Exact piezoelectric solution for misfitted inclusion in finite spherical matrix: Applications to quantum dot core/shell crystals

Piezoelectric behavior of quantum dot core/shell structures in zinc-blende and wurtzite crystals are investigated in the framework of linear piezoelectricity. Strains arising from lattice mismatch in the core/shell structure are modeled as eigenstrains resulting from size-mismatched inclusion embedded in a finite spherical piezoelectric medium. Assuming that the core/shell piezoelectric structure exhibits spherically-hexagonal anisotropy, an exact solution is obtained through the eigenvalue decomposition method and the analytical expressions of the electroelastic fields are found using appropriate boundary and continuity conditions. It is found that the electroelastic fields can become singular or vanish at the center of the core for certain cases of spherical anisotropy. The analytical solutions are verified with the finite element analysis (FEA) and found to be in excellent agreement. FEA for the case of rectilinear anisotropy was also performed which showed considerable difference from the spherically anisotropic analytical solution. The closed-form solution obtained in this work can be used for any two-layer piezoelectric structures having spherical geometry subjected to various electromechanical loads.