Two-dimensional Angular Correlation Research Articles

Study of the Structure of Porous Silicon via Positron Annihilation Experiments

We performed two-dimensional angular correlation of the electron–positron annihilation radiation (2D-ACAR) and positron lifetime measurements on a porous Si sample. From the width of the narrow 2D-ACAR component, attributed to positronium atom, we estimated the average size of the pores to be ∼2.4 nm and did not find evidence of a preferential propagation of the pores. Moreover, by comparing the 2D-ACAR spectrum with that observed in a pure Si crystal we isolated a further isotropic component to be attributed to crystal defects of unknown origin.

Intense positron beam at KEK

A positron beam is a useful probe for investigating the electronic states in solids, especially concerning the surface states. The advantage of utilizing positron beams is in their simpler interactions with matter, owing to the absence of any exchange forces, in contrast to the case of low-energy electrons. However, such studies as low-energy positron diffraction, positron microscopy and positronium (Ps) spectroscopy, which require high intensity slow-positron beams, are very limited due to the poor intensity obtained from a conventional radioactive-isotope-based positron source. In conventional laboratories, the slow-positron intensity is restricted to 10 6 e +/s due to the strength of the available radioactive source. An accelerator based slow-positron source is a good candidate for increasing the slow-positron intensity. One of the results using a high intensity pulsed positron beam is presented as a study of the origins of a Ps emitted from SiO 2. We also describe the two-dimensional angular correlation of annihilation radiation (2D-ACAR) measurement system with slow-positron beams and a positron microscope.

Study of thestructure of porous silicon via positron annihilation experiments

We performed two-dimensional angular correlation of theelectron-positron annihilation radiation (2D-ACAR) and positronlifetime measurements on a porous Si sample. From the width of thenarrow 2D-ACAR component, attributed to the positronium atom, weestimated the average size of the pores to be ~2.4 nmand did not find evidence of a preferential propagation of thepores. Moreover, by comparing the 2D-ACAR spectrum with thatobserved for a pure Si crystal, we isolated a further isotropiccomponent attributable to crystal defects of unknown origin.

Study of the Fermi surface of molybdenum and chromium via positron annihilation experiments

A quantitative mapping of the Fermi surface (FS) of molybdenum and chromium was sought by modelling the three-dimensional k -space occupancy with a small number of parameters which were determined by a least-squares fit to the two-dimensional angular correlation of the electron–positron annihilation radiation (2D-ACAR) data subjected to a Lock–Crisp–West (LCW) transformation. The resulting FS topology of molybdenum, unlike what was assumed in previous 2D-ACAR studies, does not support the nesting of its two main FS sheets. In the case of chromium, although the overall discrepancy with the FS expected from the theory is larger, the difference in shape between the same two FS sheets is of lesser extent. According to this analysis the ratio of the electron Fermi volume to the hole Fermi volume is found to deviate from unity, the value expected for compensated metals, for both materials. We suggest that these discrepancies might be due to positron wave function and/or electron–positron many-body distortions not predicted by the theory.

Full-potential LAPW calculation of electron momentum density and related properties of Li

Electron momentum density and Compton profiles in Lithium along $<100 >$, $<110>$, and $<111>$ directions are calculated using Full-Potential Linear Augmented Plane Wave basis within generalized gradient approximation. The profiles have been corrected for correlations with Lam-Platzman formulation using self-consistent charge density. The first and second derivatives of Compton profiles are studied to investigate the Fermi surface breaks. Decent agreement is observed between recent experimental and our calculated values. Our values for the derivatives are found to be in better agreement with experiments than earlier theoretical results. Two-photon momentum density and one- and two-dimensional angular correlation of positron annihilation radiation are also calculated within the same formalism and including the electron-positron enhancement factor.

Study on the Electron-Positron Momentum Density and Fermi Surface in Hf Using the 2D-ACAR Experiment

Electron momentum space density and Fermi surface of Hf were studied using two-dimensional angular correlation of annihilation radiation (2D-ACAR) experimental set-up. From the measured data, three-dimensional momentum space density ρ(P) was calculated, using the reconstruction technique based on Fourier transform. The strong d-like signal and its effect on the Fermi surface features were studied and interpreted in view of the electronic structure of Hf. The Fermi radius was obtained from the locus |∇ρ(P)|max, and it was found to deviate strongly from the free electron one. In the wave vector space, Fermi surface of Hf was constructed using LCW folding procedure, restrained within first Brillouin zone. In addition, its sheets were compared with two band structure calculations using relativistic augmented plane wave (RAPW) method and linear combination of atomic orbital (LCAO) method. Agreements and variations were obtained with the theoretical works.

Signature of Fermi surface jumps in positron spectroscopy data

A subtractionless method for solving Fermi surface sheets (FSS), from measured n-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron—electron annihilation radiation (2D-ACAR) technique, is discussed. The window least squares statistical noise smoothing filter described by Adam et al. [Nucl.Instr. & Meth. A 337 (1993) 188] is first refined such that the window free radial parameters (WRP) are optimally adapted to the data. In an ideal single crystal, the specific jumps induced in the WRP distribution by the existing Fermi surface jumps yield straightforward information on the resolved FSS. In a real crystal, the smearing of the derived WRP optimal values, which originates from positron annihilations with electrons at crystal imperfections, is ruled out by median smoothing of the obtained distribution, over symmetry defined stars of bins. The analysis of a gigacount 2D-ACAR spectrum, measured on the archetypal high- T c compound YBa 2Cu 3O 7- δ at room temperature, illustrates the method. Both electronic FSS, the ridge along ΓX direction and the pillbox centered at the S point of the first Brillouin zone, are resolved.

Electron-positron momentum density in(TMTSF)2ClO4

We have measured electron-positron momentum density in ${(\mathrm{TMTSF})}_{2}{\mathrm{ClO}}_{4}$ by the positron two-dimensional angular correlation of annihilation radiation (2D-ACAR) technique. Significant anisotropies are found in the momentum density reflecting the low dimensionality of the material. Ab initio plane-wave pseudopotential calculations have been also made to simulate the 2D-ACAR spectra. The calculated 2D-ACAR spectra are in good agreement with the experimental ones. In order to investigate the Fermi-surface structure, we constructed Lock-Crisp-West (LCW) remapped spectra. The resultant spectra show small steps at the expected Fermi-surface position for both the experiment and the calculation. The magnitude of the steps in the experimental LCW spectrum is one third of the calculated one but still one order of magnitude higher than the experimental detection limit. Although we cannot conclude the existence of an ideal Fermi surface due to the finite experimental resolution, we have confirmed, in the experiment, a structure corresponding to the calculated Fermi break.

Three-dimensional electron momentum density of aluminum by(γ,eγ)spectroscopy

We report on the measurement of the three-dimensional electron momentum density (EMD) of aluminum. 150 keV photons with an intensity of $2\ifmmode\times\else\texttimes\fi{}{10}^{11}$ photons/s from a multipole wiggler of the European Synchrotron Radiation Facility have been scattered at a 100 nm thin self-supporting aluminum foil and measured in coincidence with their recoil electrons. To improve the agreement with a full potential linear muffin-tin orbital theory, electron correlation effects have been incorporated via the so-called Lam-Platzman correction [Phys. Rev. B 9, 5122 (1974)]. A comparison with two-dimensional angular correlation of annihilation radiation has been made and demonstrates the strong influence of the positron wave function on the EMD. In analogy to these experiments, we used the first derivative of the EMD as an indication of the Fermi breaks.

A position-sensitive scintillation detector for two-dimensional angular correlation of annihilation radiation using metal-package position-sensitive photomultiplier tubes

We have constructed and tested a prototype of a new position sensitive γ-ray detector which consists of an array of 2.6×2.6×18 mm 3 BGO scintillator blocks, a light guide, and four metal-package position-sensitive photomultiplier tubes (R5900-00-C8) recently developed by Hamamatsu Photonics Co. Ltd. Scalability of the detector of this type makes it possible to construct a larger detector using many PS-PMTs, which will be useful for the two-dimensional angular correlation of annihilation radiation apparatus.

Fermi surface callipering of chromium alloys

We use maximum entropy to deconvolute the experimental resolution from (projected) 2DACAR (two-dimensional angular correlation of electron-positron annihilation radiation) data for Cr, Mo, V and their alloys. When the original data are subtracted from the deconvoluted data, the difference distribution reveals far more Fermi surface information. It is found that the difference plot may also be used to calliper the N-hole pockets of the projected Fermi surface. The dimensions that we obtain for pure Cr and Mo agree well with those from the literature, although those we obtain for V are smaller. The technique is designed to permit the callipering of the N-hole pocket in certain alloys for eventual comparison with work on oscillatory exchange coupling in magnetic multilayers.

Fermiology of Cr and Mo

An interpretation of the two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) for paramagnetic chromium (Cr) and molybdenum (Mo) is presented. Rather than explaining the significant differences in the resulting k-space occupancies in terms of different Fermi surface (FS) topologies, the recovery of a FS topology for paramagnetic Cr in agreement with band theory (and similar to the Mo experiment) through the application of a recently introduced maximum-entropy-based filtering technique suggests an explanation related to positron wavefunction perturbations.

Fermi-surface reconstruction from two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) data using maximum-likelihood fitting of wavelet-like functions

A novel method for reconstructing the Fermi surface from experimental two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) projections is proposed. In this algorithm, the 3D electron momentum-density distribution is expanded in terms of a basis of wavelet-like functions. The parameters of the model, the wavelet coefficients, are determined by maximizing the likelihood function corresponding to the experimental data and the projections calculated from the model. In contrast to other expansions, in the case of that in terms of wavelets a relatively small number of model parameters are sufficient for representing the relevant parts of the 3D distribution, thus keeping computation times reasonably short. Unlike other reconstruction methods, this algorithm takes full account of the statistical information content of the data and therefore may help to reduce the amount of time needed for data acquisition. An additional advantage of wavelet expansion may be the possibility of retrieving the Fermi surface directly from the wavelet coefficients rather than indirectly using the reconstructed 3D distribution.

Electron momentum distributions in elemental semiconductors probed by positrons

Momentum distributions of positron-electron pairs in diamond, Si, and Ge are systematically studied using state-of-the-art techniques in experiment and theory, i.e., the positron two-dimensional angular correlation of annihilation radiation (2D-ACAR) technique and two-component density-functional (TCDF) theory. It is experimentally examined that all samples are free from positron trapping. An interesting difference among the elemental semiconductors is then clarified, namely, a flat 2D-ACAR distribution of the [001] projection in the low momentum region is found in diamond, while a deep dip is observed at the origin in Si and Ge. These experimental results are compared with those of first-principles TCDF calculations within the local-density approximation based on the scheme by Puska, Seitsonen, and Nieminen [Phys. Rev. B 52, 10 947 (1995)] and the generalized-gradient approximation by Barbiellini et al. [Phys. Rev. B 53, 16 201 (1996)]. Good agreement between theory and experiment confirms the validity of the TCDF. Analysis of calculational results clarifies that the unique electron momentum distribution in diamond is due to the carbon $p$ orbital sharply localized in real space.

Momentum distributions of electron-positron pairs annihilating at vacancy clusters in Si

We report calculations of momentum densities of electron-positron pairs annihilating at various vacancy clusters in Si. The densities integrated along one direction, i.e., those corresponding to the spectra measured by the two-dimensional angular correlation of the annihilation radiation method, are shown to be isotropic if the positron is captured by a small vacancy cluster. The densities integrated along two directions correspond to the one-dimensional angular-correlation distribution or the Doppler-broadened annihilation radiation line shape. The characteristic narrowing of these one-dimensional distributions at vacancy clusters is demonstrated. The line-shape parameters $S$ and $W$ describing mainly the annihilations with valence and core electrons, respectively, are calculated and compared quantitatively with experimental data. We find a systematic increase in the $S$ and a decrease in the $W$ parameter as the size of the vacancy increases.

A study of porous silicon prepared under different HF concentrations by positron annihilation

Two-dimensional angular correlation of positron-electron annihilation radiation and positron-lifetime experiments have been performed on lightly doped porous silicons prepared under different HF concentrations. Positronium formation in the etched pores and positron trapped in voids are observed in both experiments. A surprising result is found that both positron lifetime and momentum spectra show a reduction in the size of the etched pores with decreasing HF concentration in the etching solution. This trend is different from the intuitive expectation that the pore size increases with increasing porosity. Our result can be explained in terms of the formation mechanism of porous film in lightly doped silicon.

Correlation between photoluminescence and positron annihilation spectra in porous silicon

We have performed two-dimensional angular correlation of electron-positron annihilation radiation (2D-ACAR) measurements on a series of porous silicon with photoluminescence (PL) peak energy in the range from 1.6 to 2.0 eV. The electron-positron momentum spectra of porous silicons can be well resolved into two peaks with different line width. The results shows two distinct momentum spectra for the studied samples. The samples with PL peak energy below 1.8 eV exhibit a strong positronium signal in the momentum spectra, and the obtained result shows a good correlation with PL spectra as predicted by quantum confinement. However, the samples with PL peak energy above 1.8 eV show little amount of positronium signal and the width of positronium peak remains almost constant. This behavior can be explained by the formation of silicon compounds on the surface of pores. With the result of these measurements, we suggest that the PL mechanism is different for the porous silicon with PL peak below and above 1.8 eV. For the PL peak below 1.8 eV, the emission arises from silicon nano-crystal, so that the PL spectrum highly depends on the nano-crystal size. However, for the PL above 1.8 eV, we suggest that the luminescence is dominated by the silicon compounds on the surface of the pores which block the free volume for positronium annihilation. Our suggested model can be used to resolve several difficulties in the existing PL spectra.

Two-dimensional angular correlation study of delocalized positronium in alkali halides

The two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) from KCl and KI single crystals at low temperatures has been measured. The intensities of the narrow peaks resulting from the Bloch modulation of the delocalized positronium (Ps) are studied. The intensities of the peaks except for those at the momenta corresponding to the (000) and (200) reciprocal-lattice vectors are very low for both KCl and KI. The experimental results for KCl are compared with the calculations made by Zhang and Song. Calculations with simpler approximations are also performed for both KCl and KI.

Study of the density of electrons in momentum space in the Al - Li - Cu icosahedral phase by means of positron annihilation

The three-dimensional momentum density of annihilating electron - positron pairs has been studied for a single Al - Li - Cu icosahedral quasicrystal. A direct Fourier transform method is employed to reconstruct the three-dimensional momentum density from measurements of the two-dimensional angular correlation of positron annihilation radiation (2D-ACAR). The crystallographic anisotropy in the momentum density is observed to be very small. The asphericity of the Fermi surface is not found explicitly within the experimental resolution in the momentum space. The features of the three-dimensional electron - positron momentum density agree with those obtained by means of Compton profile measurement. It is suggested that a strong lattice - electron interaction at the Fermi level occurs in this icosahedral phase.

De-noising of two-dimensional angular correlation of positron annihilation radiation data using Daubechies wavelet thresholding

Two-dimensional angular correlation of positron annihilation radiation (2D-ACAR) experiments provide a means of determining the electron - positron momentum density in metals and alloys over a wide range of temperatures. A difficult task regarding this method is the reconstruction of the three-dimensional density from a limited number of two-dimensional projections. Difficulties arise from noise superimposed on the data. This paper explains and demonstrates the use of a wavelet noise filter, and gives a comparison of wavelet and Fourier filters.