Valence-band orbital character of CdO: A synchrotron-radiation photoelectron spectroscopy and density functional theory study

$N$-type CdO is a transparent conducting oxide (TCO) which has promise in a number of areas including solar cell applications. In order to realize this potential a detailed knowledge of the electronic structure of the material is essential. In particular, standard density functional theory (DFT) methods struggle to accurately predict fundamental material properties such as the band gap. This is largely due to the underestimation of the Cd 4$d$ binding energy, which results in a strong hybridization with the valence-band (VB) states. In order to test theoretical approaches, comparisons to experiment need to be made. Here, synchrotron-radiation photoelectron spectroscopy (SR-PES) measurements are presented, and comparison with three theoretical approaches are made. In particular the position of the Cd 4$d$ state is measured with hard x-ray PES, and the orbital character of the VB is probed by photon energy dependent measurements. It is found that LDA + U using a theoretical U value of 2.34 eV is very successful in predicting the position of the Cd 4$d$ state. The VB photon energy dependence reveals the O 2$p$ photoionization cross section is underestimated at higher photon energies, and that an orbital contribution from Cd 5$p$ is underestimated by all the DFT approaches.

Figure 1

(a) Plan view of the experimental geometry used. The photon beam is perpendicular to the analyzer lens axis and the sample is placed at grazing incidence to the photon beam. The electric polarization vector is coincident with the analyzer lens axis. The $\pm {30}^{\circ }$ angular acceptance of the electron analyzer is illustrated by the shaded blue triangle. (b) The one-electron photoionization cross sections and (inset) $\beta$ dipole asymmetry parameters for the orbitals constituting the CdO valence band. Shown for photon energies 0.1 to 10 keV. Note the logarithmic scale. Data from Trzhaskovskaya et al. [19, 20].

Figure 2

DFT band structures for (a) LDA, (b) PBE, and (c) LDA + U. Blue and red lines denote conduction and valence bands, respectively, the blue shaded region shows the band gap. Note the overlap of the conduction and valence bands predicted by LDA and PBE indicating a semimetallic system. Also note the shift in Cd 4$d$ states at around $-8$ eV produced by LDA + U.

Figure 3

(a)–(c) DFT partial density of states calculated using (a) LDA, (b) PBE, and (c) LDA + U. The peak labels I and II in (a), derived from experimental data, refer to the energy ranges $-4.5$ to $-3$ eV and $-3$ to 0 eV, respectively. (d)–(i) Cd 4$d$ and VB PES spectra compared to DFT, (d) and (g) LDA, (e) and (h) PBE, and (f) and (i) LDA + U. The DFT PDOS are weighted by the photoionization cross sections and summed, shown by the gray shaded areas. The weighted PDOS after convolution with a 0.7 eV FWHM Gaussian are shown by the red line. The experimental data (blue circles) shown is taken with $h\nu =6054$ eV, and a Shirley background has been subtracted. All energy scales are referenced to the VBM. The experimental spectra and convolved DFT are normalized to the maximum of VB peak II, and the same normalization has been applied to both the VB and Cd 4$d$ regions; note the different intensity scales.

Figure 4

(a) VB-PES taken with photon energies in the range 600 eV to 7935 eV; a Shirley background has been subtracted. (b)–(d) Simulations of the VB-PES obtained by applying the photoionization cross sections to the DFT approaches. The arrows numbered 1 and 2 in (a) are guides to the eye, discussed in the text. All spectra have been normalized to the maximum of peak II. The dashed lines are guides to the eye to allow the relative intensities to be observed.

Figure 5

The VB region calculated with LDA + U showing the PDOS weighted by photoionization cross sections for photon energies (a) 600 eV and (b) 7935 eV. This allows the effects of the photon energy on the orbital components to be observed.