Fast and accurate approximate quasiparticle band structure calculations of ZnO, CdO, and MgO polymorphs

We investigate ZnO, CdO, and MgO oxides crystallizing in rocksalt, wurtzite, and zincblende structures. Whereas in MgO calculations, the conventional LDA-1/2 method is employed through a self-energy potential $\left(V_S\right)$, the shallow $d$ bands in ZnO and CdO are treated through an increased amplitude $\left(A\right)$ of $V_S$ to modulate the self-energy of the $d$ states to place them in the quasiparticle position. The LDA+$A$-1/2 scheme is applied to calculate band structures and electronic density of states of ZnO and CdO. We compare the results with those of more sophisticated quasiparticle calculations and experiments. We demonstrate that this new LDA+$A$-1/2 method reaches accuracy comparable to state-of-the-art methods, opening a door to study more complex systems containing shallow core electrons to the prize of LDA studies.

Figure 1

Plot of the amplitude $A$ vs the $d$ state position below VBM. This plot refers to WZ ZnO.

Figure 2

Orbital character of CdO (RS) valence bands: (top) LDA and (bottom) LDA+$A$-1/2. The $p$ character is represented in yellow and the $d$ character in magenta.

Figure 3

Orbital character of ZnO (WZ) valence: (top) LDA and (bottom) LDA+$A$-1/2. The $p$ character is represented in yellow and the $d$ character in magenta.

Figure 4

Band gap vs $CUT$ radius for (WZ) ZnO. The correction of the potential was obtained after the correction of cation Zn $d$ orbital by LDA+$A$-1/2 framework.

Figure 5

Schematic representation of conduction band (CB) in red, valence band (VB) in blue, and $d$ bands in black for ZnO and CdO. The reference energy for the three cases is taken as VBM. The case (a) indicates the LDA calculation, (b) the correction of $d$ band by increase of amplitude $A$, and (c) the complete correction, with the application of standard LDA-1/2 method.

Figure 6

Band structures within LDA+$A$-1/2 approach for the WZ phase of (a) ZnO and (b) CdO and LDA-1/2 approach (c) for MgO. The spin orbit (SO) and crystal field (CF) parameters are calculated using the quasicubic model for ZnO and CdO. (a) ZnO: ${\mathrm{\Delta }}_{CF}=35.1$ meV and ${\mathrm{\Delta }}_{SO}=-0.7$ meV, (b) CdO: ${\mathrm{\Delta }}_{CF}=53.8$ meV and ${\mathrm{\Delta }}_{SO}=-33.1$ meV, and (c) MgO: ${\mathrm{\Delta }}_{SO}=23.1$ meV.

Figure 7

Comparison between the LDA+$A$-1/2 total DOS (red), the $G_0{W}_0$@HSE03 DOS (blue), and XPS measurements (black) for WZ ZnO plotted in the range of (a) $\mathrm{Zn}3d$ bands and (b) $\mathrm{O}2p$ valence bands. Expt. data and $G_0{W}_0$@HSE03 DOS extracted from Ref. [21]. The VBM is used as energy zero.

Figure 8

Comparison between the ZnO (WZ) LDA+$A$-1/2 band structure (blue) and ARPES measurements (black squares). Expt. data extracted from Ref. [55].

Figure 9

Band structures within LDA+$A$-1/2 approach with SOC for RS (a) ZnO: ${\mathrm{\Delta }}_{SO}=48.0$ meV, (b) CdO: ${\mathrm{\Delta }}_{SO}=68.0$ meV, and LDA-1/2 approach (c) for MgO: ${\mathrm{\Delta }}_{SO}=37.8$ meV.

Figure 10

Comparison between the LDA+$A$-1/2 total DOS (red), the $G_0{W}_0$@HSE03 DOS (blue), and XPS measurements (black) for RS CdO plotted in the range of (a) $\mathrm{Cd}4d$ bands, (b) $\mathrm{O}2p$ valence bands. (c) LDA-1/2 total DOS (red), the $G_0{W}_0$@HSE03 DOS (blue), and XPS measurements (black) for RS MgO in the range of $\mathrm{O}2p$ valence bands. Expt. data and $G_0{W}_0$@HSE03 DOS extracted from Ref. [21]. The VBM is used as energy zero.

Figure 11

Band structures within LDA+$A$-1/2 approach with SOC for ZB (a) ZnO: ${\mathrm{\Delta }}_{SO}=2.1$ meV, (b) CdO: ${\mathrm{\Delta }}_{SO}=-28.1$ meV, and LDA-1/2 approach (c) for MgO: ${\mathrm{\Delta }}_{SO}=34.0$ meV.