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Making use of x-ray optical effects in photoelectron-, Auger electron-, and x-ray emission spectroscopies: Total reflection, standing-wave excitation, and resonant effects
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10.1063/1.4790171
/content/aip/journal/jap/113/7/10.1063/1.4790171
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/7/10.1063/1.4790171
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Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of the x-ray optical effects and spectroscopic processes for emission of photoelectrons (pe), Auger electrons (ae), or x-rays (xe) from a semi-infinite medium, with various symbols defined. Here, the x-rays are incident from medium 1 = vacuum on the surface of medium 2, with index of refraction n2 = 1 − δ + iβ. Incident, reflected, and transmitted wave are shown, together with various angles to quantitatively model the overall processes. Also shown is a schematic illustration of how the emission of an electron or an x-ray from an atom changes in relative intensity depending on its position with respect to the maxima and minima of the standing wave, with the relative magnitude of |E|2 also indicated.

Image of FIG. 2.
FIG. 2.

Schematic diagram of the x-ray optical effects and spectroscopic processes for a general multilayer sample, including roughness/interdiffusion at interfaces and with various symbols defined.

Image of FIG. 3.
FIG. 3.

Experimental data for Au 4f emission from Au at a photon energy of 1486.7 eV, as a function of incidence angle on going into total reflection from Ref. 9 , are compared to calculations using the methodology and YXRO program described here. Two different sets of optical constants have been used: those from the CXRO database 51 and those determined in Ref. 9 so as to fit experiment.

Image of FIG. 4.
FIG. 4.

X-ray optical simulations related to the O 1s photoelectron intensity from MnO as photon energy scans through the Mn 2p edges: (a) optical constants in the index of refraction n = 1 − δ + iβ across the Mn 2p edge, (b) a 3D representation of calculated reflectivity vs. incidence photon angle and energy, (c) calculated x-ray penetration depth vs. photon incidence angle: red solid curve (off resonance, hν = 611 eV) and blue solid curve (on resonance, hν = 636.4 eV), and (d) a 3D representation of the x-ray penetration vs. incidence photon angle and energy.

Image of FIG. 5.
FIG. 5.

Calculated p-polarized x-ray electric field strength |E|2 ((a) and (b)) and depth-resolved O 1s photoelectron intensity profiles ((c) and (d)) as a function of depth for MnO for energies on and off the Mn 2p 3/2 edge as a function of incidence photon angle: (a) and (c) off-resonance, (b) and (d) on-resonance, (e) a 3D representation of O 1s intensity vs. incidence photon angle and energy at a 90° take-off angle, and (f) a direct comparison of experiment and theory for O 1 s emission from MnO based on data from Ref. 54 .

Image of FIG. 6.
FIG. 6.

O x-ray emission intensity depth profiles for MnO across the Mn 2p edges as a function of incidence photon angle: (a) off-resonance and (b) on-resonance. O intensity plot vs. incidence photon angle and energy (c) for a 90° angle between x-ray incidence and exit and (d) for a 90° x-ray exit angle (normal to the surface).

Image of FIG. 7.
FIG. 7.

X-ray optical calculations for a multilayer standing wave generator [20 Å B4C/20 Å W]40 exposed to p-polarized light: (a) Reflectivity vs. incidence photon angle and energy. The dashed vertical line represents Bragg angle ϕB  = 10.9° corresponding to a reference energy of hν = 850 eV. (b) The depth profile of electric field strength normalized to an incident wave of unity as afunction of incidence photon angle for hν = 850 eV. The horizontal line represents the Bragg angle of ϕB  = 10.9°. Depth-integrated photoelectron intensities for (c) B 1s and (d) W 4f vs. incidence photon angle and energy at a 90° take-off angle (normal to the surface). Depth-resolved photoelectron intensities as a function of incident x-ray angle with 850 eV excitation for (e) B 1s and (f) W 4f. (g) Depth-integrated x-ray emission intensity for B vs. incidence photon angle and energy with a 90° in-between angle. Vertical line represents Bragg angle ϕB = 10.9° corresponding to hν = 850 eV. (h) Depth-resolved B x-ray emission as a function of incidence photon angle.

Image of FIG. 8.
FIG. 8.

Calculations for a wedge-profile sample on top of a multilayer mirror consisting of 15 Å Fe/a 35 ∼ 135 Å Cr-wedge/a multilayer of form [20 Å B4C/20 Å W]40: (a) 3D contour plot of reflectivity vs. incidence photon angle and Cr thicknesses. Note that the reflectivity peak at Bragg angle ϕB = 10.9° oscillates as a function of d Cr thus exhibiting local maxima at d Cr ∼ 65, 105, and 145 Å, and local minima d Cr ∼ 45, 85, and 125 Å. These correspond to d Fe + d Cr = 80, 120, and 160 Å ( sw) for local maxima, and 60, 100, and 140 Å for local minima, which implies that the constructive interference happens and the amplitude of standing wave becomes stronger when the thickness of Fe/Cr overlayer is the multiple of standing wave period while vice versa when the Fe/Cr layer is half periods thick. Vertical line represents Bragg angle ϕB = 10.9° again corresponding to hν = 850 eV. (b) Depth profile of electric field strength depth as a function of Cr thickness. Note the nearly constant position of the SW maximum in depth relative to the multilayer, an indication of the phase pinning. (c) Fe 2p and (d) Cr 2p photoelectron intensity profiles as a function of Cr thicknesses, and (e) and (f) their integrated intensity 3D contour plot vs. incidence photon angle and Cr thicknesses.

Image of FIG. 9.
FIG. 9.

Schematic diagram of a Fe/Cr layer with interdiffused region and magnetic moment distribution profile in a sample with configuration 15 Å Fe/ 35 ∼ 135 Å Cr-wedge/[20 Å B4C/20 Å W]40. The parameters here were derived from experimental SWEDGE measurements, as described in Ref. 21 .

Image of FIG. 10.
FIG. 10.

Calculations for a wedge-profile sample on top of a multilayer mirror consisting of 15 Å Fe/ 35 ∼ 135 Å Cr-wedge/[20 Å B4C/20 Å W]40: (a) Fe and (b) Cr x-ray emission intensity profiles as a function of Cr thicknesses, and (c) and (d) their integrated intensity vs. incidence photon angle and Cr thicknesses. The standing-wave modulation is much reduced for Cr in (d) due to the greater emission depth of Cr and the greater thickness of the wedge compared to the period of the SW.

Image of FIG. 11.
FIG. 11.

Calculations for a wedge-profile sample on top of a multilayer mirror consisting of 15 Å Fe/ 35 ∼ 135 Å Cr-wedge/[20 Å B4C/20 Å W]40, but for which the Fe/Cr interface is linearly interdiffused and has a Gaussian profile of element-specific magnetization (magnetic moment), as shown in Fig. 9 : (a) Fe 2p and (b) Cr 2p photoelectron intensity profiles as a function of Cr thicknesses. Horizontal vertical line represents Bragg angle ϕB = 10.9° corresponding to hν = 850 eV. (c) Fe 2p and (d) Cr 2p photoelectron intensity profiles that represent the magnetic moments of (c) Fe and (d) Cr as a function of Cr thicknesses.

Image of FIG. 12.
FIG. 12.

(a) Fe 2p and (b) Cr 2p 3D integrated intensity plot vs. incidence photon angle and Cr thicknesses based on Figs. 11(a) and 11(b) . Integrated contribution to the magnetic moments of (c) Fe 2p (d) Cr 2p based on Figs. 11(c) and 11(d) , again as a function of incidence angle and Cr thickness. The final MCD contour plot, against the same coordinates, for (e) Fe 2p and (f) Cr 2p.

Image of FIG. 13.
FIG. 13.

Calculation of x-ray emission for a wedge-profile sample on top of the same multilayer mirror consisting of 15 Å Fe/ 35 ∼ 135 Å Cr-wedge/[20 Å B4C/20 Å W]40 where the Fe/Cr interface is uniform in both concentration and magnetization, and the photon energy is 850 eV. The incidence angle is fixed at ϕB  = 10.9°: (a) Fe and (b) Cr x-ray emission intensity profiles as a function of Cr thickness. (c) Fe and (d) Cr photoelectron intensity profiles that represent the contributions to the magnetic moments of (c) Fe and (d) Cr as a function of Cr thicknesses.

Image of FIG. 14.
FIG. 14.

(a) Fe and (b) Cr integrated intensity plot vs. incidence photon angle and Cr thicknesses based on Figs. 13(a) and 13(b) (c) Fe moment and (d) Cr moment integrated intensity plot based on Figs. 13(c) and 13(d) . (e) Fe MCD and (f) Cr MCD contour plot. The horizontal line again indicates the Bragg angle for 850 eV.

Image of FIG. 15.
FIG. 15.

Calculation steps used in deriving layer-specific densities of states for the Fe/Cr sample of Figs. 8 and 10 14 . ((a)–(c)) 3D contour plots of the depth-resolved theoretical weighting factors W L for each layer, as defined in Eq. (43) , as a function of Cr wedge thickness d Cr and depth z for (a) W Fe, (b) W Fe/Cr interface, and (c) W Cr. Note that these include both the variation of the electric field as the SW scans through the sample and the inelastic attenuation of the escaping photoelectrons. (d) The integrals U L of W L over a given layer U Fe (black), U Fe/Cr interface (red), and U Cr (blue) are plotted versus d Cr.

Image of FIG. 16.
FIG. 16.

(a) Calculated electric-field intensity (|E|2) versus sample depth for an aperiodic multilayer structure of STO and LSMO depicted in a schematic diagram in (b) and x-rays of 5930 eV energy incident at 1.12°. At each cluster boundary, the phase of the standing wave is always either delayed or advanced by π, as shown by the inset in (a), and the net effect is to confine the standing-wave inside of the multilayer. (c) Calculated reflectivity vs. angle for the sample shown in (a). Note the near-zero value at an incidence angle of 1.12° as shown in the inset; this must be the case, since if the standing-wave modulation is zero above the surface, the reflected wave must approach zero also. Although not shown here, it appears that an incidence angle of about 1.22° should also lead to a similar standing-wave confinement, due to the very low reflectivity seen there as well.

Image of FIG. 17.
FIG. 17.

(a) Schematic cross section of a hypothetical sample which could be used to study interface phenomena in an exchange-bias junction consisting of ferromagnetic Co, antiferromagnetic FeF2 (assumed here to be 100 Å thick, although it might be grown in wedge profile as needed), and a buffer layer of MgF2, all grown on a GaAs/AlAs multilayer mirror. (b) Photoemission intensities originating from various electronic subshells are calculated as a function of x-ray grazing incidence angle for a typical hard x-ray photon energy of 5.9 keV. (c) Photoemission intensities in the region near the Bragg angle. E-field intensity as a function of depth inside the sample (d) at the Bragg angle of 1.39°, (e) at point 1 for a grazing incidence angle of 0.300°, and (f) at a grazing incidence angle of 0.375°, where the waveguide effect is observed in the MgF2 layer.

Image of FIG. 18.
FIG. 18.

(a) Schematic cross-section of a La1.2Sr1.8Mn2O7 bilayer manganite crystal chosen as a model system for a layered compound. The wavelength of the standing wave electric field, λ SW (plotted on the right) spans five single layers in the compound. (b) Change of reflectivity when tuning the photon energy across the Mn-L3 resonance and allowing quantitatively for the precise variation of δ and β. (c) Normalized photoelectron yields of Sr-3d and Mn-3p photoelectrons as a function of incidence angle near the Bragg angle. The ratio of the two yields shows a modulation of more than 30%. (d) Depth-resolved photoelectron yield of Sr-3d electrons (continuous lines) and Mn-3p electrons (dashed lines) for different photon incidence angles across the Bragg peak.

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/content/aip/journal/jap/113/7/10.1063/1.4790171
2013-02-21
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Making use of x-ray optical effects in photoelectron-, Auger electron-, and x-ray emission spectroscopies: Total reflection, standing-wave excitation, and resonant effects
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/7/10.1063/1.4790171
10.1063/1.4790171
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