In the application of the Lambert W function, the surface potential for amorphous oxide semiconductor thin-film transistors (AOS TFTs) under the subthreshold region is approximated by an asymptotic equation only considering the tail states. While the surface potential under the above-threshold region is approximated by another asymptotic equation only considering the free carriers. The intersection point between these two asymptotic equations represents the transition from the weak accumulation to the strong accumulation. Therefore, the gate voltage corresponding to the intersection point is defined as threshold voltage of AOS TFTs. As a result, an analytical expression for the threshold voltage is derived from this novel definition. It is shown that the threshold voltage achieved by the proposed physics-based model is agreeable with that extracted by the conventional linear extrapolation method. Furthermore, we find that the free charge per unit area in the channel starts increasing sharply from the threshold voltage point, where the concentration of the free carriers is a little larger than that of the localized carriers. The proposed model for the threshold voltage of AOS TFTs is not only physically meaningful but also mathematically convenient, so it is expected to be useful for characterizing and modeling AOS TFTs.

In the most of its engineering applications, ferroelectric materials are often subjected to combined loadings in the electric and mechanical fields. To simulate the influence of the biased stresses on the hysteretic dynamics of the materials, a macroscopic differential model is proposed to model the hysteresis loops and butterfly-shaped behaviors caused by the polarization orientation switching with biased stresses. A group of numerical simulations are presented, and the comparison of theoretical results with its experimental counterparts is also presented.