Interstitial zinc clusters in zinc oxide

Doped zinc oxide (ZnO) exhibits anomalous Raman modes in the range of 270 to 870 cm${}^{\ensuremath{-}1}$. Commonly, the resonance at 275 cm${}^{\ensuremath{-}1}$ is attributed to the local vibration of Zn atoms in the vicinity of extrinsic dopants. We revisit this assignment by investigating the influence of isotopically purified zinc oxide thin films on the frequency of the vibrational mode around 275 cm${}^{\ensuremath{-}1}$. For this purpose, undoped and nitrogen-doped ZnO thin-films with Zn isotope compositions of natural Zn, ${}^{64}$Zn, ${}^{68}$Zn, and a 1:1 mixture of ${}^{64}$Zn and ${}^{68}$Zn were grown by pulsed laser deposition. The isotopic shift and the line shape of the Raman resonance around 275 cm${}^{\ensuremath{-}1}$ are analyzed in terms of three different microscopic models, which involve the vibration of (i) interstitial zinc atoms bound to extrinsic defects, (ii) interstitial diatomic Zn molecules, and (iii) interstitial zinc clusters. The energy diagram of interstitial Zn-Zn bonds in a ZnO matrix is derived from density functional theory calculations. The interstitial Zn-Zn bond is stabilized by transferring electrons from the antibonding orbital into the ZnO conduction band. This mechanism facilitates the formation of interstitial Zn clusters and fosters the common $n$-type doping asymmetry of ZnO.