An analysis of flexoelectric coupling associated electroelastic fields in functionally graded semiconductor nanobeams

摘要

Strain gradient with strong size dependency and structural association (geometry or microstructure) can efficiently tune the performances of semiconductors by the flexoelectric coupling effect. In this work, we studied a novel asymmetric beam-like semiconductor made by functionally graded (FG) flexoelectric materials. When being applied with pure bending loads at two ends, it can generate a relatively large inhomogeneous strain field to achieve obvious semiconducting behaviors. Unlike the analysis for piezoelectric semiconductor materials, we considered the effects of flexoelectririty and strain gradient elasticity in constitutive equations for flexoelectric semiconductor materials. Then, the complicated mutual coupling governing equations and associated boundary conditions are rederived strictly. By the Fourier series expansion and spatial integration methods, we obtained the solutions of the set of partial differential equations with non-constant coefficients. Results show that the semiconducting electromechanical coupling performances of the beam-like FG flexoelectric semiconductor depend heavily on the ratio and structural distributions of its constituent. Moreover, it is found that the inner carrier distributions and electromechanical characteristics can be significantly tuned by the strain gradient elasticity, the flexoelectricity, and the structural size. We believe this work provides a useful guideline for the practical design and manufacture of novel electromechanical semiconductor devices.