X-ray Edges Research Articles

EXAFS Studies of Semiconductor Microstructure

Extended X-Ray Absorption Fine Structure (EXAFS) is a technique capable of probing local structure in condensed- matter systems, determining distances, coordination numbers, and species of atoms near an x-ray excited atom. Further, this information is obtained separately for each constituent atomic species. EXAFS can be applied equally well to crystals, alloys, or even systems having no long-range order such as liquids, gases, and amorphous materials.Here we review EXAFS spectroscopy and its use in studying semiconductors. First, we show EXAFS in the study of impurities to determine the local environment of Fe implanted in Si. Second, we show how EXAFS can be used to determine local structural distortion in diluted magnetic semiconductors. We next demonstrate that EXAFS can determine the nature of the phase transition in ferroelectric Pb1-x Gex Te, where the transition is revealed to have an order-disorder character in contrast to GeTe where the transition is purely displacive. The theme of these examples is that EXAFS can determine the relative positions of atoms in condensed matter and that the short-range order as determinedn by EXAFS often differs from the long-range order or theoretical expectations.In the EXAFS technique, one measures the x-ray absorption coefficient as a function of x-ray energy. The absorption spectrum shows a number of x-ray edges corresponding to the threshold of excitation of core electrons from the sample's various atomic species. At energies above each of these edges, oscillations in the absorption coefficient are due to backscattering of the photoelectron from the neighboring atoms.

X-ray holograms at improved resolution: a study of zymogen granules.

X-ray holography offers the possibility of three-dimensional microscopy with resolution higher than that of the light microscope and with contrast based on x-ray edges. In principle, the method is especially advantageous for biological samples if x-rays in the wavelength region between the carbon and oxygen K edges are used. However, until now the achieved resolution has not exceeded that of the light microscope because of the poor coherence properties of the x-ray sources and the low resolution of the detectors that were available. With a recently developed x-ray source based on an undulator on an electron storage ring, and high resolution x-ray resist, a hologram has been recorded at about 400-angstrom resolution. The experiment utilized x-rays with wavelengths of 24.7 angstroms and required a 1-hour exposure of the pancreatic zymogen granules under study.

A slitless double crystal monochromator for EXAFS and XANES measurements

Recently a double crystal monochromator has been commissioned on the EXAFS station 8.1 at the Daresbury Synchrotron Radiation Source (SRS). This monochromator is designed to operate in an UHV compatible chamber in the energy range 3–14 keV. It utilises three seperate pairs of crystals to cover the total range and to provide the optimum energy resolution 1–3 eV required for EXAFS and XANES measurements. The crystal pair for the high energy range (8–14 keV) is special in that the second crystal is curved with a radius of 55 m in the plane of diffraction and also with a radius of 2.5 m perpendicular to the plane of diffraction. The crystal pairs for the other ranges are bent only in the plane of diffraction to take account of the vertical divergence of the X-rays from the SRS. In the low energy ranges, the focussing is provided by an ellipsoidal mirror. The second crystal is translated to keep the position of the exit beam fixed and is also adjusted to suppress the higher harmonics. The first crystal is water-cooled to avoid excessive thermal loading. Some results are presented for a number of X-ray edges (K-edge, Ti, V, Cu and L III-edge Pt and Au) to illustrate the performance of the monochromator.

X-ray edges of superconducting metals.

The existence of the energy gap in the excitation spectrum of superconducting electrons prevents the excitation of an infinite number of low-energy quasiparticles, i.e., prevents the infrared catastrophe. The ground states of the conduction electrons with and without the presence of an impurity potential are no longer orthogonal. Effects on x-ray edges and x-ray photoemission spectra of superconducting metals are discussed. It appears that all the edges are divergent in the limit of infinite hole lifetime and that the photoemission spectra become discrete, reflecting the fact that the quasiparticles in superconductors have finite minimum energy.

X-ray-edge problem in metals. I. Universal scaling in alkali-alkali alloys.

We report outer-core excitation spectra of alkali-alkali alloys. The results are obtained by differential reflectance methods using synchrotron radiation on quench-condensed samples. Striking changes of line shape take place with changing composition. All available threshold profiles for alkali-metal alloys and pure metals conform to a universal scaling relationship defined by parameters related to the electronic structure of the excited configuration. The sharp ``x-ray edges'' with an overshoot at threshold occur only when the excited alkali-metal-atom valence orbitals localize at or below the band bottom and other atoms of the same type neighboring the active core in the Periodic Table. A linear absorption profile rising from zero absorption at threshold is observed when the excited orbitals mix strongly with conduction-band states.

Off-diagonal disorder and X-ray edges

The combined effects of off-diagonal disorder and electron-hole pair production (the X-ray edge effect) are studied for a one-dimensional Anderson model of a liquid metal with a half-full band.

Spin-density calculations for core-electron photoemission and Auger electron line shapes, x-ray-edge exponents, and solid-state shifts

Spin-polarized density-functional conduction-electron screening calculations for core ionization and Auger transition for elements Li, Be, Na, Mg, Al, and Ca are performed. The screening is described by conduction-electron scattering phase shifts obtained from self-consistent-field ab initio calculations. Both spins are treated separately in order to study the spin-polarization effects. The core-electron states are resolved by a Hartree-Fock-Slater method, which makes it possible to apply the same local-density exchange and correlation approximation to all electrons, including the conduction electrons. X-ray-edge exponents and x-ray photoelectron (XPS) line singularity indices are extracted from the phase shifts. Auger line singularity indices are also evaluated. In the case of Na, Mg, and Al metals the results agree with those of the previous spin-symmetric calculations and experimental values. The screening of Li and Be is, however, strongly spin-polarized, which both increases the singularity index and decreases the edge exponents. This partly explains the broad $K$ edge of Li. The spin-polarized method seems to be necessary to describe the peculiar conduction-electron response to the core hole in Ca. The screening in this case is localized in energy, totally spin polarized, and of $d$-electron type. This should cause very broad x-ray edges and the most asymmetric XPS and Auger lines. By performing the corresponding free-atom calculations with the same method, the solid-state shifts (extra-atomic relaxation energies) for the photoelectron energies (binding energies) and Auger electron energies are obtained. The density-functional results agree better with the experiments than the results of the excitonic model or excited-atom model, for example. In the case of Ca the shift values are exceptionally large due to the localized $d$-electron screening.

Core excitons in ionic crystals: I. A Born-Haber-type cycle for the energy of the core-exciton associated with the Na, LII,IIIedge in NaF

The connection between fundamental core excitations and X-ray edges in non-metallic solids is reviewed. By means of a cycle of the Born-Haber type which is described herein, a connection is established for an alkali halide crystal between the energy of the fundamental exciton based on a given alkali-ion core level and the energy of the corresponding excitation based on the related core level in the free alkali atom (not ion). An overview of the series of papers on core excitons of which this is the first is presented.

Histogram equalisation with S and π functions in detecting X-ray edges

An algorithm consisting of a histogram equalisation technique followed by further enhancement using S and π membership functions is described to detect the small variation in grey levels of X-ray images. The effectiveness of the algorithm in identifying the different regional contours related to growth of normal bones is demonstrated.

Self-absorption and the soft X-ray edges of Be metal

Measurements are reported for the K emission and self-absorption edges of metallic beryllium. The self-absorption effect is small in this material and both edges are dominated by large core level widths.

Emission and absorption x-ray edges of Li

The $K$ x-ray emission edge of Li is measured between 85 and 490 K and analyzed to obtain the temperature dependences of the edge position and of a Gaussian edge-broadening function. Full width at half-maximum edge widths range from 0.22 \ifmmode\pm\else\textpm\fi{} 0.05 eV at 85 K to 0.38 \ifmmode\pm\else\textpm\fi{} 0.05 eV at 440 K. Edge positions shift from 54.81 \ifmmode\pm\else\textpm\fi{} 0.02 eV at 85 K to 54.86 \ifmmode\pm\else\textpm\fi{} 0.02 eV at 440 K and to 54.91 \ifmmode\pm\else\textpm\fi{} 0.02 eV after melting. Emission and absorption spectra measured with the same spectrometer establish a 0.10 \ifmmode\pm\else\textpm\fi{} 0.02 eV separation between the emission and absorption edges. These results are compared with recent theories describing incomplete lattice relaxation about the core hole. We conclude that for a core-hole lifetime of 0.016 to 0.030 eV the theories give a satisfactory explanation of the premature peak in the emission spectra. We suggest also that phonon---core-hole interactions provide the dominant edge-broadening mechanism, and that many-body effects are small.

Theory of X-ray edges

The current status of the theory of X-ray edges is reviewed, including the predictions of threshold exponents by means of sum rules and the recent exact solutions of the Nozières-de Dominicis model.

The spherical-solid model: An application to x-ray edges in Li, Na, and Al

In order to treat highly localized excitations in a solid a simple spherical model has been developed. The Coulomb potential from the nucleus at the site of the excitation is treated exactly, while the potentials from the surrounding sites are turned into pseudoion pontentials. Only the spherical average of these potentials is retained and separate self-consistent calculations for the ground state and for the excited state are made. These states are mistreated by the model but the difference accurately describes the large effects of polarization involved. The positions of the x-ray edges are obtained with an accuracy of 0.5 eV for singly ionized levels and 1 eV for doubly ionized levels. The phase shifts relevant to the Nozi\`eres-De Dominicis theory of x-ray absorption and emission edges and x-ray photoemission line shapes are also calculated. We obtain a noticeable many-body enhancement of the ${L}_{2,3}$ edge in Na while the many-body effect in Li and Al is negligible. Our exponents agree with those extracted from recent x-ray photoemission experiments, but they do not agree with those extracted from x-ray emission or absorption spectra. We argue that the exponents taken from the photoemission experiment are more reliable but no definite conclusion concerning the validity of the present many-body theory should be drawn until the experimental situation has become more clear.

Theory of soft-x-ray-absorption thresholds: AmorphousMgxSb1−xalloys and metallic Li, Na, Mg, and Al

The trends as a function of free-electron density, $n={[(\frac{4}{3})\ensuremath{\pi}{r}_{s}^{3}{a}^{3}]}^{\ensuremath{-}1}$, in the soft-x-ray absorption spectra ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ of amorphous ${\mathrm{Mg}}_{x}{\mathrm{Sb}}_{1\ensuremath{-}x}$ alloys and metallic Li, Na, Mg, and Al are analyzed in terms of the many-electron theory of x-ray threshold anomalies: ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})={A}_{l}^{2}{[\frac{(\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}{E}_{T})}{\ensuremath{\xi}}]}^{\ensuremath{-}{\ensuremath{\alpha}}_{l}}$. The threshold exponents ${\ensuremath{\alpha}}_{l}$ are calculated as functions of ${r}_{s}$ using the Nozi\`eres-deDominicis theory and a (Hulth\'en) screened-potential approximation to the electron-hole interaction. These calculated exponents are in marked disagreement with the empirical rule ${\ensuremath{\alpha}}_{0}\ensuremath{\approx}0.068{r}_{s}$ for Na, Mg, and Al. The cutoff energy $\ensuremath{\xi}$ is extracted from ${\mathrm{Mg}}_{x}{\mathrm{Sb}}_{1\ensuremath{-}x}$ alloy data and, within experimental error, is independent of $x$. Thus $\ensuremath{\xi}$ cannot be identified with a Fermi energy. The value $\ensuremath{\xi}=0.24\ifmmode\pm\else\textpm\fi{}0.1$ eV is too small to be identified as a conduction-band width, but could be identified with the exciton rydberg $R=13.6(\frac{m}{{m}_{0}{\ensuremath{\epsilon}}_{0}^{2}})$ eV, where $m$ is the conduction-band mass and ${\ensuremath{\epsilon}}_{0}$ is the static dielectric constant of ${\mathrm{Mg}}_{3}$${\mathrm{Sb}}_{2}$. The analyses indicate the qualitative importance of final-state interactions in shaping the absorption thresholds, but improved, quantitatively accurate, theoretical understanding of the threshold exponents ${\ensuremath{\alpha}}_{l}$ and the characteristic energy $\ensuremath{\xi}$ is needed. Future experiments on x-ray edges of alloys such as ${\mathrm{Mg}}_{x}{\mathrm{Sb}}_{1\ensuremath{-}x}$ should be coupled with independent experimental determination of the variation of ${r}_{s}$ with composition $x$, in order to facilitate comparison of the many-electron theory with data.

On the K X-ray emission edge shapes of free-electron metals

It is shown that the Mahan-Nozieres-de Dominicis (MND) theory of X-ray edges (1967-1969) predicts enhanced K edges for all free-electron metals. The K absorption and emission edges of Li and Al overlap, strongly suggesting that the primary source of K edge rounding is core-hole broadening rather than the MND orthogonality catastrophe effect.

Divergent enhancement of forbidden x-ray edges by lattice vibrations

Divergent enhancement of forbidden x-ray edges by lattice vibrations

Transmittance of Tin Films in the Far Ultraviolet

The transmission spectra of tin films ranging in thickness from 680 to 1690 A have been studied in detail in the spectral range 1000–80 A, utilizing both photoelectric and photographic detection. The photoelectric results, using a multiline source, give measured values of transmittance, while the photographic results, using the pure continuum radiated by the NBS 180-MeV electron synchrotron, show the behavior of the transmittance curves between measured data points. These new measurements, giving continuous and extended information, allow an interpretation of the transmission characteristics of tin in terms of atomic and solid-state parameters. In particular, the photographic data locate the NIV,V x-ray edges with increased accuracy [NV = 23.8(±0.1) eV; NIV = 24.9(±0.1) eV]. Of practical importance, a film of thickness 680 A has a transmittance of over 20% from 700 to 525 A. Of theoretical significance is a broad absorption feature centered near 190 A, due to the high oscillator strength for transition of the 4d electron to continuum states of f symmetry.

Thin Films and Their Uses for the Extreme Ultraviolet

The transmittance characteristics in the extreme ultraviolet of unbacked films are discussed; data are presented for films of Al, In, Bi, Ge, Si, and certain organic materials. Generally, the metals begin to transmit shortward of their critical wavelengths, determined by the electron eigenloss, and reach maximum transparency at the nearest x-ray edge; to shorter wavelengths regions of transparency exist between the other x-ray edges. Their use in order-sorting, and for eliminating long-wavelength stray light, is illustrated with laboratory spectra and solar spectra obtained from rockets.