Band mapping in x-ray photoelectron spectroscopy: An experimental and theoretical study of W(110) with 1.25 keV excitation

Angle-resolved photoemission spectroscopy (ARPES) has generally been carried out at energies below ∼150 eV, but there is growing interest in going to higher energies so as to achieve greater bulk sensitivity. To this end, we have measured ARPES spectra from a tungsten (110) crystal in a plane containing the [100], [110], and [010] directions with a photon energy of 1253.6 eV. The experimental data are compared to free-electron final-state calculations in an extended zone scheme with no inclusion of matrix elements, as well as highly accurate one-step theory including matrix elements. Both models provide further insight into such future higher-energy ARPES measurements. Special effects occurring in a higher-energy ARPES experiment, such as photon momentum, phonon-induced zone averaging effects, and the degree of cryogenic cooling required are discussed, together with qualitative predictions via appropriate Debye-Waller factors for future experiments with a number of representative elements being presented.

Figure 1

The real-space geometry of the experiment, with the key wave-vector conservation rules indicated.

Figure 2

(a) The raw experimental data, taken at room temperature, with no correction for the weak nondispersing density-of-states-like background. (b) The raw experimental data, taken at liquid nitrogen temperature. At right here, we also show the angle-integrated intensity, in comparison to a simple DOS from GGA theory. (c) Experimental data that have been corrected for phonon effects and photoelectron diffraction using the two-step normalization in Eqs. (2, 3, 4, 5). Overlaid on this are curves representing simple free-electron final-state theory. (d) The results of one-step photoemission calculations, including matrix-element effects, with free-electron final-state theory curves again overlaid. (e) The repeated band structure of tungsten along H-N-H, which Fig. 3c indicates should be approximately sampled in the angle region covered by reciprocal lattice vectors ${\mathrm{g⃗}}_1$ and ${\mathrm{g⃗}}_2$.

Figure 3

The reciprocal-space geometry of the experiment. (a) The tungsten Brillouin zone, with the range of directions spanned by our detector images indicated by the red arc. (b) The correction for photon momentum, indicating a 1.63° shift of ${\mathrm{k⃗}}_f-{\mathrm{k⃗}}_{\mathit{hv}}$ relative to the actual emission direction. (c) The reciprocal lattice vectors involved in spanning the data of Fig. 2.

Figure 4

Indication of the sensitivity of soft-x-ray ARPES data to a tilt misalignment of the sample orientation in which the [110] direction is tilted away from the azimuthal axis and towards [101] by 2.0°, as judged by one-step calculations including matrix element effects.

Figure 5

(a) Plot of the photon energies yielding valence-band Debye-Waller factors of 0.5, as a rough estimate of 50% direct-transition behavior, at a 20 K measurement temperature, as a function of atomic mass and Debye temperature. The points show various elements. This plot can be used to estimate the feasibility of high-energy ARPES experiments for other materials. (b) Plot of recoil energy as a function of atomic number and photon energy, permitting an upper-limit estimate of energy shifts and broadening.