In order to evidently improve the working performance of piezotronic devices, non-uniform piezoelectric semiconductor fibers with contoured profiles are designed. However, apart from the finite element method, it's hard to achieve analytical descriptions of the electromechanical fields in these non-uniform piezoelectric semiconductor fibers because of the governing equations with variable coefficients. For solving this bottleneck and exploring improved performance and new phenomena caused by the non-uniform profile, a power series expansion method is proposed based on the framework of the one-dimensional linearized model and is further applied to analyze the piezotronic performances of n-type non-uniform piezoelectric semiconductor fibers and PN junctions. It is revealed via systematical numerical simulations that the antisymmetry of the electromechanical fields in piezoelectric semiconductor fibers is broken because of the contoured profile and the piezotronic coupling. Meanwhile, the barrier configuration in a non-uniform PN junction is sensitive to the variation of cross-sectional area. Furthermore, the current-voltage relation of a necking heterogeneous piezoelectric semiconductor PN junction can be manipulated more conveniently by external mechanical loadings, meaning that the sensitivity of the device is improved. Not limited by non-uniform piezoelectric semiconductor fibers with contoured profiles, this method exhibits broad applicability, which is still available for solving multiple-coupled properties of functional graded piezoelectric semiconductor media.