K.Y. Xu

Abstract:

This report presents an exact closed-form solution for the Eshelby problem of a polygonal inclusion with a graded eigenstrain in an anisotropic piezoelectric full or half-plane with a traction-free surface condition. Using the line-source Green's function, the line integral is then carried out analytically for the linear eigenstrain case, with the final expression involving only elementary functions. Finally, the solutions are applied to the quantum wires (QWRs) of square, triangular, circular and elliptical shapes within semiconductor GaAs substrates respectively, with results clearly illustrating that there are various influencing factors on the induced fields. The present solution should be particularly appealing to the more realistic nanoscale quantum-wire structure analysis where strain and electric fields could be induced by the non-uniform misfit strain.