Band mapping in higher-energy x-ray photoemission: Phonon effects and comparison to one-step theory

Abstract

We have studied the temperature dependence of W͑110͒ soft x-ray angle-resolved photoemission spectra excited at photon energies of 260 and 870 eV and between 300 and 780 K. The experimental results have been compared to both a free-electron final-state model and theoretical one-step model calculations of the photocurrent. At 300 K, clear band dispersions can be observed in the data. The temperature dependence of the data can be analyzed qualitatively in terms of a direct-transition band-dispersion regime ͑"UPS" limit͒ versus a nondirect-transition density-of-states regime ͑"XPS" limit͒. The ratio between direct and nondirect transitions is estimated from a Debye-Waller factor, which for example at h = 870 eV predicts 70% direct transitions at 300 K, and 41% at 780 K, and these values qualitatively describe our data. Beyond this, the state-of-the-art one-step theoretical calculations reproduce well the band dispersions and matrix element effects in the measured spectra at room temperature. However, simulating the temperature dependence is more complicated, and including phonon effects via complex phase shifts accounts for the suppression of existing direct-transition features, but does not reproduce new, density-of-states-related background intensity which shows up in highertemperature experimental spectra. Finally, we also discuss the implications of this work for future experiments on other materials and at even higher photon energies up to 10 keV.

Functional materials for information and energy technology: Insights by photoelectron spectroscopy

“…At high temperatures signatures of the band dispersions fade out in E( k) maps and the valence band photocurrent reaches the matrix-element weighted density-of-states limit (MEWDOS, also often termed the XPS limit), typically also modulated by X-ray photoelectron diffraction effect [13]. Fraction of direct transitions can be estimated from the temperaturedependent Debye-Waller factor W (T ) ≈ exp (−g 2 u 2 (T ) ), where g is the reciprocal lattice vector to allow direct transitions, i.e.…”

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

“…In addition, deviations from the dipole approximation in photoelectron excitation mean that the momentum of the photon, which is negligible in the case of low energy photons, can result in a nonnegligible shift of the position of the initial-state wave vector in the reduced Brillouin zone (BZ), as pointed out some time ago 10,14,15 . Phonon creation and annihilation during photoemission also smears out the specification of the initial state in the BZ via wave vector ( k ) conservation, and leads to the need for cryogenic cooling to minimize such phonon effects in order to more clearly observe direct or k conserving transitions [16][17][18][19][20][21] . As a semi-quantitative predictor of the effects of phonons, the total intensity Tot I (E,k ) at a given energy E and k can be roughly divided into zerophonon direct transitions I DT (E, k ) and phonon-assisted non-direct transitions I NDT (E, k ) as:…”

“…Tungsten (110) was chosen as a model system that has been well-studied, both from experimental 4, 14,15,25,26 , as well as from theoretical 16,27,28 , points of view. But a principal reason for choosing it here is its excellent properties for high energy ARPES.…”

Influence of elastic scattering on the measurement of core-level binding energy dispersion in X-ray photoemission spectroscopy

“…In addition to that, there exist two mechanisms that introduce a broadening into the measurement. These are the quasi elastic scattering of the photoelectron with the atoms of the crystal 4,5 as well as the influence of phonons on the photoemission process 6,7 . A third factor which has not been considered until now and that can introduce a systematic error to the measurement of the dispersion in core-level binding energies is introduced in this paper with the demonstration of an angular dependent artificial shift, created by the existence of unresolved energetically shifted surface core levels.…”