Length and polarity dependent saturation of the electromechanical response of piezoelectric semiconducting nanowires

The question of the length dependence of the electromechanical response of semiconducting (SC) piezoelectric nanowires (NWs) was explored. We identified a new physical mechanism of piezoresponse saturation, which originates from the combination of the influence of interface traps and piezoelectric polarization in the depleted NW. Our results are in better qualitative agreement with experimental observations than presently existing theories. To do so, we used the finite element method to simulate the coupled set of equations describing mechanical, piezoelectric and SC properties. In order to reduce the number of parameters, simulations focused on the case of uniform ZnO NWs grown along the c-axis. Saturation was explained by the incapacity of surface traps to maintain depletion along the whole NW beyond a certain length, as a result of the electric potential shift induced by piezoelectric polarization. An analytical model was developed to support this analysis. It provided the dependence trends of saturation length and piezoresponse as a function of NW dimensions, doping level, surface traps density and crystal polarity, as well as with external pressure, in fair agreement with simulation results. Moreover, we discovered that one consequence of this mechanism was that crystal polarity had an impact on the smoothness of the radius-dependent transition between high and low piezoresponse under axial stress. These results have important implications for the optimization of electromechanical sensors and nanogenerators based on piezoelectric SC NWs and related composite materials.