First-principles calculation of resonant x-ray emission spectra applied to ZnO

A framework for calculating the $k$-conserving component of K edge resonant x-ray emission spectroscopy measurements of anisotropic solids is presented. The crystalline band structure is calculated using a quasiparticle self-consistent GW implementation. Coherent spectra are calculated in the Kramers-Heisenberg formalism, and the effect of the experimental geometry in the dipole approximation is fully considered. Coherent spectra are calculated for ZnO and successfully compared to previously measured data.

Figure 1

The X1B experimental geometry. The laboratory coordinates $x^{\prime },y^{\prime },z^{\prime }$ (black) and the sample coordinates $x,y,z$ (red) are shown. Photons (black arrows) are incident along $z^{\prime }$ and emitted photons are collected along $x^{\prime }$. The angle between the sample normal and the incident beam, $\theta$, is freely changed during the experiment.

Figure 2

Intensity map of the calculated band structure. The intensity of each band is proportional to the $p_{\mathit{xy}}$ (left) and $p_z$ (right) character of the band at that point in the Brillouin zone.

Figure 3

Calculated (dashed red lines) and measured (solid black circles) ZnO (0001) CRXES at (a) near normal (${20}^{°}$) and (b) near grazing (${70}^{°}$) incidence. Each spectrum is labeled with its excitation energy; photon energy is shown on the right, and energy relative to the VBM is shown on the left.

Figure 4

The four unique CRXES cross sections, calculated for excitation energies of $3.8$ (solid lines) and $11.9$ eV (dashed lines).