Radiative lifetime of excitons in ZnO nanocrystals: The dead-layer effect

We theoretically investigate exciton states of colloidal nearly spherical ZnO nanocrystals with diameters from $2\mathrm{nm}\text{to}6\mathrm{nm}$. 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 $1.6\mathrm{nm}$ for the nanocrystal with diameter of $6\mathrm{nm}$. Based on our calculations we proposed an analytical approximation for the exciton radiative-lifetime dependence on radius $R$ in ZnO nanocrystal written as ${\tau }_0∕[1+{(R∕R_0)}^3]$ with ${\tau }_0=73.4\mathrm{ps}$ and $R_0=2.55\mathrm{nm}$. Presented results and proposed analytical approximation can be used for interpretation of experimental data, and optimization of ZnO quantum dot structures for optoelectronic applications.

Figure 1

Calculated exciton ground state energy in ZnO quantum dots as a function of the quantum dot radius (semiaxis) for spherical (ellipsoidal) quantum dots. Results are shown for two different ambient media: water $(\epsilon =1.78)$ and air $(\epsilon =1)$. For comparison we show experimental data points from Refs. 4, 5.

Figure 2

(Color online) Energies of the excited exciton states (counted from the exciton ground state) as a function of the radius of spherical ZnO quantum dot in water. The oscillator strength of the corresponding transitions is depicted with circles. The size of the circles is proportional to the oscillator strength.

Figure 3

(Color online) Optically active component of the exciton wave function (with equal electron and hole coordinates) of the first (a) and the second (b) bright exciton states for three different sizes of spherical ZnO quantum dots in water. The $c$ axis of wurtzite ZnO is directed vertically.

Figure 4

(a) Fitting parameters for Eq. (4) as a function of ZnO QD radius; $d$ is the dead layer thickness and $a_B$ is the exciton Bohr radius. (b) Wave function of the exciton’s center of mass along $x$ and $z$ axes for the $4\mathrm{nm}$ in diameter ZnO QD; thin solid line shows a fit by Eq. (4).

Figure 5

(Color online) Distribution of the probability density of an electron and an exciton (center of mass) over the volume of the $4\mathrm{nm}$ in diameter spherical ZnO QD. The innermost and middle isosurfaces contain $1∕3$ and $2∕3$ of the total probability density, respectively.

Figure 6

Radiative lifetime of the exciton ground state in ZnO quantum dots as a function of the quantum dot radius (semiaxis) for spherical (ellipsoidal) quantum dots.