Electronic Structure of the Muonium Center as a Shallow Donor in ZnO

The electronic structure and the location of muonium centers (Mu) in single-crystalline ZnO were determined for the first time. Two species of Mu centers with extremely small hyperfine parameters have been observed below 40 K. Both Mu centers have an axial-symmetric hyperfine structure along with a $⟨0001⟩$ axis, indicating that they are located at the antibonding (${\mathrm{A}\mathrm{B}}_{\mathrm{O},\parallel }$) and bond-center (${\mathrm{B}\mathrm{C}}_{\parallel }$) sites. It is inferred from their small ionization energy ($\simeq 6$ and 50 meV) and hyperfine parameters ($\sim {10}^{-4}$ times the vacuum value) that these centers behave as shallow donors, strongly suggesting that hydrogen is one of the primary origins of $n$ type conductivity in as-grown ZnO.

Figure 1

The crystal structure of ZnO and the geometry of $\mu \mathrm{S}\mathrm{R}$ measurements. The [0001] axis is parallel with the initial muon polarization ${\overrightarrow{P}}_{\mu }$, while the transverse field $\overrightarrow{B}$ is either (a) perpendicular to or (b) parallel with $[11\overline{2}0]$ axis. Tilted field ${\overrightarrow{B}}^{\prime }$ is in a plane defined by $\overrightarrow{B}$ and ${\overrightarrow{P}}_{\mu }$. “BC” refers to the bond-center sites and “AB” to the antibonding sites.

Figure 2

$\mu \mathrm{S}\mathrm{R}$ time spectrum in ZnO at 5.0 K, where the external field $\overrightarrow{B}$ ($|\overrightarrow{B}|=27\mathrm{m}\mathrm{T}$) was applied $45°$ to the [0001] axis. A fitting result with two species of muonium centers are shown with corresponding errors (difference between data and fitted curve).

Figure 3

Frequency spectrum obtained by the maximum entropy method for ZnO at (a) 7.0 K with $TF=4\mathrm{m}\mathrm{T}$ perpendicular to [0001] axis, and those at different temperatures (b)–(d) with $TF=27\mathrm{m}\mathrm{T}$ $45°$ tilted to the [0001] axis.

Figure 4

The fractional yield of ${\mathrm{M}\mathrm{u}}_{\mathrm{I}}$ (open triangles), ${\mathrm{M}\mathrm{u}}_{\mathrm{I}\mathrm{I}}$ (open squares), and a diamagnetic muon (closed circles) versus temperature in ZnO.