctly the position and shape of the NO reststrahlen band due to the LO mode ${B}_{1}$ in the reflectance spectrum from the (100) face.This band occurs only for oblique incidence and transversal-magnetic (TM) polarization of the ir beam. The computed TM-polarized, off-axis transmittance spectra through bc crystal plates of BNP in the NO stretching region are in good agreement with spectroscopic data and exhibit a sharp, strong absorption band at 1982 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ which is due to the coupling of the LO mode ${B}_{1}$ with the ir radiation. Our results show that strongly absorbing LO modes polarized perpendicularly to the plate can be easily identified and their frequencies measured accurately in relatively thick samples of an anisotropic substance. Finally, a least-squares fit to reflection data of the calculated TE reflectance on a (001) plane of BNP, derived from a damped harmonic-oscillator model for the dielectric constant along a, leads to a value for the transition strength of the NO stretching which is in accordance with values obtained by independent spectroscopic measurements.

Determining the optical constants of metals by the Kramers-Kronig method

Determining the optical constants of metals by the Kramers-Kronig method

Determination of the optical constants of a thin film from transmittance measurements of a single film thickness

A subtractive Kramers-Kronig method is presented for obtaining the optical constants, n and k, of a uniform absorbing film on a substrate using the transmittance spectrum of a single film thickness. We give the results of tests on the reliability of our method, demonstrate the usefulness of the method when only transmittance data are available, and give examples of thin films whose optical constants depend on their thickness.

Vacuum ultraviolet (VUV) reflectivity and electron states in LiNbO 3

In the present paper the near-normal incidence reflectance for LiNbO 3 has been measured in the energy region 1.0 to 35.0 eV. Optical functions for the 0–35.0 eV range were determined by the Kramers-Kronig method (including the results for the low-energy region obtained previously). On the base of the experimental results, the energy transition diagram for LiNbO 3 has been drawn, and the NbO 6 octahedron is shown to be prominent in the formation of the band structure of the crystal studied. At low temperatures ( T = 6K) indirect optical transitions are observed for LiNbO 3.

Surface roughness as a physical cause of the dip in the results of a Kramers–Kronig analysis of Zn_3P_2

The dip in the absorption-coefficient curve calculated by the Kramers–Kronig method is analyzed. Methods of removing the dip are proposed and used for Zn3P2. Roughness of the sample surface is suggested to be a cause of the dip.

Use of supplementary information in determining the reflection coefficient by the Kramers-Kronig method

Use of supplementary information in determining the reflection coefficient by the Kramers-Kronig method

Reflectance spectra and dielectric functions for Ag in the region of interband transitions

New measurements have been made of the reflectances of single crystals of Ag and of Ag films in the (3.5-30)-eV range. The data were analyzed with the Kramers-Kronig method and the resultant dielectric functions were compared with those in the literature and with recent calculations. We find all structures previously seen, and a new weak peak at 11.5 eV. Our magnitudes for ${\ensuremath{\epsilon}}_{2}$ are in considerably better agreement with those of the calculated spectra than are those in the literature. Second-derivative spectra of the absorption coefficient have been calculated and compared with previously measured thermotransmission spectra, showing the latter to arise primarily by temperature-dependent broadening.

Dielectric function and critical-point transitions in boron-doped graphite

Optical reflectivity spectra of graphite substitutionally doped with 0.5-at.% boron were measured in the energy range 0.1-6.0 eV and analyzed by the Kramers-Kronig method to yield the $q=0$ dielectric function. A screened free-carrier plasma edge occurs at 0.5 eV, and the onset of interband transitions indicates a Fermi-level shift of 0.2 eV. Thermoreflectance spectra in the range 0.3-1.5 eV reveal changes in critical-point transitions which are consistent with the shift in Fermi energy. Both experiments can be understood in terms of a rigid-band model with spatially uniform charge density. This result is in contrast to the situation in dilute intercalation compounds, in which interlayer screening must be accounted for.

Optical properties ofβ′-CoAl

The optical absorptance of ${\ensuremath{\beta}}^{\ensuremath{'}}$-CoAl in the (0.1-2.5)-eV region was measured and analyzed by the Kramers-Kronig method. The optical conductivity shows interband features beginning below 0.1 eV, with several structures below 2 eV. These structures agree with those calculated from the energy bands of Moruzzi, Williams, and Gelatt. The experimentally observed systematics in CoAl and NiAl confirm our previous interpretation of the spectra of ${\ensuremath{\beta}}^{\ensuremath{'}}$-NiAl, and disagree with other experimental and theoretical attempts to understand the optical properties of these compounds.

Plasma-sprayed chromium oxide: control of mechanical properties using infrared specular reflection

The infrared reflection spectra of Cr 2O 3 samples prepared by the plasma-spray technique are analyzed using the Kramers-Kronig method. As the degree of orientation of the crystalline surface, and hence its mechanical properties, depends on the deposition conditions, infrared reflection spectroscopy provides a convenient method of controlling the quality of plasma-sprayed deposits.

Optical constants of bismuth tellurium sulfide

The optical constants of crystals of bismuth tellurium sulfide have been determined from reflectance measurements. Because it is a uniaxial crystal, two sets of optical constants are associated with it. One of these sets, denoted by (nc, kc), corresponding to the component of an E vector parallel to the symmetry axis (c axis) has been determined in the wavelength range 1–16.5 μm. The other set, denoted by (na, ka), corresponding to the perpendicular component of an E vector, has been obtained in the range 0.2–16.5 μm. Two methods of analysis, the classical oscillator method and the Kramers–Kronig method, are used to obtain the (na, ka) set, but the (nc, kc) set is obtained by using the classical oscillator method alone. A brief discussion on the uniqueness of the constants as obtained by a single method of analysis is presented.

Vibrational spectra and conformations of RSO2CH2X sulfones

transitions in germanium," Solid State Commun., 21, 385-387 (1977). 5. J. W. Perram, "Interpretation of spectra," J. Chem. Phys., 49, 4245-4246 (1968). 6. B. G. M. Vandeginste and L. De Galan, "Critical evaluation of curve fitting in infrared spectrometry," Anal. Chem., 47, 2124-2132 (1975). 7. W. F. Maddams, "The mathematical separation of overlapping peaks: fact or fancy?" UV Spectrom. Group Bull., No. 6, 41-53 (1978). 8. ~. M. Bartetski, K. Ya. Kuzhak, and A. Yu. Shteinberg, "Use of least-squares method to resolve spectral contours and determine number of bands in the electronic absorption spectra of complex compounds," Zh. Prikl. Spektrosk., 31, 1017-1022 (1979). 9. V. V. Sobolev, Intrinsic Energy Levels of Group-AIV Solids [in Russian], Shtiintsa, Kishinev (1978), pp. 180-189. i0. T. Moss, Optical Properties of Semiconductors [Russian translation], IL, Moscow (1961), p. 29. ii. T. A. Witten and S. R. Nagel, "Argand diagrams of dielectric response," Solid State Commun., 16, 185-188 (1975). 12. A. I. Galuza, V. V. Eremenko, and A. P. Kirichenko, "Analysis of hermatite reflection spectrum by the Kramers-Kronig method," Fiz. Tverd. Tela, 21, 1125-1129 (1979). 13. V. D. Checherskii and V. P. Romanov, Programs for the Analysis of Complex Nuclear Gamma-Resonance Spectra. Preprint 15-77 of the Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR [in Russian], Khar'kov (1977).

Lattice Vibration Spectra XXIV*. Far-Infrared Reflection Spectra, Optical and Dielectric Constants, and Effective Charges of the Pyrite Type Compounds FeS2, MnS2, MnSe2, and MnTe2

Abstract From the far-infrared reflection spectra of the pyrite type compounds FeS2, MnS2, MnSe2, and MnTe2 we determined the TO and LO phonon frequencies at wave vector | q | ≈ 0 by both Kramers-Kronig analysis and classical oscillator fit method. In the case of MnSe2 and MnTe2 we found for the first time all five group-theoretically allowed reststrahlen bands. The phonon frequencies obtained from both single crystal and pressed pellet reflection measurements do not show any significant differences. The calculated optical and dielectric constants however are strongly affected by the surface quality of the sample. Effective ionic charges (Born effective charge, Szigeti charge) were calculated from the experimentally determined TO/LO splittings. They demonstrate an increasing ionicity in the order FeS2<MnTe2<MnSe2<MnS2.

On the article by L. I. Al' perovich and R. A. Dmitriev, "application of the Kramers-Kronig method to analysis of internal reflection spectra in the region of intense infrared bands"

On the article by L. I. Al' perovich and R. A. Dmitriev, "application of the Kramers-Kronig method to analysis of internal reflection spectra in the region of intense infrared bands"

Optical constants of single crystal GaAs

The optical constants of single crystal GaAs were determined in the range 0.6 to 4.2 eV, using Tomlin’s method and are compared in the light of the earlier results obtained using the Kramers-Kronig analysis method.

Optical properties of cosputtered gold-chromium alloy films

Optical properties of cosputtered thin-film (1500 Å) polycrystalline Au-Cr alloys have been investigated in the energy range 0.2–6.1 eV. Cosputtering of Au and Cr has extended the solubility limits of Cr in Au from 20 to 48 at.%. The reflectance data were analyzed by the Kramers-Kronig method and presented in terms of intraband, and interband contributions. The observed frequency dependence of the relaxation time is explained on the basis of a two carrier mode. The shift in the Fermi level with increasing Cr concentration is found to be closer to the prediction of the Friedel theory than the rigid band model. The character of critical points for the interband transitions has been identified.

Collective oscillation in liquid normal tetradecane and normal heptadecane

The optical properties of the liquids normal tetradecane (C14H30) and normal heptadecane (C17H36) were determined for photon energies from 4 to 25 eV. Near normal incidence (15 °) reflectance measurements were analyzed by a Kramers–Kronig method to yield the optical parameters n and k, the refractive index and extinction coefficient, respectively. The dielectric properties and the energy loss function were calculated. Structure from optical data in the liquid state is compared with vapor data for normal paraffin hydrocarbons and with solid data for the 26- and 36-normal paraffins. Evidence of collective excitation of electrons in the n-alkanes is compared with plasma resonances previously identified in the insulating liquids water, glycerol, tetramethyltetraphenyltrisiloxane (DC-704), and trimethylpentaphenyltrisiloxane (DC-705).