Theory of asymmetric and piezotronically modified double Schottky barriers

Abstract

We present a theoretical model for double Schottky barriers at zinc oxide grain boundaries that accounts for piezotronically modified barrier heights resulting in generally asymmetric current–voltage (I–V) characteristics with respect to the applied electrical field direction. The model is based on charge distributions in the vicinity of the barrier and its related electrical potential distributions and can be considered as a generalization of the famous model of Blatter and Greuter. The natural asymmetry of current with respect to forward and reverse bias can be explained by different grain orientations and donor densities. The previously experimentally found change of I–V curves due to the application of mechanical loads can be reproduced via the piezotronic effect, leading to changes in the barrier potential profile due to piezoelectrically induced surface charges. Also, the I–V characteristics of degraded grain boundaries can be interpreted in terms of asymmetric changes in the donor densities. In addition, a second approach is presented that is able to explain experimental data of asymmetric I–V curves of wide grain boundaries with different surface terminations (O and Zn-polar).