Extension of a piezoelectric semiconductor fiber with consideration of electrical nonlinearity

Abstract

We study the extension of a piezoelectric semiconductor fiber with consideration of the electrical nonlinearity due to the drift current which is the product of the unknown electric field and the unknown carrier concentration. The analysis is based on a one-dimensional model. A perturbation analysis is performed. The first-order solution is the linear solution known in the literature. The second- and third-order nonlinear solutions obtained in this paper are new. Numerical results show that when the axial load is small the linear and nonlinear solutions are essentially the same. As the axial load increases, the linear and nonlinear solutions gradually become more different. The nonlinear solution is valid for a larger range of load and establishes the range of applicability of the linear solution. It is also found that while the electromechanical fields predicted by the linear solution are either symmetric or antisymmetric about the middle of the rod, the fields described by the nonlinear solutions lose this symmetry and antisymmetry.