## 1 Introduction
obtained the closed-form solutions for the electromechanical fields based on the Newmark model, in which the effects of interfacial parameter, flexoelectricity, and initial carrier concentration have been taken into account. To capture the electric nonlinear property between the electric field and carriers that is ignored in most of the related studies, a novel size-dependent nonlinear model of PS nanofiber with asymmetric crystal structures related to flexoelectricity and semiconducting properties was developed by [PERSON] et al. [11]. In addition to the above existing efforts, a groundbreaking theoretical framework about the thermoelectric effects of PS was also taken into consideration in the existing literature [12]. From the view of mechanics, to comprehensively understand the underlying mechanism of PS macroscopic structures, a series of other mechanics problems has also been assessed by an increasing number of researchers from the mechanics community, such as transient analysis of surface-heated PS plate [13], dynamic wave particle drag effect investigation related to free carrier (i.e., electron and hole) motion and flexoelectric waves [14], wave propagation [15,16,17,18,19,15,19,16,17,19,18,15,16,19,19,17,18,19,19,19,18,17,19,19,19,19,18,  
thermo-PS plates [36], double trigonometric series solution method for electromechanical behaviors of PS and flexoelectric semiconductor plate [37; 38], 1D theoretical model for interaction between static and dynamic bending deformations and electromechanical fields in composite flexoelectric semiconductor beams [39], electromechanical field distribution and evolution in non-uniform PS fibers [40; 41], thermally induced electric potential distribution and free carrier redistribution [42], cracks [43; 44], modulation of local electromechanical coupling field distributions in PS structures [45; 46; 47], and other modulation methodologies of PS devices [48; 49]. Clearly, the theoretical development of PS structures with rich results in both fundamental theory and applied science has been rapid, and the comprehensive studies of mechanical behavior of PS have become already an active area in the field of theoretical and applied mechanics, which can provide a theoretical basis for structural design, performance optimization, and device fabrication. Compared to 1D PS fibers, an increasing number of PS thin-film devices are emerging with the development of 2D materials. Usually, these multi-field coupled materials and devices work in a complex environment, such as coupled mechanical, thermal, electrical, and semiconductive fields. Owing to material anisotropy, these structural devices inevitably exhibit obvious thermo-deformation-polarization-carrier coupling characteristics [27; 28], which creates a great challenge of exactly calculating static and dynamic properties and simulating their working performances. From material physics to mechanics, the theoretical analyses of PS structures and devices are highly interdisciplinary and multi-physical, which simultaneously present sizeable mechanical and mathematical challenges. So far, despite the existing efforts, to the best of authors' knowledge, the understanding of the 2D higher-order theory of PS thin-film device structures considering the thermo-deformation-polarization-carrier coupling effect is still relatively low and scattered. Especially, in a 2D PS thin-film device with thermal field excitations, for active manipulation methodology and mechanism of electromechanical fields (including deformations, electric potential, potential barriers/wells, electron and hole concentrations, drift and diffusion currents, and their evolution versus external stimulus field and various physical and geometric parameters), there seem to be few reported results. This is precisely the deficiency of the current research situation and research motivation of this article. Considering this, our research aims to fill the gap in the 2D higher-order theory of PS thin-film device structure space and provide an effective and reliable theoretical solution.