Defects in virgin and N + -implanted ZnO single crystals studied by positron annihilation, Hall effect, and deep-level transient spectroscopy

High-quality single crystals of ZnO in the as-grown and ${\mathrm{N}}^{+}$ ion-implanted states have been investigated using a combination of three experimental techniques---namely, positron lifetime/slow positron implantation spectroscopy accompanied by theoretical calculations of the positron lifetime for selected defects, temperature-dependent Hall (TDH) measurements, and deep level transient spectroscopy (DLTS). The positron lifetime in bulk ZnO is measured to be $(151\ifmmode\pm\else\textpm\fi{}2)\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ and that for positrons trapped in defects $(257\ifmmode\pm\else\textpm\fi{}2)\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$. On the basis of theoretical calculations the latter is attributed to $\mathrm{Zn}+\mathrm{O}$ divacancies, existing in the sample in neutral charge state, and not to the Zn vacancy proposed in previous experimental work. Their concentration is estimated to be $3.7\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. From TDH measurements the existence of negatively charged intrinsic defects acting as compensating acceptors is concluded which are invisible to positrons---maybe interstitial oxygen. This view is supported from TDH results in combination with DLTS which revealed the creation of the defect $E1$, and an increase in concentration of the defect $E3$ after ${\mathrm{N}}^{+}$ ion implantation, and peculiarities in the observation of the defect $E4$.