Singularity analysis at the vertex of polygonal quantum wire inclusions

Singular behavior near the vertex/corner of polygonal inclusions in anisotropic piezoelectric planes is identified and investigated. Using a recently derived exact closed-form solution, the elastic and electric fields associated with regular polygon-shaped quantum wires are analyzed in detail, revealing the effect of factors such as material orientation, type of eigenstrain, and number of sides of polygons on the singular behavior. Our study shows that by adjusting these factors properly, one could avoid the singular behavior or reduce the level of singularity, which could be of significance in the design and fabrication of the semiconductor devices.