Microscopic simulation of the mechanically modulated electrical conductivity of piezoelectric semiconductors

Abstract

Piezoelectric semiconductors have drawn significant attention in recent decades due to their unique physical properties. The coupling of piezoelectric and semiconductive effects allow possibilities to tune the electric potential in the material. Evidently, by mechanical loading, the charge flow of the circuit is adjustable. This effect is named as piezotronics effect and brings possibilities in producing new devices, such as light-emitting diode and new mechanically tuned field-effect transistors. Among all the piezotronic materials, ZnO is regarded as the most prominent one, due to its highest piezoelectric coefficient, high abundance of Zn, and a mature production of nanostructures. However, the understanding of grain boundary potential barriers of ZnO is insufficient because the physical mechanism for barrier development and its modification by external influence factors are complex. It has been shown that the barrier height can be significantly modulated by mechanically induced piezoelectric charge. Consequently, this makes ZnO-ZnO interfaces advanced piezotronic systems because the conductivity can be controlled by mechanical stress. Using this effect in applications, however, needs the possibility of tailoring the interfaces and an accurate physical description of the piezoelectric impact. For this purpose, reliable models are strongly desired. In order to understand the physical principles of the coupling effect specifically at the double Schottky barrier and making better use of it, a classical phenomenological model has been improved, and a finite element (FE) model has been developed. An extended phenomenological model is proposed to rationalize the potential barriers of the varistor like boundaries for piezoelectric semiconductors. Comparing to other phenomenological models, the model developed in this work self-consistently takes the internal electric field effect near the grain boundary into account. The effect is originated from the double Schottky barrier at a grain boundary, which gives rise to a strong internal electric field in the depletion layer. Due to the inverse piezoelectric effect, this electric field leads to mechanical strain and, consequently, piezoelectric charge at a grain boundary, and more importantly, an additional space charge associated with the polarization inhomogeneity. The piezoelectric charges, in return, impacts the barrier height. Results show that the piezoelectric charge induced by the internal field tends to adjust the grain boundary charge and lowers the barrier height. Moreover, the barrier height becomes less sensitive to mechanical stress and applied voltage if the influence of the internal field is taken into account. The extended model with the inverse piezoelectric effect of the internal field allows elucidating their piezotronic response further. The work improves the barrier height theory of piezoelectric ceramics and enriches the study of the piezoelectrics and other junction devices. Furthermore, an electromechanically coupled finite element model is developed in this work. Due to the full coupling effect, the model requires few prior assumptions on the charge distribution, enables multi-dimensional simulations of multigrain, and allows access to quantities such as the charge, energy, and electric field distributions. Moreover, the FE model inherently includes inverse piezoelectric and anisotropy effect, which are shown to have a significant impact on barrier height. Additionally, it is illustrated that this model can be used for advanced 3D microstructure simulations taking the complexity of the interface properties into account. Fully coupled electromechanical finite element simulations have also been carried out to study the varistor behaviour under bias voltage and mechanical loading. Thereby the quasi-Fermi energies are taken into account, bringing more physical foundations into the model. Comparing to the phenomenological model, the FE model demonstrates that the breakdown is highly related to the gradient of the band structure and the strong shrink of the barrier height. Hence, the finite element model conveys a more insightful understanding of how the piezoelectric varistor works. Both the modified phenomenological and finite element models proposed in this work demonstrate that considering the internal electric field reduces the barrier height and increases the current. It implies that if the internal electric field induced GB polarization charge and the polarization charge density in the screening layer is regarded, the determined grain boundary trap charge densities are expected to be higher than those obtained by the previous models. With the proposed models, systematic parameter studies have been carried out in the end to study the influence of mechanical loading on the grain boundary barrier height and varistor features. The obtained data were used to train a Neural Networks model to make the parameter-property relation accessible to a broad community. The knowledge achieved in the thesis is not limited to the grain boundaries of ZnO but has practical consequences on the study of general junction devices.