Josef Humlíček

Optimized computation of the voigt and complex probability functions

Abstract Methods for computing the complex probability function w(z) = e−z2 erfc (−iz), which is related to the Voigt spectrum line profiles, are developed. The basic method is a rational approximation, minimizing the relative error of the imaginary part on the real axis. It is complemented by other methods in order to increase efficiency and to overcome the inevitable failure of any rational approximation near the real axis. The procedures enable one to evaluate both real and imaginary parts of w(z) with high relative accuracy. The methods are simple, as demonstrated by a sample FORTRAN program.

An efficient method for evaluation of the complex probability function: The Voigt function and its derivatives

Abstract An efficient method is developed to evaluate the function w ( z )= e - z 2 (1+(2 i /√ π )∫ z 0 e t 2 dt ) for the complex argument z = x + iy . The real part of w(z) is the Voigt function describing spectral line profiles; the imaginary part can be used to compute derivatives of the spectral line shapes, which are useful, e.g. in least-squares fitting procedures. As an example of the method a simple and fast FORTRAN subroutine is listed in the Appendix from which w(z) in the entire y ⩾ 0 half-plane can be calculated, the maximum relative error being less than 2 × 10 -6 and 5 × 10 -6 for the real and imaginary parts, respectively.

Optical spectra of SixGe1−x alloys

We report pseudodielectric functions of SixGe1−x alloys at room temperature, measured ellipsometrically on polycrystalline samples and single‐crystal epitaxial layers, in the 1.7–5.6 eV range. Accurate values of the E1 threshold energies are obtained from numerically differentiated spectra. The measured dependence of E1 on x provides an efficient way to determine the alloy composition x. The spectral and compositional dependence of the optical constants forms a data base for optical studies of Si/SiGe layered structures.

Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives

This paper discusses the fundamentals, applications, potential, limitations, and future perspectives of polarized light reflection techniques for the characterization of materials and related systems and devices at the nanoscale. These techniques include spectroscopic ellipsometry, polarimetry, and reflectance anisotropy. We give an overview of the various ellipsometry strategies for the measurement and analysis of nanometric films, metal nanoparticles and nanowires, semiconductor nanocrystals, and submicron periodic structures. We show that ellipsometry is capable of more than the determination of thickness and optical properties, and it can be exploited to gain information about process control, geometry factors, anisotropy, defects, and quantum confinement effects of nanostructures.

Lattice vibrations of Y1-xPrxBa2Cu3O7 : theory and experiment

Abstract We report measurements of the far-infrared reflectance of Y 1− x Pr x Ba 2 Cu 3 O 7 thin films. Detailed understanding of the experimental lineshapes is achieved with the proper treatment of the SrTiO 3 substrate, the finite film thicknesses, the background contribution of free carriers and the mid-infrared band, and the phonon modes. Shell-model calculations predict the frequencies of the infrared-active phonons to be very similar for YBa 2 Cu 3 O 7 and PrBa 2 Cu 3 O 7 with the exception of rare-earth-related vibrations. The experimental frequencies of the in-plane as well as z -polarized infrared-active phonons of PrBa 2 Cu 3 O 7 agree satisfactorily with the calculated ones. An in-plane mode at 270 cm -1 , assigned to vibrations confined to the Y/Pr and neighboring oxygen ions, is found to be sensitive to the rare-earth-ion substitution. We report also the frequencies of the Raman-active B 2g and B 3g phonons of PrBa 2 Cu 3 O 7 , thus giving a nearly complete picture of all k =0 eigenmode frequencies in the RBa 2 Cu 3 O 7 crystal structure.

Optical functions of silicon at high temperatures

The optical spectra of silicon are studied ellipsometrically at temperatures between 300 and 1200 K in the spectral range from 2 to 4.3 eV. We present a database of optical constants for pure and heavily doped samples, with the highest concentration of free carriers of 4×1020 cm−3. We cover the photon energy range between 0.2 and 2 eV by using an oscillator representation of the visible and ultraviolet ellipsometric data. We also report the results for the temperature dependence of the E1 interband transition. The values of the energy shift and Lorentzian broadening of this spectral feature are obtained from analytical critical-point line shapes by fitting differentiated dielectric functions; alternatively, we apply the numerical convolution with Lorentzian contours to describe quantitatively the increased broadening with increasing temperature.

Effects of oxygen deficiency on the optical spectra of YBa2Cu3O7−x

Abstract We report on the variation of ellipsometric spectra of the YBa2Cu3o7−x high Tc compounds with oxygen content 0≤x≤1. Beside the structures observed in the x=0 compound two new, rather intense peaks are observed at ∼ 1.75 eV and ∼ 4.1 eV in the semiconducting compound (x>0.5). Their intensity strongly depends on the oxygen content, whereas the energy shows a weak dependence both on oxygen content and temperature. Several minor features become significant upon cooling the samples to 7 K. We associate the 4.1 eV peak to excitations involving transitions from Ba(5d) and/or Cu(3d) states to O(2p) states. The 1.75 eV peak is possibly due to Cu(3d) and O(2p) states.

Sensitivity extrema in multiple-angle ellipsometry

A quantitative study of sensitivity of multiple-angle-of-incidence ellipsometry in determining several parameters of stratified structures is presented. The principles of determination of parameter errors caused by random and systematic errors in measured ellipsometric angles and by the use of incorrect values of fixed parameters are given. An appropriate choice of angles of incidence is discussed. The sensitivity for dielectric films on low-loss substrates is studied in detail, and large variations with the parameters, especially with film thickness-to-wavelength ratio, are observed.

Anomalies of the infrared-active phonons in underdoped YBa2Cu3Oy as evidence for the intra-bilayer Josephson effect

The spectra of the far-infrared c-axis conductivity of underdoped YBCO crystals exhibit dramatic changes of some of the phonon peaks when going from the normal to the superconducting state. We show that the most striking of these anomalies can be naturally explained by changes of the local fields acting on the ions arising from the onset of inter- and intra-bilayer Josephson effects.The spectra of the far-infrared c-axis conductivity of underdoped YBCO crystals exhibit dramatic changes of some of the phonon peaks when going from the normal to the superconducting state. We show that the most striking of these anomalies can be naturally explained by changes of the local fields acting on the ions arising from the onset of inter- and intra-bilayer Josephson effects.

Temperature dependence of optical excitations in MBa2Cu3O6 (M=Y,Sm)

Abstract We have studied ellipsometric spectra of semiconducting, antiferromagnetic MBa 2 Cu 3 O 6 (M = Y,Sm) samples in the temperature range from 80 to 730 K. No noticeable change of the spectra is observed when crossing the Neel temperature. Two intense absorption bands located at 1.77 and 4.08 eV display different variations with temperature. The 1.77 eV band shifts strongly to lower energies and broadens with increasing temperature, while the 4.08 eV band changes substantially less. We assign the 1.77 eV structure to excitonic charge-transfer transitions from oxygen to copper in the CuO planes. The composite structure at 4.08 eV is associated with localized transitions within the central OCuO complex and with interband transitions to unoccupied Ba states.