Role of Si and Ge as impurities in ZnO

The electronic and structural properties of Si in ZnO are studied using density functional calculations with both the generalized gradient approximation and a hybrid functional. Our calculations show substitutional Si on the Zn site $\left({\text{Si}}_{\text{Zn}}\right)$ to be significantly lower in energy than the Si interstitial $\left({\text{Si}}_i\right)$ and Si on an O site $\left({\text{Si}}_{\text{O}}\right)$. ${\text{Si}}_{\text{Zn}}$ is predicted to be a shallow donor in ZnO with a formation energy low enough to lead to significant incorporation of Si in the ZnO crystal. Interestingly, we find that ${\text{Si}}_{\text{Zn}}$ has a lower formation energy (and therefore higher solubility) under Zn-rich conditions than under O-rich conditions. We also study the properties of Ge in ZnO for comparison, finding behavior similar to the Si impurity, but with an even lower formation energy. Our results suggest Si and Ge as suitable $n$-type dopants in ZnO.

Figure 1

(Color online) Band structure of wurtzite ZnO calculated using the HSE hybrid functional. The calculated band gap is 3.4 eV and the zero of energy was set at the valence-band maximum.

Figure 2

Formation energies as a function of the Fermi-level position for ${\text{Si}}_{\text{Zn}}$ and ${\text{Ge}}_{\text{Zn}}$ in ZnO in Zn-rich conditions, according to the (a) GGA-PBE and (b) HSE hybrid functional. In each case the range of Fermi levels corresponds to the computed band gap (0.63 eV in PBE, 3.24 eV in HSE). Both ${\text{Si}}_{\text{Zn}}$ and ${\text{Ge}}_{\text{Zn}}$ act as shallow donors, with the $+2$ charge state being stable across the band gap.

Figure 3

Alignment between VBM and CBM of zinc-blende ZnO calculated using the PBE and HSE functionals. The alignment of the averaged electrostatic potentials $\overline{V}$ between PBE and HSE is also indicated. The electrostatic potential in vacuum is used as a reference.

Figure 4

(Color online) Local lattice relaxations around (a) ${\text{Si}}_{\text{Zn}}^{2+}$ and (b) ${\text{Ge}}_{\text{Zn}}^{2+}$ centers in the ZnO lattice. Both defects caused an inward relaxation of the nearest-neighbor oxygen atoms. The ${\text{Si}}_{\text{Zn}}\text{-O}$ and ${\text{Ge}}_{\text{Zn}}\text{-O}$ bond lengths are indicated expressed as a fraction of the equilibrium Zn-O bond length $d_0$.