<p>This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor (PSC) plate. Under the linear assumption of drift-diffusion current for a small electron concentration perturbation, the governing equations are solved by extending the classical Stroh formalism to involve all the physical fields of PSCs. The general solutions are obtained and then utilized to analyze three-dimensional (3D) problems of static deformation and free vibration of the PSC plate. To investigate the multi-physics interactions along the plate thickness, the distribution forms of electromechanical fields and electron concentration perturbation are given exactly, which are helpful for the development of the PSC plate theory. The differences between the PSC and purely piezoelectric as well as purely elastic counterparts are emphasized, in the context of evaluating the material performances with changing initial electron concentration. The results demonstrate that the PSC coupling exists only within a specific range of the initial electron concentration, where it exhibits a transition from the piezoelectric characteristics to the elastic ones. In addition, the dependence of coupling behaviors on the plate thickness is clarified. These results can not only be benchmarks in the development of PSC plate theories or other numerical methods, but also be guidance for the design of plate-based PSC devices.</p>