Radiative lifetime of excitons in ZnO nanocrystals: The dead-layer effect
Abstract
We theoretically investigate exciton states of colloidal nearly spherical ZnO nanocrystals with diameters from $2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The sizes of considered ZnO nanocrystals are chosen to be slightly larger than the exciton Bohr radius of bulk ZnO. A number of characteristic features of excitons are revealed in this intermediate quantum confinement regime. The exciton center of mass is found to be prolate along the $c$ axis of wurtzite ZnO and squeezed to the center of the ZnO nanocrystal, thus forming a dead layer near the nanocrystal surface. The thickness of the exciton dead layer is found to increase with the nanocrystal size reaching the value of about $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for the nanocrystal with diameter of $6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Based on our calculations we proposed an analytical approximation for the exciton radiative-lifetime dependence on radius $R$ in ZnO nanocrystal written as ${\ensuremath{\tau}}_{0}∕[1+{(R∕{R}_{0})}^{3}]$ with ${\ensuremath{\tau}}_{0}=73.4\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ and ${R}_{0}=2.55\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Presented results and proposed analytical approximation can be used for interpretation of experimental data, and optimization of ZnO quantum dot structures for optoelectronic applications.