Axially Non-Uniform Properties Effected Electro-Elastic Fields in Bended Piezoelectric Semiconductor Beams

This paper studied the effects of axially non-uniform material and non-uniform doping on the electro-elastic fields in bent piezoelectric semiconductor beams. The mathematical model is established based on the phenomenological theory of piezoelectric semiconductor and Euler's beam theory. To solve the governing equations with variable coefficients, the differential quadrature method is adopted. As two representative structures, the pure bending beam and cantilever beam are studied, respectively. From the calculated results, it can be found the varied material properties changed the effective stiffness, as a result, all the field quantities are altered. Meanwhile, the symmetry of all field quantities in a pure bending beam is broken. Considering different Gaussian doping parameters σn and Rn, it can be observed that the distribution rule of perturbation carrier density becomes complex. The increment of σn broadens the width of optimum range-producing carriers, however, the increment of Rn describes the moving of the optimum range from left to right. Importantly, the introduction of non-uniform doping breaks the limitation of perturbation carrier density in a cantilever beam with uniform material properties, the maximum value of perturbation carrier density does not appear at the fixed end only. The obtained results could be the guidance in designing high-performance electric devices.