Structure-function relationship between preferred orientation of crystallites and electrical resistivity in thin polycrystalline ZnO:Al films

Thin polycrystalline films are often observed to develop a preferred orientation or texture that may have significant effects on film properties, especially in the case of anisotropic crystal structures. We report on a x-ray diffraction study of texture evolution in hexagonal ZnO:Al films, which were performed with a highly sensitive large-area detector enabling the investigation of films with thicknesses of some 10 nm only. In a set of magnetron-sputtered ZnO:Al films with thicknesses between 20 and 500 nm the resistivity was found to decrease with increasing thickness. A comprehensive texture analysis was performed within the framework of the series expansion method of the orientation distribution function (ODF). The investigations reveal a clear correlation between preferred grain orientation and electrical properties in ZnO:Al films. A general model is presented which relates the electronic mobility in polycrystalline films with the ODF by assuming the mobility to be composed of an intra-grain and an inter-grain fraction. It turns out that intra-grain anisotropy in ZnO:Al films cannot account for the observed variations in resistivity. Regarding the charge carrier scattering at grain boundaries the model relates the resistivity to the degree of grain alignment and makes use of the texture index $J.\mathrm{}$ On the basis of these assumptions it is shown that the resistivity scales with $1/J.$ The model also predicts the attainable minimum resistivity of thin ZnO:Al films with perfectly aligned crystallites which is in accordance with previously published results.