2D-ACAR Spectra Research Articles

Bulk Fermi surface and momentum density in heavily doped La2−xSrxCuO4using high-resolution Compton scattering and positron annihilation spectroscopies

We have observed the bulk Fermi surface (FS) in an overdoped ($x$=0.3) single crystal of La$_{2-x}$Sr$_x$CuO$_4$ by using Compton scattering. A two-dimensional (2D) momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory (DFT) calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. In particular the predicted FS topology is found to be in good accord with the corresponding experimental data. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and the DFT based computations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either the theory or the experiment.

Optimization of three-dimensional positron annihilation spectroscopy system (3DPASS) for three-dimensional momentum measurements

A three-dimensional positron annihilation spectroscopy system (3DPASS) was characterized. 3DPASS permits determination of three-dimensional electron–positron ( e −– e + ) momentum distributions by simultaneously measuring angles and energies for coincident two-gamma annihilation photons. 3DPASS collects a single dataset of correlated energies and positions for two coincident annihilation photons from a pair of solid-state double-sided strip detectors (DSSDs). Subpixel-interpolated positions are determined by transient charge analysis. 3DPASS performs simultaneous two-dimensional angular correlation of annihilation radiation (2D ACAR) and two-detector coincidence Doppler-broadening of annihilation radiation (CDBAR) measurements, which are typically collected independently. The 2D ACAR response of 3DPASS was measured for single-crystal Cu and 6H-SiC, with and without compensation for subpixel detection efficiency. Variation of efficiency across the width of DSSD charge collection electrodes was dominated by the event selection criteria required by the subpixel interpolation method. The DBAR resolution was optimized by adjusting the energy range of CDBAR events included in the Doppler-broadening (DB) lineshape. 2D ACAR and DBAR spectra from 3DPASS were compared to previously published results for single-crystal Cu and 6H-SiC. Detailed analysis of the ACAR spectra and the DB lineshapes highlighted momentum features not previously reported.

Image of electron densities from line and plane projections

We compare Fourier transforms with orthogonal polynomials techniques applied in reconstructing three-dimensional electron–positron momentum densities from two-dimensional angular correlation of annihilation radiation (2D-ACAR) spectra and electron momentum densities from one-dimensional Compton profiles (1D-CP). In the case of Fourier transforms, we show results for two different algorithms: filtered back projection and Fourier–Bessel method. These techniques are presented for 2D-ACAR spectra in Y, ErGa3 and model profiles.

Electron-positron momentum distributions associated with isolated silicon vacancies in3C−SiC

Two-dimensional angular correlation of annihilation radiation (2D-ACAR) and coincidence Doppler broadening (CDB) of annihilation radiation measurements have been performed on electron-irradiated $n$-type $3C\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}$ in which isolated silicon vacancies are responsible for positron trapping. After irradiation, the intensity of the CDB spectrum increased and decreased in low- and high-momentum regions, respectively. These features were explained by a theoretical calculation considering silicon vacancies. The central region of the 2D-ACAR spectra became isotropic after iradiation, while the overall anisotropies extending within the Jones zone were conserved suggesting that isolated silicon vacancies have tetrahedral symmetry, as expected from a previous electron spin resonance study.

Influence of experimental noise on densities reconstructed from line projections

AbstractThe influence of experimental noise on densities ρ(p) reconstructed by the Cormack method from their line projections, e.g. 2D ACAR spectra, is investigated. Simulations of statistical noise are performed for various sets of 2D spectra for two model ρ(p) having the cubic symmetry. For the reconstructed densities propagation of the statistical error in terms of standard deviations, σ[ρ(p)], is estimated. We observe that the distribution of σ[ρ(p)] has its extremes along the main symmetry directions and also a tendency to accumulate for small p. Moreover, the more density components, ρn(p), have to be taken to description of ρ(p) the less anisotropic is the distribution of σ[ρ(p)]. Additionally, the error generated by the reconstruction method itself is discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Depth-Selective 2D-ACAR and Coincidence Doppler Investigation of Embedded Au Nanocrystals in MgO

Depth-Selective 2D-ACAR and Coincidence Doppler Investigation of Embedded Au Nanocrystals in MgO

Positron–electron autocorrelation function study of E-center in silicon

Two-dimensional angular correlation of annihilation radiation (2D-ACAR) spectra have been taken for 1019 cm−3 phosphorus-doped Si in the as-grown state after having been subjected to 1.8 MeV electron fluences of 1×1018 and 2×1018 cm−2. Positron annihilation lifetime spectroscopy confirms, in accordance with previous works, that positrons are saturation trapping into (VSi:P) pair defect (E-center) monovacancy sites in the electron irradiated samples. In the as-grown case, the positron–electron autocorrelation functions along the [111] and [1-10] directions, obtained through Fourier transformation of the 2D-ACAR data, reveal zero-crossings that deviate only slightly from the lattice points, in a manner consistent with positron–electron correlation effects. Conversely, in the spectra of the irradiated samples, the zero-crossing points are observed to move outward further by between 0.15 and 0.50 Å. This displacement is associated with positron annihilation with electrons in localized orbitals at the defect site. An attempt is made to extract just the component of the defect’s positron–electron autocorrelation function that relates to the localized defect orbitals. In doing this features are found that correspond to the expected atomic positions at the vacancy defect site suggesting that this real-space function may provide a convenient means for obtaining a mapping of localized orbitals. The observed approximate separability of positron and electron wave-function autocorrelates leads to an estimate of 0.22 eV for the positron binding energy to the E-center.

Electronic Structure of the Superconducting Layered Non-Cuprate Sr2RuO4 from 2D-ACAR Measurements

The three-dimensional electron density in momentum space ?(P) and in wave vector space n(k) were constructed for Sr 2 RuO 4 . The measurements were achieved using 512 detectors to yield two dimensional angular correlation of annihilation radiation 2D-ACAR spectra. ?(P) Spectra disclosed a d-like character that was interpreted via the electronic configuration of Ru. From another standpoint, the Fermi surface topology was compared to the theoretical band structure calculation based on the local density approximation (LDA). It clarified that two electron surfaces are running along the Γ-Z direction and one hole surface around the X point. It was noteworthy that, while Sr 2 RuO 4 has a low critical temperature T c , its Fermi surface is large and complex similar to that of a high-temperature superconductor (HTS).

Methods for defect characterisation in thin film materials by depth-selective 2D-ACAR

The advent of intense positron beams makes it possible to perform depth-selective 2D-ACAR (two-dimensional angular correlation of annihilation radiation) studies. The Delft POSH–ACAR setup employs a strong permanent magnet for focusing of the POSH beam on the sample, which leads to a ∼15% spread in implantation energy. The effects of this spread on positron depth-profiling data are discussed, and are shown to be consistent with Doppler experiments on Si(1 0 0) with a subsurface layer of nanocavities. A method is presented to decompose depth-selective 2D-ACAR spectra reliably into their various (layer) components. This is used to reveal strong positron trapping in the nanocavities in Si(1 0 0).

Positron annihilation 2D-ACAR study of semi-coherent Li nanoclusters in MgO( [formula omitted]) and MgO( [formula omitted

Depth selective positron annihilation two-dimensional angular correlation of annihilation radiation (2D-ACAR) is used to determine the electronic structure of Li nanoclusters formed by implantation of 10 16 cm −2 6 Li ions (with an energy of 30 keV) in MgO(1 0 0) and (1 1 0) crystals, and subsequently annealed at 950 K. The 2D-ACAR spectra of Li-implanted MgO obtained with 4 keV positrons reveal the semi-coherent ordering state of the embedded metallic Li nanoclusters. The results agree with ab initio Korringa–Kohn–Rostoker calculations.

Fermi Surface of Nanocrystalline Embedded Particles in Materials: bcc Cu in Fe

We report that a positron can act as a probe to directly reveal electronic structures of nanocrystalline embedded particles in materials. The Fermi surface (FS) of "bcc" Cu nanoparticles in an Fe matrix is observed as the first example. A two-dimensional angular correlation of the positron annihilation radiation (2D-ACAR) method is used to measure the momentum distribution which reflects the FS topology. The obtained 2D-ACAR spectra show strong and characteristic anisotropy associated with the necks of the FS around the [110] Brillouin zone boundaries of the bcc Cu, which are well reproduced by full-potential linearized argumented plane-wave calculations.

Three-Dimensional Reconstruction of the Fermi Surface of LaB<sub>6</sub>

The 2-dimensional angular correlations of the positron annihilation radiation (2D-ACAR) on a single crystal of LaB6 was measured for three projections. The 2D-ACAR spectra were subjected to the Van Citter-Gerhard deconvolution alghorithm. From the experimental spectra we produced the 3D k-space density rho(k) via three different methods: i) we reconstructed the 3D electron-positron momentum density rho(p) via the Cormack method. rho(k) was then obtained by applying the 3D LCW transformation to rho(p). ii) The same steps of point i) were repeated adopting a modified Fourier-transform-based algorithm. iii) The 3d k-space occupancy rho(k) was obtained directly by parameterising the Fermi surface volume with prolate ellipsoids whose axes were determined by a least-square fit to the 2D LCW transformations applied to two high symmetry projections. The ellipsoids diameters along high symmetry directions of the cubic Brillouin zone (BZ), as a fraction of the BZ size, were 0.64 (dir. X-M) and 0.82 (dir. Gamma-X). The resulting Fermi volume, as a fraction of the BZ volume, was 0.55. These results agree within 1% with those obtained via the de Haas van Alphen experiments.

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.

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.

Ion-implantation Generated Nanovoids in Si and MgO Monitored by High Resolution Positron Beam Analysis

AbstractThe formation of nanovoids in Si(100) and MgO(100) by 3He ion implantation has been studied. Contrary to Si in which the voids are generally almost spherical, in MgO nearly perfectly rectangular nanosize voids are created. Recently, the 2D-ACAR setup at the Delft Positron Research Center has been coupled to the intense reactor-based variable-energy positron beam POSH. This allows a new method of monitoring thin layers containing nanovoids or defects by depth-selective high-resolution positron beam analysis. The 2D-ACAR spectra of Si with a buried layer of nanocavities reveal the presence of two additional components, the first related to para-positronium (p-Ps) formation in the nanovoids, and a second one most likely related to unsaturated Si-bonds at the internal surface of the voids. The positronium is present in excited kinetic states with an average energy of 0.3 eV. Refilling of the cavities by means of low dose 3He implantation (1×1014 cm−2) followed by annealing reduces the formation of Ps and the width of the Ps peak in the ACAR spectrum. This width reduction is due to collisions of Ps with He atoms in the voids. In MgO, p-Ps formed with an initial energy of ~3 eV shows a final average energy of 1.6 eV at annihilation due to collisions with the cavity walls. Possibilities of this new, non-destructive method of monitoring the sizes of cavities and the evolution of nanovoid layers will be discussed.

Ion-implantation Generated Nanovoids in Si and MgO Monitored by High Resolution Positron Beam Analysis

ABSTRACTThe formation of nanovoids in Si(100) and MgO(100) by 3He ion implantation has been studied. Contrary to Si in which the voids are generally almost spherical, in MgO nearly perfectly rectangular nanosize voids are created. Recently, the 2D-ACAR setup at the Delft Positron Research Center has been coupled to the intense reactor-based variable-energy positron beam POSH. This allows a new method of monitoring thin layers containing nanovoids or defects by depth-selective high-resolution positron beam analysis. The 2D-ACAR spectra of Si with a buried layer of nanocavities reveal the presence of two additional components, the first related to para-positronium (p-Ps) formation in the nanovoids, and a second one most likely related to unsaturated Si-bonds at the internal surface of the voids. The positronium is present in excited kinetic states with an average energy of 0.3 eV. Refilling of the cavities by means of low dose 3He implantation (1×1014 cm-2) followed by annealing reduces the formation of Ps and the width of the Ps peak in the ACAR spectrum. This width reduction is due to collisions of Ps with He atoms in the voids. In MgO, p-Ps formed with an initial energy of ∼3 eV shows a final average energy of 1.6 eV at annihilation due to collisions with the cavity walls. Possibilities of this new, non-destructive method of monitoring the sizes of cavities and the evolution of nanovoid layers will be discussed.

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.

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.

Positron annihilation study of the electronic structure ofLaB6andCeB6

We measured the two-dimensional angular correlation of the positron annihilation radiation (2D-ACAR) on a single crystal of ${\mathrm{LaB}}_{6}$ for two projections. The anisotropies of the 2D electron-positron momentum density were very similar to those observed for the isostructural heavy-fermion (HF) system ${\mathrm{CeB}}_{6}$ in the paramagnetic phase and consistent with those of the calculated electron-positron momentum density of ${\mathrm{LaB}}_{6}.$ The standard Lock-Crisp-West (LCW) analysis was in reasonable agreement with the LCW folding of the calculated 2D-ACAR spectrum and the de Haas--van Alphen findings. From the projected $\mathit{k}$-space density we could evaluate the Fermi volume, corresponding to $1.10\ifmmode\pm\else\textpm\fi{}0.04$ electrons per formula unit, and deduce that the effect of the nonuniform positron density does not play a significant role. The apparent discrepancy with the LCW analysis of ${\mathrm{CeB}}_{6},$ where filtering procedures were required to recover a $\mathit{k}$-space density similar to that obtained for ${\mathrm{LaB}}_{6},$ is discussed.

Positron annihilation study of the electronic structure of LaB 6

We measured the two-dimensional angular correlation of the positron annihilation radiation (2D-ACAR) on a single crystal of LaB 6 for two projections. The anisotropies of the 2D electron-positron momentum density were very similar to those previously observed for the isostructural heavy-fermion (HF) system CeB 6 in the paramagnetic phase and consistent with those of the calculated electron-positron momentum density of LaB 6. The standard LCW analysis was in reasonable agreement with calculations of the LCW-folded 2D-ACAR spectrum and de Haas van Alphen (dHvA) findings. From the projected k-space density we could evaluate the Fermi volume, corresponding to 1.10 ± 0.04 electrons per formula unit, and deduce that the effect of the non-uniform positron density does not play a significant role.