## 1 Introduction  
With the improvement in material processing technology and development of 3D printing, various new PS materials and their one-dimensional (1D) and 2D structures, including fibers, spirals, helices, belts, tubes, and films, have been developed and synthesized using the so-called third-generation semiconductor materials represented by ZnO, GaN, and MoS\({}_{2}\) because of their excellent features, i.e., a wider band gap, higher thermal conductivity, and a higher electron saturation rate [1; 2]. Different from conventional semiconductors, in these PS materials and structures, mechanical fields can produce electric polarization through piezoelectric coupling, which acts on mobile holes and electrons and affects their motion, distribution, and transport behavior [3; 4]. This unique interaction among mechanical fields, polarization, and mobile charges is the main characteristic of PS,which can be used to develop novel electronic devices. Furthermore, the investigation of PS devices is growing rapidly in the form of single structures or arrays. Based on their unique structures and coupling of semiconductor and piezoelectricity properties, an increasing number of PS multifunctional devices (such as, nanogenerators, piezotronic acoustic tweezers, field-effect transistors, logic nanodevices, piezotronic and chemical sensors, etc.) have been successfully developed and applied in phototronics and electronics [1,2]. For various PS devices, the basic behavior can be described through a coupled-field phenomenological theory [5], consisting of the theory of linear piezoelectricity, the conservation of charge for electrons and holes, and the drift-diffusion theory of semiconductors. Here, it should be stressed that the macroscopic theory of PS is inherently nonlinear because of drift current terms, i.e., products of unknown electric field and carrier concentrations [6]. Especially, from material physics to mechanics, the theoretical analyses of PS structures and devices are highly interdisciplinary and multi-physical, which have formed new research areas called piezotronics and piezophototronics [1,2], simultaneously presenting sizeable mechanical and mathematical challenges. Due to the coexistence of semiconductor and piezoelectricity of PS materials and structures, the multi-field coupling interactions related to physical and mechanical mechanisms of novel PS structures and devices between the mechanical deformation, electric polarization, and carriers require a comprehensive understanding from the perspective of device research and development and applied science. Here, some representative research studies and results are listed and reported one by one from the existing literature. For example, in PS materials with advanced structures and unique features, to reveal the novel indentation characteristics induced via the interaction between semiconductor and piezoelectric coupling, [PERSON] and his coauthors [7] investigated the indentation responses of a PS half-space subjected to an insulating and rigid spherical indenter, and the theoretical and numerical results indicated that the existence of semiconducting property (i.e., steady carrier concentration) can decrease the indentation resistance of PS materials and further affect the indentation force and electric potential. By considering the principle of virtual work, [PERSON] et al. [8,9] established PS circular cylindrical shell models based on the Kirchhoff-Love assumption and the first-order shear deformation theory, analyzed the static bending and forced vibration problems, and then obtained the fundamental coupling relations between mechanical deformation, piezoelectric polarization, and mobile charges. In Ref. [10], by simultaneously considering the imperfect interface, piezoelectricity, and flexoelectricity in a PS bilayer composite beam system subjected to uniform temperature variation, [PERSON] et al.