$p$ Doping in Expanded Phases of ZnO: An Ab Initio Study

The issue of $p$ doping in nanostructured cagelike ZnO is investigated by state-of-the-art calculations. Our study is focused on one prototypical structure, namely, sodalite, for which we show that $p$-type doping is possible for elements of the V, VI, and VII columns of the periodic table. However, some dopants tend to form dimers, thus impairing the stability of this kind of doping. This difference of behavior is discussed, and two criteria are proposed to ensure stable $p$ doping.

Figure 1

Band structure of ZnO sodalite structure in DFT LDA and sc-$GW$. The gap is direct at $\Gamma$ and estimated to be 4.2 eV in sc-$GW$ and 0.9 eV in LDA. (a) presents an elementary cage of the sodalite illustrated in (b).

Figure 2

Electronic density of states of N-, Cl-, and Te-doped ZnO sodalite projected on the states of the constituents. The Fermi level is located at 0 eV. The contribution of each atom is, respectively, Zn [shaded (blue) areas]; O [solid (red) lines]; and N, Te, and Cl [dotted (green) lines]. The dopant states are strongly localized near the top of the valence band. The DOS of pure ZnO sodalite is pictured in the bottom panel. The DOS of the different conduction bands has been multiplied ($\times 10$) for the sake of visibility as well as the contribution of Cl ($\times 5$). The dopant atomic concentration is $1\%$.

Figure 3

Electronic density of states of N- and Te-doped ZnO sodalite projected on the states of the constituents. The Fermi level is located at 0 eV. Two dopants are placed in two neighboring cages of the ZnO sodalite, and the insets illustrate the position of the atoms after relaxation. The DOS of the different conduction bands has been multiplied ($\times 5$) for the sake of visibility as well as the contribution of the N and Te dopants ($\times 2$). The dopant atomic concentration is $2\%$.

Figure 4

Magnitude of the energy barrier in doped ZnO sodalite as a function of the cohesion energy of the dimer. The circled areas enclose the dopants which do not dimerize. Each symbol corresponds to a different row of the periodic table.